light travelling through a glass block

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Refraction of light.

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Refraction is the bending of light (it also happens with sound, water and other waves) as it passes from one transparent substance into another.

This bending by refraction makes it possible for us to have lenses, magnifying glasses, prisms and rainbows. Even our eyes depend upon this bending of light. Without refraction, we wouldn’t be able to focus light onto our retina.

Change of speed causes change of direction

Light refracts whenever it travels at an angle into a substance with a different refractive index (optical density).

This change of direction is caused by a change in speed. For example, when light travels from air into water, it slows down, causing it to continue to travel at a different angle or direction.

How much does light bend?

The amount of bending depends on two things:

Change in speed – if a substance causes the light to speed up or slow down more, it will refract (bend) more.
Angle of the incident ray – if the light is entering the substance at a greater angle, the amount of refraction will also be more noticeable. On the other hand, if the light is entering the new substance from straight on (at 90° to the surface), the light will still slow down, but it won’t change direction at all.

Refractive index of some transparent substances

All angles are measured from an imaginary line drawn at 90° to the surface of the two substances This line is drawn as a dotted line and is called the normal.

If light enters any substance with a higher refractive index (such as from air into glass) it slows down. The light bends towards the normal line.

If light travels enters into a substance with a lower refractive index (such as from water into air) it speeds up. The light bends away from the normal line.

A higher refractive index shows that light will slow down and change direction more as it enters the substance.

A lens is simply a curved block of glass or plastic. There are two kinds of lens.

A biconvex lens is thicker at the middle than it is at the edges. This is the kind of lens used for a magnifying glass. Parallel rays of light can be focused in to a focal point. A biconvex lens is called a converging lens.

A biconcave lens curves is thinner at the middle than it is at the edges. Light rays refract outwards (spread apart) as they enter the lens and again as they leave.

Refraction can create a spectrum

Isaac Newton performed a famous experiment using a triangular block of glass called a prism. He used sunlight shining in through his window to create a spectrum of colours on the opposite side of his room.

This experiment showed that white light is actually made of all the colours of the rainbow. These seven colours are remembered by the acronym ROY G BIV – red, orange, yellow, green, blue, indigo and violet.

Newton showed that each of these colours cannot be turned into other colours. He also showed that they can be recombined to make white light again.

The explanation for the colours separating out is that the light is made of waves. Red light has a longer wavelength than violet light. The refractive index for red light in glass is slightly different than for violet light. Violet light slows down even more than red light, so it is refracted at a slightly greater angle.

The refractive index of red light in glass is 1.513. The refractive index of violet light is 1.532. This slight difference is enough for the shorter wavelengths of light to be refracted more.

A rainbow is caused because each colour refracts at slightly different angles as it enters, reflects off the inside and then leaves each tiny drop of rain.

A rainbow is easy to create using a spray bottle and the sunshine. The centre of the circle of the rainbow will always be the shadow of your head on the ground.

The secondary rainbow that can sometimes be seen is caused by each ray of light reflecting twice on the inside of each droplet before it leaves. This second reflection causes the colours on the secondary rainbow to be reversed. Red is at the top for the primary rainbow, but in the secondary rainbow, red is at the bottom.

Activity ideas

Use these activities with your students to explore refration further:

Investigating refraction and spearfishing – students aim spears at a model of a fish in a container of water. When they move their spears towards the fish, they miss!
Angle of refraction calculator challenge – students choose two types of transparent substance. They then enter the angle of the incident ray in the spreadsheet calculator, and the angle of the refracted ray is calculated for them.
Light and sight: true or false? – students participate in an interactive ‘true or false’ activity that highlights common alternative conceptions about light and sight. This activity can be done individually, in pairs or as a whole class .

Useful links

Learn more about different types of rainbows, how they are made and other atmospheric optical phenomena with this MetService blog and Science Kids post .

Learn more about human lenses, optics, photoreceptors and neural pathways that enable vision through this tutorial from Biology Online .

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Snell's Law

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Andrew Ellinor
Rishik Jain
Someguy Noname

Snell's law , also known as the law of refraction , is a law stating the relationship between the angles of incidence and refraction, when referring to light passing from one medium to another medium such as air to water, glass to air, etc.

Explanation

Refraction through a glass slab, lateral displacement and it's calculation, normal shift, total internal reflection, effects and applications of total internal reflection, snell's law - problem solving.

Snell's Law states that the ratio of sine of angle of incidence and sine of angle of refraction is always constant for a given pair of media. \[\dfrac{\sin i}{\sin r}=\text{constant}=n=\text{refractive index}\]

Let us consider that light enters from medium 1 to medium 2,

\[\therefore \dfrac{\sin i}{\sin r}=n_{21}=\dfrac{n_2}{n_1}=\dfrac{\color{blue}{v_1}}{\color{blue}{v_2}}=\dfrac{\color{blue}{\lambda_1}}{\color{blue}{\lambda_2}}\]

Here, $v_n$ is the velocity of light in respective medium and $\lambda_n$ is the wavelength of light in respective medium. You may be wondering how we obtained the expression in blue color, well if we define it in an easy way, the basic cause of refraction is due to the change in velocity of light by entering a medium of different refractive index. So, if a medium has less refractive index, then the velocity of light in that medium would be more but if a medium has more refractive index then the velocity of light in that medium would be comparatively less.

\[\therefore v \propto \dfrac{1}{n} \Rightarrow \dfrac{v_1}{v_2}=\dfrac{n_2}{n_1}=n_{21}\]

Question: A ray of light travelling in air is incident on the plane surface of a transparent medium. The angle of incidence is found to be $45^{\circ}$ and the angle of refraction is $30^{\circ}$. Find the refractive index of the medium. Solution: We know that $\hat i=45^{\circ}$ and $\hat r=30^{\circ}$ Therefore refractive index, \[\begin{align} n=\dfrac{\sin i}{\sin r} &= \dfrac{\sin 45^{\circ}}{\sin 30^{\circ}}\\ &= \dfrac{1/\sqrt{2}}{1/2}= \sqrt{2} \end{align}\]

A ray of light is incident on a surface at an angle of $60^\circ$, refracts at an angle of $45^\circ$. Find it's refractive index.

Round your answer to 3 decimal places.

Absolute Refractive Index:

When we compare the speed of light in a medium to that of the speed of the light in vacuum , then we would be dealing with something called absolute refractive index. We generally refer to the absolute refractive index of a medium when we say that a certain object's refractive index is $x$.

The expression for the absolute refractive index of a medium would thus be: \[\text{absolute refractive index}=\dfrac{\text{speed of light in vacuum}}{\text{speed of light in the given medium}} = \dfrac{c}{v}\]

Note: As the speed of light is at its maximum in vacuum, the absolute refractive index always greater than $1$. Also note that the refractive index is a relative quantity and thus it had no units.

Question: The absolute refractive index of a glass window is $1.5$. What is the speed of light when it is traveling through the glass window? Assume that the speed of light in vacuum $=3\times 10^8m/s$. Solution: According to the question, we have: \[\dfrac{\text{speed of light in vacuum}}{\text{speed of light in the given medium}}=1.5\\ \implies \dfrac{3\times 10^8}{\text{speed of light in the given medium}}=1.5\\ \implies \text{speed of light in the given medium}=\dfrac{3\times 10^8}{1.5}=\boxed{2\times 10^8 m/s}\]

Question: The absolute refractive index of diamond is $2.42$. What is the speed of light in diamond? (Take speed of light in vacuum= $3 \times 10^8 m/s$ Solution: Absolute refractive index of diamond is \[=\dfrac{\text{speed of light in vacuum}}{\text{speed of light in diamond}}\quad\therefore\dfrac{c}{v}=2.42\\ \implies v=\dfrac{c}{2.42} \implies v=\dfrac{3 \times 10^8}{2.42} \\\boxed{v=1.24 \times 10^8 m/s}\]

Refraction of a ray of light in a glass slab

In this case, we will try to prove $\angle i_1=\angle r_2$ or the incident ray is parallel to the emergent ray,

Applying Snell's Law when the light is incident on the glass slab's surface,

\[\dfrac{\sin i_1}{\sin r_1}=n=\text{refractive index of glass}\]

Now, applying Snell's Law when the light ray is leaving the glass slab through another surface,

\[\dfrac{\sin i_2}{\sin r_2}=\dfrac{1}{n}\Rightarrow \dfrac{\sin r_2}{\sin i_2}=n=\text{refractive index of glass} \\ \therefore \dfrac{\sin i_1}{\sin r_1}=\dfrac{\sin r_2}{\sin i_2}\]

Now, $\angle r_1=\angle i_2$ as they are alternate angles, thus, $\sin r_1=\sin i_2$,

\[\therefore \sin i_1=\sin r_2\Rightarrow \angle i_1=\angle r_2 \]

So, the incident ray is parallel to the emergent ray but it is laterally displaced from it.

Question: A ray of light travelling in air falls on the surface of a transparent glass slab. The ray makes and angle of $45^{\circ}$ with the normal to the surface. Find the angle made by the refracted ray with the normal within the slab. Given that refractive index of the glass slab is $\sqrt{2}$. Solution: We know that $ n=\dfrac{\sin i}{\sin r} = \dfrac{\sin 45^{\circ}}{\sin r}$, here the refractive index is $\sqrt{2}$. \[\begin{align} \dfrac{\sin 45^{\circ}}{\sin r}&=\sqrt{2}\\ \implies\sin r &= \dfrac{1}{\sqrt{2}}\times \sin 45^{\circ}\\ =\dfrac{1}{\sqrt{2}}\times \dfrac{1}{\sqrt{2}} &=\dfrac{1}{2} \end{align}\] Thus, as $\sin r$ = $\dfrac{1}{2}$, the angle of refraction would be $r=\sin^{-1}\left(\dfrac 12\right)=30^\circ$.

As discussed earlier, the emergent ray is parallel to the incident ray but appears slightly shifted, and this shift in the position of the emergent ray as compared to the incident ray is called Lateral displacement .

Lateral Displacement The perpendicular distance between the incident ray and the emergent ray is defined as lateral shift. This shift depends upon the angle of incidence, the angle of refraction and the thickness of the medium. It is given by the following expression: \[S_{\text{Lateral}}=\dfrac{t}{\cos r}\sin{(i-r)}\]

We shall now try to derive the above stated formula for a Glass slab. In the figure given below, $AB$ is the incident ray, $BC$ is the refracted ray and $CD$ is the emergent ray. The ray is striking the slab at an angle of $i_1$ and it is emerging from the slab at an angle of $r_2$.

Refraction of a ray of light in a glass slab with it's corresponding angles

In $\triangle BCK$,

\[\sin (i_1-r_1)=\dfrac{CK}{BC} \Rightarrow CK=BC \sin (i_1-r_1)\]

In $\triangle BCN'$,

\[\cos r_1=\dfrac{BN'}{BC}=\dfrac{t}{BC} \Rightarrow BC=\dfrac{t}{\cos r_1}\]

Here, $t$ is the thickness of slab.

Substituting the value of $BC$ in the first equation,

\[S_L=\text{Lateral Displacement }(CK)=t\dfrac{\sin(i_1-r_1)}{\cos r_1}\]

Question: The thickness of a glass slab is $0.25m$, it has a refractive index of $1.5$. A ray of light is incident on the surface of the slab at an angle of $60^\circ$. Find the lateral displacement of the light ray when it emerges from the other side of the mirror. You may assume that the speed of light is $3\times 10^8 m/s$. Solution: From the previous topics, we know: \[\text{refractive index}=\dfrac{\sin i}{\sin r}=1.5\text{ (in this case)}\\\sin r=\dfrac{1.5}{\sin 60}\approx 0.57735\\\implies r = \sin^{-1}(0.57735)\approx 35.25^\circ\] Now, applying the values in the formula for lateral displacement we get: \[S_L=\dfrac{0.25}{\cos(35.25)}\times\sin(60-35.25)\approx 0.1281 m =\boxed{12.81cm}\]

Many a time you might have seen the floor of the swimming pool raised/ the letters appearing to be raised under a glass slab, ever wondered why this happens? If you observe clearly, you'll find that refraction explains it. Let's see the definition.

The vertical distance by which an object appears to be shifted when an object placed in one medium is observed from another medium of different refractive indices, is called Normal shift. It is given by the formula: \[S_{\text{Normal}}=t\left(1-\dfrac{1}{_{\text r}n_{\text d}}\right)\quad\text{where}\quad _{\text r}n_{\text d}=\mu=\dfrac{\text{real depth}}{\text{apparent depth}}\]

The thickness of a glass slab is $0.2m$, and it is placed over a flat book, the refractive index of the glass slab is $1.5$. A student looks through it and finds that the normal shift is $x$, find $x$. Solution: We know that: \[\begin{align} S_N&=t\left(1-\dfrac{1}{\mu}\right)\\ &=0.2\left(1-\dfrac{1}{1.5}\right)\\ &=0.2\times \dfrac 13= 0.066m \end{align}\]

When light travels from a denser to rarer medium with an angle greater than the critical angle, the ray of light does not deviate in its path or does not refract, but it undergoes a reflection known as total internal reflection. The angle beyond which light in a given medium undergoes total internal reflection is called the critical angle .

The critical angle differs from medium to medium. If the refractive index of a given medium is $\mu$, then it's critical angle is given by the formula: [1]

\[\mu =\dfrac { 1 }{ \sin{ \theta }_{ c } }\quad\\\theta_c=\sin^{-1}\left(\dfrac 1\mu\right)\]

This is very useful as it is used in fiber glasses where total internal reflection helps in fast movement of wavelengths.

Sparkle of the diamond Whenever your mom wears it you notice it, yes the sparkling beauty of the diamond never misses our eye. But have you ever wondered why the diamond sparkles? Well it is due to the phenomenon we've been discussing now, total internal reflection . Sparking beauty of the hope diamond [2]

Mirage Formation This very old illusion ,which had fooled many people, is due to the magic of Total Internal relfection! Mirage is an optical illusion caused by refraction and total internal reflection. We know that the temperature of air varies with height, and also refractive index depends on the temperature of the medium. Mirage Formation on a road [3] During hot summers, the Surface of the Earth gets hotter, and the layers of air with decreasing temperature are formed. But the hot air has a refractive index lower than the cold air, that is hot air is optically rarer than cold air, and we know if a ray of light passes through a rarer medium from a denser medium, then the light rays bend away from the normal. So, at some points the light rays get totally reflected internally and reach the eyes of an observer, creating the reflection of an object on the surface of the Earth.

Looming Very similar to mirage formation,thus phenomenon makes the objects appear to be levitating in the sky. This is mostly seen in the polar regions (as opposed to mirages, which are generally frowned in hot deserts). In these places the surface of the Earth is very cold and as we go up, layers of air with increasing temperatures are formed. As a result, the layers of atmosphere near the Earth have a higher refractive index than the layers above them, this layer is called as an inversion layer . The objects appear to be floating due to the phenomemnon of looming [4] When the light from any object (normally ships) reaches an observer, it undergoes a series of refractions which makes the light rays bend away from the normal, and at a point, they reach a stage where the angle incidence is greater than the critical angle and thus the rays undergo total internal reflection and reach the eye of an observer and creates and optical illusion that the object is really floating in the sky!

Fibre Optics Optical fibres are the devices used to transfer light signals over large distances with negligible loss of energy . It is a revolutionary idea in terms of communication. But it's working is based on this simple phenomenon of total internal reflection. If you take a close look at an optical fibre you will observe that it consists of a thin transparent material, this is know as the core . This core is coated with something known as cladding and has a higher refractive index than the surrounding medium [5] , it prevents the absorption of light by any means. The internal structure and the transfer of light signal in a single optical fibre [6] When the light rays enter the acceptance cone, some rays which are incident at an angle greater than the critical angle gets reflected internally and then it undergoes a series of Total Internal reflections until it reaches the other end of the firbe. But we should note that not all of the rays get reflected internally because they may not have struck the surface at the required angle (as seen in the figure above).

The critical angle is the angle of incidence above which total internal reflection occurs. If the speed of light is $1.5 \times 10^8\text{ m/s}$ in a particular medium, then what is the critical angle of the light passing through this medium into the air?

The speed of light in the air is $3.0 \times 10^8\text{ m/s}.$

Optical fibers are devices used for guiding light in many applications, most notably for fast communication. A fiber consists of a glass cylinder surrounded by a wall covered in a special coating.

The fibers work on a principle called total internal reflection : light enters the fiber at an angle such that it does not get transmitted through the wall of the fiber when it hits the inside of the wall. Therefore, the refraction index of the glass part of the fiber has to be higher than that of its coating.

What is the maximum entering angle in degrees a light ray can pass from the air to the glass fiber for the total internal reflection to occur?

Details and Assumptions:

Measure the entering angle from the axis of the fiber.
Use the following refraction indexes: $n_{\text{air}} = 1.00$, $n_{\text{glass}} = 1.50,$ and $n_{\text{coating}} = 1.46$.

[1] Total Internal reflection, rp-encyclopedia.com . Retrieved 16:45, March 15, 2016, from https://www.rpphotonics.com/total internal reflection.html .

[2] Image from https://en.m.wikipedia.org/wiki/Diamond#/media/File%3AThe Hope Diamond - SIA.jpg under the creative Commons license for reuse and modification.

[3] Image credit http://epod.usra.edu/blog/2010/03/highway-mirage.html : Universities Space Research Association

[4] Image from https://en.m.wikipedia.org/wiki/File:Illustration of looming refration phenomenon.jpg under the creative Commons license for reuse and modification.

[5] Optical Fibres, rp-encyclopedia.com . Retrieved 08:56, March 17, 2016, from https://www.rpphotonics.com/fibers.html .

[6] Image credit http://www.pacificcable.com/Fiber-Optic-Tutorial.html .

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Snell's Law Calculator

Table of contents

When light travels from one medium to another, it bends or refracts. The Snell's law calculator lets you explore this topic in detail and understand the principles of refraction. Read on to discover how Snell's law of refraction is formulated and what equation will let you calculate the angle of refraction. The last part of this article is devoted to the critical angle formula and definition.

Snell's law of refraction

Snell's law describes how exactly refraction works. When a light ray enters a different medium, its speed and wavelength change. The ray bends either towards the normal of two media boundaries (when its speed decreases) or away from it (when its speed increases). The angle of refraction depends on the indices of refraction of both media:

n 1 n_1 n 1 is the refractive index of medium 1 (from which the ray travels);
n 2 n_2 n 2 is the refractive index of medium 2 (into which the ray travels);
θ 1 \theta_1 θ 1 is the angle of incidence - the angle between a line normal (perpendicular) to the boundary between two media and the incoming ray;
θ 2 \theta_2 θ 2 is the angle of refraction - the angle between the normal to the boundary and the ray traveling through medium 2.

🔎 You can check how the speed of light can change in different media in the wave velocity calculator .

You can find some of the values of n 1 n_1 n 1 and n 2 n_2 n 2 for common media in the index of refraction calculator .

Generally, Snell's law of refraction is only valid for isotropic media. In anisotropic ones, such as crystals, the ray may be split into two rays.

Finding the angle of refraction - an example

Let's assume you want to find the angle of refraction of a light beam that travels from air to glass. The angle of incidence is 30°.

Find the index of refraction of air. It is equal to 1.000293 1.000293 1.000293 .
Find the index of refraction of glass. Let's assume it is equal to 1.50 1.50 1.50 .
Transform the equation so that the unknown (angle of refraction) is on the left-hand side: sin ⁡ ( θ 2 ) = n 1 sin ⁡ ( θ 1 ) n 2 \sin(\theta_2) = \frac{n_1 \sin(\theta_1)}{n_2} sin ( θ 2 ) = n 2 n 1 s i n ( θ 1 ) .
Perform the calculations: sin ⁡ ( θ 2 ) = 1.000293 sin ⁡ ( 30 ° ) 1.50 = 0.333 \sin(\theta_2) = \frac{1.000293 \sin(30\degree)}{1.50} = 0.333 sin ( θ 2 ) = 1.50 1.000293 s i n ( 30° ) = 0.333 .
Find the arcsin of this value: θ 2 = arcsin ⁡ ( 0.333 ) = 19.48 ° \theta_2 = \arcsin(0.333) = 19.48 \degree θ 2 = arcsin ( 0.333 ) = 19.48° .
You can also save yourself some time and simply use the Snell's law calculator.

Critical angle formula

Sometimes while applying the Snell's law of refraction, you will receive the sin ⁡ ( θ 2 ) \sin(\theta_2) sin ( θ 2 ) as a value greater than 1. This is, of course, impossible. If this happens, it means that all light is reflected from the boundary (this phenomenon is known as the total internal reflection). Our Snell's law calculator will advise you when this happens.

The highest angle of incidence, for which the light is not reflected, is called the critical angle. The refracted ray travels along the boundary between both media. It means that the angle of refraction is equal to 90°. Hence, you can find the critical angle by using the following equation:

After simplification, n 1 sin ⁡ ( θ 1 ) = n 2 ⋅ 1 n_1 \sin(\theta_1) = n_2 \cdot 1 n 1 sin ( θ 1 ) = n 2 ⋅ 1 .

Solving for the angle of incidence, θ 1 = arcsin ⁡ ( n 2 n 1 ) \theta_1 = \arcsin(\frac{n_2}{n_1}) θ 1 = arcsin ( n 1 n 2 ) .

🙋 Thirsty for more knowledge? Check our De Broglie wavelength calculator to read about the wave-particle duality, which explains light refraction.

What is Snell's law?

Snell's law , or the law of refraction , describes the relationship between the angles of incidence θ₁ and refraction θ₂ and the refractive indices ( n ₁, n ₂) of two media: n ₁sin(θ₁) = n ₂sin(θ₂). The law of refraction allows us to predict the amount of bend when light travels from one medium to another .

Does Snell's law apply to all waves?

Yes , you can apply Snell's law to all isotropic materials , in all phases of matter . This happens because Snell's law is related only to the propagation of the wave and not to the details of the wave itself. Therefore, it works for sound waves as well.

What will be the angle of refraction if the angle of incidence is 10°??

7.5° . Let's say a light beam enters the water at 10° . To find an angle of refraction:

Find the refractive indices of air, n ₁ =1, and water, n ₂ = 1.33.
Solve Snell's law equation for θ₂: sin(θ₂) = n ₁sin(θ₁)/ n ₂. Therefore, θ₂ = arcsin(1×sin(10°)/1.33) = 7.5°.

How can I calculate the refractive index of the glass using Snell's law?

Assuming that light travels from air to glass , the angle of incidence is 30°, and the angle of refraction is 20°. To calculate the refractive index, follow these steps:

Identify the refractive index of air: n ₁ = 1.
Modify Snell's law to find the refractive index of glass: n ₂ = n ₁sin(θ₁)/sin(θ₂).
Enter data : n ₂ = 1×sin(30°)/sin(20°) = 1.46.

What are the limitations of Snell's law?

The limitation of Snell's law of refraction is when light falls on the surface of the separation of two media normally or through a normal (perpendicular line). This is because when light falls through the normal, the angle of incidence θ₁ is equal to zero . Hence from Snell's law, sin(θ₁) = sin(0°) = 0 , and the angle of refraction is also equal to zero .

$Snell's law illustration. Image presenting light refraction, with refraction indices and angles of incidence an refraction marked.$

Refractive index 1 (n₁)

...of medium 1.

Refractive index 2 (n₂)

...of medium 2.

Angle of incidence (θ₁)

Angle of refraction (θ₂)

How Does Light Travel Through Glass?

I've mentioned before that I'm answering the occasional question over at the Physics Stack Exchange site, a crowd-sourced physics Q&A. When I'm particularly pleased with a question and answer, I'll be promoting them over here like, well, now. Yesterday, somebody posted this question :

Consider a single photon (Î»=532 nm) traveling through a plate of perfect glass with a refractive index n=1.5. We know that it does not change its direction or other characteristics in any particular way and propagating 1 cm through such glass is equivalent to 1.5 cm of vacuum. Apparently, the photon interacts with glass, but what is the physical nature of this interaction?

I didn't have a ready answer for this one, but I'm pretty happy with what I came up with on the spot, so I'll expand on it a little bit here. I think it's an interesting question not only because the issues are a little bit subtle, but because it also shows the importance of understanding classical models as well as quantum ones. The key to understanding what's going on here in the quantum scenario is to recognize that the end result is the same as in the classical case, and adapt the classical method accordingly.

So, how do you explain this classically, that is, in a model where light is strictly a wave, and does not have particle character? The answer is, basically, Huygens's Principle .

To understand the propagation of a wave through a medium, you can think of each component of the medium-- atoms, in the case of a glass block-- as being set into motion by the incoming wave, and then acting as a point source of its own waves. In the picture above, you can see that each of the the little yellow spots in the gap in the barrier is at the center of its own set of concentric rings, representing the emitted waves.

When you work this out, either by drawing pictures like the above, or by doing out the math, you find that these waves interfere constructively with one another (that is, all the peaks line up) in the forward direction, but that the waves headed out sideways to the original motion will interfere destructively (the peaks of one wave fall in the valleys of another), and cancel out. This means that the light continues to move in the same direction it was originally headed.

When you work out the details, you also find that the wave produced by the individual point sources lags behind the incoming wave by a small amount. When you add that in, you find that the wave propagating through the medium looks like it's moving slightly slower than the wave had been moving outside the material. Which is what we see as the effect of the index of refraction.

This model of light propagation through a medium is fantastically successful, so our quantum picture should reproduce the same features as long as you're at a frequency where quantum effects don't play a role. So, how do we carry this over to the quantum case, thinking about light in terms of photons?

This is a tricky question to answer, because in many ways it doesn't make sense to talk about a definite path followed by a single photon. Quantum mechanics is inherently probabilistic, so all we can really talk about are the probabilities of various outcomes over many repeated experiments with identically prepared initial states. All we can measure is something like the average travel time for a large number of single photons passing through a block of glass one after the other. We can come up with a sort of mental picture of the microscopic processes involved in the transmission of a single photon through a solid material, though, that uses what we know from the classical picture.

To make the classical picture quantum, we say that a single photon entering the material will potentially be absorbed and re-emitted by each of the atoms making up the first layer of the material. Since we cannot directly measure which atom did the absorbing, though, we treat the situation mathematically as a superposition of all the possible outcomes, namely, each of the atoms absorbing then re-emitting the photon. Then, when we come to the next layer of the material, we first need to add up all the wavefunctions corresponding to all the possible absorptions and re-emissions.

Thus, we more or less reproduce the Huygens's Principle case, and we find that just as in the classical case, the pieces of the photon wavefunction corresponding to each of the different emissions will interfere with one another. This interference will be constructive in the forward direction, and destructive in all the other directions. So, the photon will effectively continue on in the direction it was originally headed. Then we repeat the process for the next layer of atoms in the medium, and so forth.

It's important to note that when this picture is valid the probability of being absorbed then re-emitted by any individual atom is pretty tiny-- when the light frequency is close to a resonance in the material, you would need to do something very different. (But then, if the light was close to a resonant frequency of the material, it wouldn't be a transparent material...) while the probability of absorption and re-emission is tiny for any individual atom, though, there are vast numbers of atoms in a typical solid, so the odds are that the photon will be absorbed and re-emitted at some point during the passage through the glass are very good. Thus, on average, the photon will be delayed relative to one that passes through an equal length of vacuum, and that gives us the slowing effect that we see for light moving through glass.

Of course, it's not possible to observe the exact path taken by any photon-- that is, which specific atoms it scattered from-- and if we attempted to make such a measurement, it would change the path of the photon to such a degree as to be completely useless. Thus, when we talk about the transmission of a single photon through a refractive material, we assign the photon a velocity that is the average velocity determined from many realizations of the single photon thought experiment, and go from there.

The important and interesting thing here is that the effect that we see as a slowing of a particle-- a photon taking a longer time to pass through glass than air-- is actually a collective effect due to the wave nature of the photon. The path of the light is ultimately determined by an interference between parts of the photon wavefunction corresponding to absorption and re-emission by all of the atoms in the material at once. And since we know the photon has wave characteristics as well as particle characteristics, we can use what we know from classical optics to understand the quantum processes involved.

This is, as I said, an explanation invented on the spot yesterday, when I started thinking about the question, but I think it's fairly solid. As always, if you see a major hole in it, point it out in the comments.

And if you have physics questions, I encourage you to take them to the Stack Exchange site. I've got dozens of other things I'm supposed to be doing, so I won't necessarily have time to address specific questions, but that's the beauty of the crowd-sourced option-- there's bound to be somebody out there who isn't too busy to answer...

More like this

Mathematical proof that god spoke creation (if you buy his book), making waves, another revolution in physics crackpottery: electromagnetic gravity, chemistry of the quantum kind.

So is the idea here that if you had a particular atom and photon, absorption and re-emission would be a stochastic process (and we wouldn't know which direction it'd emit).

But when you have a whole bunch of atoms and the photon can't really be said to be absorbed by any one in particular, then the interference effects of all the possible paths it can take would add up to the classical description of refraction? Because all the paths include being absorbed and emitted by all the atoms, and in all directions, and the sum of those is back to the classical deterministic path?

I had been avoiding absorption-emission in my own conceptualization of optical transmission but I see now I didn't have to...

It's been a while since I read it, but didn't Feynman use the passage of light through a transparant refractive medium as an example in his book QED?

Actually, I think he also tied in why there is partial reflection when light passes through a junction of materials with two different indices of refraction as well. My recollection is that when the photon interacts with an atom, it stands a chance of being scattered forward or backward (so a transmission through, say, 3 layers of atoms could be forward-forward-forward (and go through) or backward (and be reflected, or forward-backward-forward-forward-forward (and go through seemingly a bit slowly) or any number of other combinations). Since, under QED, the overall amplitude is the sum over all possible paths, the end result is delayed from what it would be without the media.

Wow -- what an over-explanation.

You could just put up Maxwell's equations in dielectrics -- that's the answer. Hundreds and thousands of words to "explain" 4 equations that still aren't fully covered by all the words.

If you want to derive them from quantum mechanics -- then do it, instead of talking about it.

The photon case sounds a lot like a kinematic wave.

Frog -- you miss the point that, yeah, sure, Chad could just put up Maxwell's equation including material terms, and derive a wave equation that has a speed lower than c in in it. Which might be illuminating for somebody who knows vector calculus and partial differential equations. What he did write, however, might be illuminating for others as well... and might also help those who *do* know vector calculus and PDEs understand how to interpret the equations that they've seen.

Frog - that's all very well if you a) know that particular formation of Maxwell's equations and b) understand it. Those of us without that level of physics education but who are interested in this sort of thing find a textual and graphical explanation much more useful, thank you very much.

Over explanation? That depends very strongly on your audience.

The question reminded me for some reason of Bob Shaw's "Light of Other Days" which tells a story of a place that sells slow glass. Slow glass panes are placed facing beautiful scenes. The glass captures the light over a period of years and eventually the light starts coming out the other side. That's when people buy the panes. It eventually occurred to me that light means energy, and that fairly thin pane has to contain all the energy of the light that falls on it over many years. It must get pretty hot.

"When you work out the details, you also find that the wave produced by the individual point sources lags behind the incoming wave by a small amount." So what you are saying is that there is a time lag between when the "point source" ie atom, receives the incoming wave and when it re-emits a wave? These time lags add up. Is my interpretation correct?

Owen: "Those of us without that level of physics education but who are interested in this sort of thing find a textual and graphical explanation much more useful, thank you very much."

I think you're misleading yourself. I understand your point -- you feel as if you understand it, but I think that all there is to understand is Maxwell's equations. If you can't do that -- you don't actually understand it. You can't actually predict experimental results with the graphics and the verbalization.

It's like arguments over what QM "means". Huge amounts of hot air go on -- when the only real explanation are the equations for the wave functions. The words at best are just a way to make the equations palatable.

As a bonus, Maxwell's equations are particularly simple. You don't have to try to bend your head in 20 ways to understand them -- if you know what a vector is and a few measurements, you've got all of electrodynamics in your head.

All of classical electrodynamics. Maxwell's equations aren't the complete story of electrodynamics, because if they were, we wouldn't need quantum electrodynamics (QED).

Now, it's true that you don't need QED to describe the propagation of light through a dielectric medium well off resonance. However, we know that QED is a more complete theory of reality (because Maxwell's equations aren't sufficient to describe non-classical states of light such as single-photon states), so it is perfectly reasonable to ask how you would explain propagation through a medium in quantum terms. While the results you get won't differ appreciably from what you'd get using Maxwell's equations, it can be illuminating (heh) to think about how those results arise from the deeper quantum theory.

If I were interested in predicting the results of a photon propagation experiment, then I'd be a quantum physicist. But I'm not. So I'll settle for Chad's very interesting (and well written) explanation, while you, frog, can go hide in a hole with the other eletists and calculate numbers.

Chad's post is not an over explanation. Ok, it does not explain how to model this situation. An explanation of how to model the situation using Maxwell's equations might be shorter than Chad's post. But that totally misses the point; Chad's post (and blog in general) is about the ideas behind the quantum model, and how they relate to ideas about the classical model.

You might call this type of writing scholarly writing (in this case aimed at a general audience), rather than technical writing. Scholarly writing tends to be under-appreciated, and also under-identified, in the math and physics world. At least, that's my experience as a mathematician.

This reminds me of something I heard many years ago that I found bothersome at the time--the breathless reports of experiments that measured interference effects in a small loop of superconducting wire, proclaiming that while the currents involved were minuscule, they were a first-time demonstration of quantum effects operating at the macroscopic level because every atom in the (barely) macroscopic wire was "participating" in conducting the currents.

But how is that really any different than conducting, say, a two-slit experiment submerged in water, or inside a solid block of glass? A substantial fraction of the atoms in the medium "participate" in the propagation of a single photon, and so they all "participate" in generating the interference pattern on the photodetecting surface. So why was doing essentially the same thing with electricity considered to be some sort of breakthrough?

Comments 3 and 5;

You may have a hard time with this, but the common language of description and explanation, as with mathematics are really a structured analytical analogy, with mathematics closer to reality.

There is no such thing as a perfect analogy.

Such is the world...experience rules.

To convey a process to the masses both can be used in conjunction, though it is rarely done successfully and accurately, as it can be difficult.

Much better understanding can be achieved with a higher language and mathematics but then you leave out a whole slew of people.

so is them glass transparent due to the way the atoms are arranged i did not now that. Forgive me im hoping to become a physicist but in the south our education is lacking im only now getting to the university physics courses.

The behavior of photons is all probabilistic then can this characteristic be expressed on the large scale ie the wave functions are interfering constructively on the large scale and can this behavior be induced in an observable way

@Sphere: You may have a hard time with this, but the common language of description and explanation, as with mathematics are really a structured analytical analogy, with mathematics closer to reality.

The question is what is the cut-off -- at what point are words simply insufficient. The historical progress has been from verbal to mathematical descriptions. You can still do some physics primarily using words and drawings -- at least a first cut of ballistics can be done that way.

But at some points words simply mislead. It's too easy to make a mistake (see my eliding of "classical" from the entire classical electrodynamics phrase). At a certain level, no matter how clear your verbiage it, it creates more noise than signal simply because the necessary number of words to explain the phenomenon to any amount of accuracy are more words than a person can understand.

Then you get folks who "think" they understand it, when they simply don't. See almost any popular discussion of quantum mechanics, which is almost much more wrong than it is right. How much effort is wasted in "understanding" wave/particle duality or uncertainty? Words simply don't suffice.

Some things just simply require a certain "elite" understanding -- the essence is in the numbers and not in the words. Making that clear to people is important, I think. There's no short-cut to carpentry or physics. You either can build a bookshelf or you can't (but you can always practice and try to learn). But a sculpture of building bookshelves just isn't terribly useful -- if that's elitism or a "misunderstanding", then I guess I stand guilty.

And I wonder how "elitist" it is to say -- well, you can't understand the real physics, so here's something that'll make you feel involved and happy, even if you can never predict a single experiment with what I give you.

I guess it's the old question from Feynman's intro -- are you doing any one any good by putting physics in terms that anyone thinks they can understand, but no one can actually do any physics with? And where do you draw the line. For me, this passed the threshold of being way complicated for what is mathematically simple -- that's a sign that you're simply trying to do the impossible and non-useful. We're not talking here actually nasty mathematics where you can really argue that you capture a good chunk in the words and the math only adds a few decimal points.

I'm not sure I buy your explanation of the change in propagation speed, at least in the classical case. You say "when you work out the details" you see this but I think the details require more than Huygen's principle. The wave crest from a particular "Huygens" point moves out from that point at the same speed as it arrived, so the front of the wave in medium shouldn't be any slower. This might change of course if there is a delay between absorption and emission of photons from atoms, but that isn't Huygen's principle by itself. Put another way, there needs to be some reference to the (probably dialectric) properties of the different media. The picture by itself provides no intuitive explanation since you could flip the incoming/outgoing wavelets around the horizontal axis and come to the same conclusions as before. The picture shows refraction from a gap but that's about it at the classical level.

I was under the impression that in classical optics we simply take for granted that the speed of light is reduced in many materials, by a factor of the material's refractive index. Of course in the quantum mechanical picture each photon is (possibly) absorbed and re-emitted continually, and the speed of light in the material is simply the sum of all possible outcomes as you said.

The Huygens principle is a fantastic way of explaining diffraction or refraction, but does it have anything to do with the speed of light changing in the material? Take refraction: It's easy to directly "see" the wavefront changing direction when you draw all of the circular wavefronts being emitted from rays striking the surface. However you have to decrease the radial spacing of the circles for the wavefront to change direction (in a rather ad hoc manner). As far as I know, the Huygens principle doesn't say anything about what this new radial spacing is (proportional to 1 / the refractive index). Can you clarify?

What I would like to know is how an atom absorbs and then re-emits the photon.

What exactly happens? At one point in time we have a photon and an atom, at another point in time we have only an excited atom - what exactly happens in between? How the photons energy get's absorbed by atom's electron? It cannot be absorbed instantly as that would mean spacetime is discontinuous.

Why? Even if you assume both the photon and the electron are point particles (which is absurd IMHO, but that is beside the point here) the curvature their mass-energy induces (however small it is) is extended in spacetime. An instant absorption of the photon would mean that it's curvature vanishes "instantly and simultaneously in an extended region of space" but that makes no sense from relativity POV, first simultaneity is observer dependent, but even worse it would make spacetime curvature discontinuous.

So because of general relativity the process of absorption has to be gradual and the mass-energy configuration of the photon+atom state has to continuously transform into mass-energy configuration of the excited atom state.

But how exactly does that happen?

Much agreed,and I personally don't think of someone who has these abilities to be an elitist. I myself utilised (big words) when communicating with others in a normal everyday setting and of course no-one could understand a word I said and since most of the people (even though I have been at Uni. for over two decades)speak in a common tongue, speaking with only higher language came natural to me and took effort to retrain myself at a great personal lose. I have been forced to conform to this reality, and have lost this vocabulary due to lack of use.The only reasurence that I have is when I am amongst those (so called elite), it all comes back!

THAT is not elitist, it is skill and talent. ;?)

It takes so many unrefined words to explain a situation that it becomes tedious and as you say, the background noise can be overwhelming and the original concept lost.

I have thought about this for many years and have come to the conclusion that any and all papers that I should write would take four forms or levels, Mathematical,A higher language, the common tongue, the metaphysical. In this way one could start from the level most comfortable and progress. I think that each of these communication forms, operating in their own parameter, overlap, and in such a way a higher standing can be achieved to anyone with the desire to pursue.

Analogies are great, yet nothing beats experiment, and since experiment is not always available to the masses, a difficult situation is before the communicators of our time.

The math should be spoon fed at every possible opportunity along with, side by side, at every step, common and/or high. In this way, overtime, understanding could come to fruition.It is redundant, tedius and ugly for those already trained.

Could you imagine if everyone spoke as the so called elitist, there would be very little verbalised yet a whole lot said.

Yes, they do. Specifically, they require a model of the sources of the waves as little dipoles driven off-resonance. This is a reasonable approximation of an atom-- negative electrons outside a positive nucleus-- and works to get you what you need.

The crucial factor is that when you drive the dipoles by applying an oscillating electric field that pulls the electrons back and forth (by a tiny amount-- we're not talking big distortions, here, so it's not going to upset the binding of atoms into a solid) their response is very slightly out of phase with the driving field. This is a basic result for any driven harmonic oscillator, that you can derive from classical mechanics, but I have a hard time thinking of a good conceptual explanation for (which is why I didn't put it into the post).

That slight phase lag in the oscillation means that the waves emitted by the little dipoles are slightly out of phase with the incoming field doing the driving. When you add those two waves together, you get a wave of the same frequency that lags a little behind the incoming wave, and thus moves more slowly than the incoming wave.

If you want to see this all worked out in detail, the bible for classical optics stuff like this is the textbook by Hecht. I was supposed to teach an upper-level elective on classical optics next term, so I was mentally reviewing some of it recently, hence this response.

(Alas, the class had to be cancelled due to low enrollment. Sigh.)

Two comments (which I may steal for my own posts!): The technically inclined may be interested to know that photon wavefunctions are tricky things. In some important senses, photons don't have one at all. Among other things, Schrodinger's equation doesn't work with m = 0. You can construct correlation functions that work more or less like a photon wavefunction, but this isn't quite the same thing. You know this of course, and conceptually it makes no difference for the intuitive explanation, but it's a neat thing to think about.

Second, "When you add those two waves together, you get a wave of the same frequency that lags a little behind the incoming wave, and thus moves more slowly than the incoming wave." Usually! But it's also possible to have a refractive index of less than 1, which means a phase velocity greater than c. This doesn't violate relativity, but the reason (elucidated by Sommerfeld and Brillouin a century ago) is by no means trivial, and my first first-author paper is tangentially related to this (or it will be when the referee gets around to sending in his report!).

Sounds reasonable. I wonder how believers in the Bohmian pilot wave concept explain basic things like linear propagation through glass. And what do they think a "photon" is, anyway? I can intuitively get the idea of "an electron" (tiny locus of electric field) being "a true classical object" that is guided into apparent interference etc., but "a photon": imagined in flight and not just as a receiving-end quantum of energy, is ... what?

BTW transparent things are of course a way to detect passage of a photon without "affecting the target" in any significant way (and I *don't* mean the E-V bomb scheme.) Just send the photon through a piece of glass, and if normal incidence there is no residual momentum transfer etc. You could either count for delay in photon reception, or better: use interference to show it's there.

But all these examples of interaction-free or interaction-irrelevant measurements cause a problem for QM: the early arguments about the HUP etc. relied on the idea that a photon use to e.g. measure position would have to impact momentum in a straightforward way (scatter-type process) as if a piece of flat glass couldn't be found in a position, but with negligible momentum transfer. What gives?

I have to agree that Huygens principle is a better explanation than Maxwell's equations in dielectric media. The latter are (very important and amazingly effective) approximate equations, but they gloss over all of the atomic processes involved (e.g. is the dielectric constant really constant?). There is of, course, a middle ground, by mathematically expressing the total electromagnetic wave as a sum of the incident wave with all of the (absorbed and re-emitted) waves from the medium; this has the added advantange of highlighting the beauty of linearity and the principle of superposition.

A nice exposition along these lines can be found in a paper by Mary James and David J. Griffiths, "Why the speed of light is reduced in a transparent medium": http://ajp.aapt.org/resource/1/ajpias/v60/i4/p309_s1 . From the abstract: "This paper offers some elucidation of the ââmiracleââ by which the radiation from many induced molecular dipoles conspires to produce a single wave propagating at the reduced speed."

Frog, about use of words: we need to words to explain what the math is doing, otherwise "f = ma" is the same as "a = fm" etc, they are just labels for the same function.

I have to quibble with Chad saying this: "All we can measure is something like the average travel time for a large number of single photons passing through a block of glass one after the other." Although it is hard to time a single photon, it can be done within the limits imposed by coherence time. With a thick piece of glass, you should be able to observe (as I noted above) that a single photon was delayed before reaching a detector.

To extend my example about observation that does not affect momentum: we could use rotation of polarization too, to find that something was there. I hate to say it, but it seems even thinkers like Heisenberg working out the "Heisenberg microscope" are looking for the example that seems to prove their point. They aren't saying, as we must do to be candid: "what if there's another case where my wonderful illustration does not work?"

According to a more complete theory, if a process deals with a low number of action, then the Proper Time Tau have to be substituted by the Action S, and that is not a invariant nor a continuous but a discrete dimension:

0 â 1/hÂ² dSÂ² - 1/tplÂ² ( dtÂ² - 1/cÂ² {dq1Â² + G0Â²/GÂ² [ dq2,3Â² - ...]}) with G0 = tplÂ²câµ/h â G

With this, we have to expect a delay on each pass near an atom which will be an 'interaction' with it (which happens or not happens - discretely). The amount of the delay is question of the 'metric coefficient' omitted in above formula, but it is potentially either one frequence of the photon, or one planck time.

In its own sistem, the photon feels only the events of absorbtion and emission; its own sistem consists of these two events, separated by one planck quantum or almost-zero. It depends now entirely on the sistem of the world of any observer, if this almost-zero is splitted into an appearent light-speedy motion (observed in a world whose two relevant coordinates have a quotient c in the metrics), or if it is considered in smaller scales where implicitely becomes relevant the dimension of the action, resulting then in quantum effects.

Thus, in the curvature formula above, on each passagem near an atom which in the world and dimension of us (observer) is an discrete 'interaction', that must be an event or action together with the production of a new fact (f.ex. the exact amount of the scattering or miss vector), which needs going together with a small delay of the coordinate time, so that their sum dS^2 - E dt^2 is zero, because as explained in the proper sistem of the photon the two effects together also results in zero or unperceived by the photon.

Thus, the relative delay, directly calculable from the diffraction index, means that in the average, in Glass, after all 2 or 3 waves way occurs one event of an interaction and a corresponding delay by 1 full wave.

At this opportunity, it should be noted, that in an absorbtion-reemission model, the photon would not be the same, but on any of this occurence change its identity, so that the 'light speed' in media would be the delay of the absorption and reemission. Obviously, such an explanation isnt possible because we would expect the speed depending on the intensity too - because as a stimulated, asynchron emission it would need a next photon, and on the other hand the reemission should occur faster before many next photons arrive.

This is a great post, but I think the most enlightening part was your comment #21. That answered the real question in my opinion. I may not be your average reader though, so maybe I'm wrong about what most people would need explained to them.

By the way, Hecht is great, but if you're talking specifically about Huygens principle, and the scalar diffraction theory which follows, the one true reference is Goodman.

In my post above, dS^2 - E dt^2 should be dSÂ² - E dtÂ² , that's zero in the photon's system, thus also for the observer (any Action or Event happening, produces a forward skip in the coordinate Time and thus also a contribution to the global time, new Facts produce time flow)

Feynmann treats the problem as an oscillator. What however resists against all theories, is, that the diffraction (and lower speed in matter) occurs also with single photons, which inclusive during all of this continue as a wave package - as f.ex. in astronomy we observe single photons with refractors.

Purity and clarity of concept is a reward for the initiated. First we understand in part, then we refine our understanding.

The arguments against analogy discount the importance of recruiting the uninitiated in producing future experts. Those who refuse to modify their language for their audience earn their reputation as a bad communicator, and teacher. They also set the standard by which certain fields are judged hopelessly rarefied. Criticizing others for lacking strict adherence to technical language also reveals academic vanity. Either you enjoy lording over those on the path, or you forget nobody can be an expert in everything.

I'm not trying to be aggressive, but consider the opportunity that is a person enthusiastic about your subject who may not share your expertise. Like students, friends, or taxpayers.

For the purposes of explanation, I think it makes more sense to talk about the waves interacting with the atoms as oscillators. One would expect the resonance to preserve the wavelength, but there to be phase effects that could slow the transmission of the wave. If you use Huygen's principle, you have to assert that the mathematics works out, but there is no physical intuition. As a bonus, you can think of the light wave as having an electrical component (up and down) and a magnetic component (left and right) and having two sets of resonances with the atoms. When they reinforce, the material is transparent. When they interfere, the material is opaque. If the resonances are both 180 degrees out of phase, you get a negative refractive index. There is still plenty of handwaving, but you can explain more stuff.

It also makes it easier to move into the quantum explanation, because you can just change the "wave" to the "photon" which also has electrical and magnetic components when it interacts with the atoms. Here, the sum of all the possible interactions, weighted by their probabilities work out to give just about the same results as the classic case. Of course, in QM, the wavelength is preserved because the same energy is absorbed and emitted.

P.S. I'll apologize for my quantum approach to commenting. I'm probably about 70% correct here, but I've preserved the wavelength.

Hey everybody! I love you guys! all this stuff is way way over my head. I love it! but I have a couple questions for all you brainiacs (that's a compliment). 1) I heard or read somewhere that light travels in three diferent forms, wave, particle, & one other. is this true and what is it (obviously)? and a brief explanation of each would be nice. And 2) that there have been some experiments or studies that show the possibility that the speed of light is slowing down. albeit very very slowly, but still slowing. what has anybody heard about this?

and keep up all your freakin' studying! I wish I could understand half this stuff! oh, and please put yer anser en laymens turmz pleez. :0)

Maybe Iâm wrong; I think there may be a simpler view or hypothesis. Light or for that matter, any energy is in waves, correct? Like light, sound, heat, invisible light, inaudible sound, smell, etc. just like a human canât detect maybe what a dog or animal can. If we look at energy and really all matter, at the atomic level itâs all the same thing. Whether it atoms, electrons, neutrons, photons etc. It seems to me that light is just a massive string of phonons or energy traveling in a wave depending on its frequency it may or may not be visible depending on its medium and destination.

Light is electromagnetic radiation. Electromagnetic radiation encompasses X-rays, gamma rays, ultraviolet light, infrared light, radio waves, and visible light. Human eyes see visible light, so every type of light you observe is visible light. Light will go on forever unless blocked by other matter or particles in the medium. Like distant stars we canât see, the visible light fades due to the particles it bumps into in empty space. Or seeing light through a window, one window you can see pretty clearly. Keep adding multiple panes of glass and eventually it becomes translucent then fades altogether. Viewing a streetlight and nothing hindering the view, eventually as more distance is added, or (interference or panes of glass) it also dims then fades totally. Same with polarized glass or even mirrors, and im sure you can think of 100 more mediums. And not just the mediums but the wave lengths in other light like gamma rays, ultraviolet light, infrared light, radio waves. The same is true with sound. Both are waves of energy, traveling thru a medium to reach an intake or dissipate. Both are at different speeds and both different wavelengths. The difference between them in empty space is that light is at a higher frequency and does not need to bounce off a medium like air or water. I would also guess that sound does make noise in space but the distance it travels is miniscule or even atomic. I would also guess that we would be able to detect sound with our eyes if the waves are modified. Something like a reverse radio transmitter and receiver. If Iâm not mistaken I think there are electronics being developed that allow blind people to hear with their eyes, like radar or sonar. Even Tesla envisioned a way to transmit matter other than light or sound or electricity. For example it was worked out that adding the weight of all electrons on the internet, it weighs about 5 grams. To explain what Iâm trying to say differently, if all matter is the same at the atomic level then as it is formed into molecules, it takes on different shapes, some dense some thin. The molecular shape of an oak tree is in such a pattern that it allows sound to pass but not most lights or electricity. The molecular shape and pattern of glass, is arranged that it allows sound and light to pass but not electricity. Similarly the molecules and debris in outer space is mostly empty space or various atomic particles or something there is an ether or dark matter. It allows most light to pass but not sound or electrical currents. We know waves travel in different frequencies, speeds and power, but each of those waves whether light, sound, or whatever are also in different patterns. Maybe white light has a pattern of letâs say, -------------------------- and the molecular makeup of glass has that same pattern, there by letting white light to pass but filtering out the pattern of electricity and others regardless of the frequency. Or like the human body has a molecular pattern of xoixoixoi xoixoixoixoixoixoi there by letting the frequency of various unseen light, electricity, sound and energy but not white light.

Thats about all i could come up with. i have read the posts here and i think i understand the differing theories. i love to learn and if anyone can point out any fallacies or mistakes in my simple thinking please let me know.

thanks! [email protected]

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How does light travel through glass?

Part of the show do animals use toilet paper, wine-glasses.

I believe that light is considered to be both waves and particles. My understanding is that particles are physical objects. If that is true, how is light able to travel through glass? Is it just the light waves that travel through glass or can the particles also penetrate glass?

The first thing is that any solid object that looks solid to us is actually has huge amount of space in it...

Even in an atom, the nucleus of the atom is about a hundred thousandth of the size of the actual atom. So there's immense amounts of empty space only containing electrons, which are even smaller than the nuclei, so there's lots and lots of space for things to travel through, as long as it doesn't interact with the nuclei or electrons.

A light wave is actually quite big compared to the size of an atom. It's a quantum mechanical object - it's kind of a particle, but it's kind of a wave. You can think of it as wave which only arrives in particles - not really something with which we have a handle on.

It's a lot easier to think of it as a wave in the circumstance. The only way to stop a wave is with something which will actually absorb it or scatter it, and in something like glass there's just nothing there which will absorb or to scatter it. So it just carries on going in a straight line.

Addendum for clarity:

Light is an electromagntic wave; that means that it comprises a changing electric field, which produces a changing magnetic field, which produces a changing electric field and so on... This is how the light propagates through space.

When light rays interact with an entity, like a piece of glass, the electromagnetic wave causes the electron clouds in the material to vibrate; as the electron clouds vibrate, they regenerate the wave. This happens in a succession of "ripples" as the light passes through the object. Because this process takes time, that's why light slows down slightly in optically more dense materials like glass.

Different colours of light have different frequencies; light that is visible to us passes through glass because the arrangement of the atoms in glass means that they can sustain the ripple effect described above at those frequencies, so light can pass through.

But other materals, with a different configuration of atoms in the crystal structure, cannot permit light to propagate and instead absorb the energy. A good example of this is an X-ray. It will go straight through a human body mostly unchanged, but the lead apron worn by the radiographer stops it in its tracks.

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How a Lens Refracts Light

First lets consider a double convex lens . Suppose that several rays of light approach the lens; and suppose that these rays of light are traveling parallel to the principal axis . Upon reaching the front face of the lens, each ray of light will refract towards the normal to the surface. At this boundary, the light ray is passing from air into a more dense medium (usually plastic or glass). Since the light ray is passing from a medium in which it travels fast (less optically dense ) into a medium in which it travels relatively slow (more optically dense ), it will bend towards the normal line. This is the FST principle of refraction . This is shown for two incident rays on the diagram below. Once the light ray refracts across the boundary and enters the lens, it travels in a straight line until it reaches the back face of the lens. At this boundary, each ray of light will refract away from the normal to the surface. Since the light ray is passing from a medium in which it travels slow (more optically dense ) to a medium in which it travels fast (less optically dense ), it will bend away from the normal line; this is the SFA principle of refraction .

The above diagram shows the behavior of two incident rays approaching parallel to the principal axis. Note that the two rays converge at a point; this point is known as the focal point of the lens. The first generalization that can be made for the refraction of light by a double convex lens is as follows:

Now suppose that the rays of light are traveling through the focal point on the way to the lens. These rays of light will refract when they enter the lens and refract when they leave the lens. As the light rays enter into the more dense lens material, they refract towards the normal; and as they exit into the less dense air, they refract away from the normal. These specific rays will exit the lens traveling parallel to the principal axis.

The above diagram shows the behavior of two incident rays traveling through the focal point on the way to the lens. Note that the two rays refract parallel to the principal axis. A second generalization for the refraction of light by a double convex lens can be added to the first generalization.

The Thin Lens Approximation

Rules of refraction for diverging lenses.

Now let's investigate the refraction of light by double concave lens. Suppose that several rays of light approach the lens; and suppose that these rays of light are traveling parallel to the principal axis . Upon reaching the front face of the lens, each ray of light will refract towards the normal to the surface. At this boundary, the light ray is passing from air into a more dense medium (usually plastic or glass). Since the light ray is passing from a medium in which it travels relatively fast (less optically dense ) into a medium in which it travels relatively slow (more optically dense ), it will bend towards the normal line. This is the FST principle of refraction . This is shown for two incident rays on the diagram below. Once the light ray refracts across the boundary and enters the lens, it travels in a straight line until it reaches the back face of the lens. At this boundary, each ray of light will refract away from the normal to the surface. Since the light ray is passing from a medium in which it travels relatively slow (more optically dense ) to a medium in which it travels fast (less optically dense ), it will bend away from the normal line. This is the SFA principle of refraction . These principles of refraction are identical to what was observed for the double convex lens above .

The first generalization can now be made for the refraction of light by a double concave lens:

Now suppose that the rays of light are traveling towards the focal point on the way to the lens. Because of the negative focal length for double concave lenses, the light rays will head towards the focal point on the opposite side of the lens. These rays will actually reach the lens before they reach the focal point. These rays of light will refract when they enter the lens and refract when they leave the lens. As the light rays enter into the more dense lens material, they refract towards the normal; and as they exit into the less dense air, they refract away from the normal. These specific rays will exit the lens traveling parallel to the principal axis.

The above diagram shows the behavior of two incident rays traveling towards the focal point on the way to the lens. Note that the two rays refract parallel to the principal axis. A second generalization for the refraction of light by a double concave lens can be added to the first generalization.

A Third Rule of Refraction for Lenses

The above discussion focuses on the manner in which converging and diverging lenses refract incident rays that are traveling parallel to the principal axis or are traveling through (or towards) the focal point. But these are not the only two possible incident rays. There are a multitude of incident rays that strike the lens and refract in a variety of ways. Yet, there are three specific rays that behave in a very predictable manner. The third ray that we will investigate is the ray that passes through the precise center of the lens - through the point where the principal axis and the vertical axis intersect. This ray will refract as it enters and refract as it exits the lens, but the net effect of this dual refraction is that the path of the light ray is not changed. For a thin lens , the refracted ray is traveling in the same direction as the incident ray and is approximately in line with it. The behavior of this third incident ray is depicted in the diagram below.

Now we have three incident rays whose refractive behavior is easily predicted. These three rays lead to our three rules of refraction for converging and diverging lenses. These three rules are summarized below.

These three rules of refraction for converging and diverging lenses will be applied through the remainder of this lesson. The rules merely describe the behavior of three specific incident rays. While there is a multitude of light rays being captured and refracted by a lens, only two rays are needed in order to determine the image location. So as we proceed with this lesson, pick your favorite two rules (usually, the ones that are easiest to remember) and apply them to the construction of ray diagrams and the determination of the image location and characteristics.

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The Anatomy of the Eye

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What is Refraction of Light ?

A material is transparent if you can see through it. If you can see through it, it means that light can travel through it. Transparent materials include air , Perspex , glass , and water .

Light travels at different speeds in different materials because they have different densities . The higher the density , the slower light travels. Light travels fastest in space (a vacuum ) and a little slower in air . Light moves noticeably more slowly in glass than in air because glass is obviously more dense .

Refraction of Light along a Normal .

A line drawn at right angles to the boundary between the two media ( air and glass ) is called a normal .

Light that enters a glass block along a normal does not change direction but it does travel more slowly through the glass and so its wavelength is smaller ( continued ).

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How Does Light Travel Through Glass?

I’ve mentioned before that I’m answering the occasional question over at the Physics Stack Exchange site, a crowd-sourced physics Q&A. When I’m particularly pleased with a question and answer, I’ll be promoting them over here like, well, now. Yesterday, somebody posted this question :

Consider a single photon (Î»=532 nm) traveling through a plate of perfect glass with a refractive index n=1.5. We know that it does not change its direction or other characteristics in any particular way and propagating 1 cm through such glass is equivalent to 1.5 cm of vacuum. Apparently, the photon interacts with glass, but what is the physical nature of this interaction?

I didn’t have a ready answer for this one, but I’m pretty happy with what I came up with on the spot, so I’ll expand on it a little bit here. I think it’s an interesting question not only because the issues are a little bit subtle, but because it also shows the importance of understanding classical models as well as quantum ones. The key to understanding what’s going on here in the quantum scenario is to recognize that the end result is the same as in the classical case, and adapt the classical method accordingly.

So, how do you explain this classically, that is, in a model where light is strictly a wave, and does not have particle character? The answer is, basically, Huygens’s Principle .

To understand the propagation of a wave through a medium, you can think of each component of the medium– atoms, in the case of a glass block– as being set into motion by the incoming wave, and then acting as a point source of its own waves. In the picture above, you can see that each of the the little yellow spots in the gap in the barrier is at the center of its own set of concentric rings, representing the emitted waves.

When you work out the details, you also find that the wave produced by the individual point sources lags behind the incoming wave by a small amount. When you add that in, you find that the wave propagating through the medium looks like it’s moving slightly slower than the wave had been moving outside the material. Which is what we see as the effect of the index of refraction.

This model of light propagation through a medium is fantastically successful, so our quantum picture should reproduce the same features as long as you’re at a frequency where quantum effects don’t play a role. So, how do we carry this over to the quantum case, thinking about light in terms of photons?

This is a tricky question to answer, because in many ways it doesn’t make sense to talk about a definite path followed by a single photon. Quantum mechanics is inherently probabilistic, so all we can really talk about are the probabilities of various outcomes over many repeated experiments with identically prepared initial states. All we can measure is something like the average travel time for a large number of single photons passing through a block of glass one after the other. We can come up with a sort of mental picture of the microscopic processes involved in the transmission of a single photon through a solid material, though, that uses what we know from the classical picture.

Thus, we more or less reproduce the Huygens’s Principle case, and we find that just as in the classical case, the pieces of the photon wavefunction corresponding to each of the different emissions will interfere with one another. This interference will be constructive in the forward direction, and destructive in all the other directions. So, the photon will effectively continue on in the direction it was originally headed. Then we repeat the process for the next layer of atoms in the medium, and so forth.

It’s important to note that when this picture is valid the probability of being absorbed then re-emitted by any individual atom is pretty tiny– when the light frequency is close to a resonance in the material, you would need to do something very different. (But then, if the light was close to a resonant frequency of the material, it wouldn’t be a transparent material…) while the probability of absorption and re-emission is tiny for any individual atom, though, there are vast numbers of atoms in a typical solid, so the odds are that the photon will be absorbed and re-emitted at some point during the passage through the glass are very good. Thus, on average, the photon will be delayed relative to one that passes through an equal length of vacuum, and that gives us the slowing effect that we see for light moving through glass.

Of course, it’s not possible to observe the exact path taken by any photon– that is, which specific atoms it scattered from– and if we attempted to make such a measurement, it would change the path of the photon to such a degree as to be completely useless. Thus, when we talk about the transmission of a single photon through a refractive material, we assign the photon a velocity that is the average velocity determined from many realizations of the single photon thought experiment, and go from there.

The important and interesting thing here is that the effect that we see as a slowing of a particle– a photon taking a longer time to pass through glass than air– is actually a collective effect due to the wave nature of the photon. The path of the light is ultimately determined by an interference between parts of the photon wavefunction corresponding to absorption and re-emission by all of the atoms in the material at once. And since we know the photon has wave characteristics as well as particle characteristics, we can use what we know from classical optics to understand the quantum processes involved.

This is, as I said, an explanation invented on the spot yesterday, when I started thinking about the question, but I think it’s fairly solid. As always, if you see a major hole in it, point it out in the comments.

And if you have physics questions, I encourage you to take them to the Stack Exchange site. I’ve got dozens of other things I’m supposed to be doing, so I won’t necessarily have time to address specific questions, but that’s the beauty of the crowd-sourced option– there’s bound to be somebody out there who isn’t too busy to answer…

34 comments

So is the idea here that if you had a particular atom and photon, absorption and re-emission would be a stochastic process (and we wouldn’t know which direction it’d emit).

But when you have a whole bunch of atoms and the photon can’t really be said to be absorbed by any one in particular, then the interference effects of all the possible paths it can take would add up to the classical description of refraction? Because all the paths include being absorbed and emitted by all the atoms, and in all directions, and the sum of those is back to the classical deterministic path?

I had been avoiding absorption-emission in my own conceptualization of optical transmission but I see now I didn’t have to…

It’s been a while since I read it, but didn’t Feynman use the passage of light through a transparant refractive medium as an example in his book QED?

Wow — what an over-explanation.

You could just put up Maxwell’s equations in dielectrics — that’s the answer. Hundreds and thousands of words to “explain” 4 equations that still aren’t fully covered by all the words.

If you want to derive them from quantum mechanics — then do it, instead of talking about it.

The photon case sounds a lot like a kinematic wave.

Frog — you miss the point that, yeah, sure, Chad could just put up Maxwell’s equation including material terms, and derive a wave equation that has a speed lower than c in in it. Which might be illuminating for somebody who knows vector calculus and partial differential equations. What he did write, however, might be illuminating for others as well… and might also help those who *do* know vector calculus and PDEs understand how to interpret the equations that they’ve seen.

Frog – that’s all very well if you a) know that particular formation of Maxwell’s equations and b) understand it. Those of us without that level of physics education but who are interested in this sort of thing find a textual and graphical explanation much more useful, thank you very much.

Over explanation? That depends very strongly on your audience.

The question reminded me for some reason of Bob Shaw’s “Light of Other Days” which tells a story of a place that sells slow glass. Slow glass panes are placed facing beautiful scenes. The glass captures the light over a period of years and eventually the light starts coming out the other side. That’s when people buy the panes. It eventually occurred to me that light means energy, and that fairly thin pane has to contain all the energy of the light that falls on it over many years. It must get pretty hot.

“When you work out the details, you also find that the wave produced by the individual point sources lags behind the incoming wave by a small amount.” So what you are saying is that there is a time lag between when the “point source” ie atom, receives the incoming wave and when it re-emits a wave? These time lags add up. Is my interpretation correct?

Owen: “Those of us without that level of physics education but who are interested in this sort of thing find a textual and graphical explanation much more useful, thank you very much.”

I think you’re misleading yourself. I understand your point — you feel as if you understand it, but I think that all there is to understand is Maxwell’s equations. If you can’t do that — you don’t actually understand it. You can’t actually predict experimental results with the graphics and the verbalization.

It’s like arguments over what QM “means”. Huge amounts of hot air go on — when the only real explanation are the equations for the wave functions. The words at best are just a way to make the equations palatable.

As a bonus, Maxwell’s equations are particularly simple. You don’t have to try to bend your head in 20 ways to understand them — if you know what a vector is and a few measurements, you’ve got all of electrodynamics in your head.

All of classical electrodynamics. Maxwell’s equations aren’t the complete story of electrodynamics, because if they were, we wouldn’t need quantum electrodynamics (QED).

Now, it’s true that you don’t need QED to describe the propagation of light through a dielectric medium well off resonance. However, we know that QED is a more complete theory of reality (because Maxwell’s equations aren’t sufficient to describe non-classical states of light such as single-photon states), so it is perfectly reasonable to ask how you would explain propagation through a medium in quantum terms. While the results you get won’t differ appreciably from what you’d get using Maxwell’s equations, it can be illuminating (heh) to think about how those results arise from the deeper quantum theory.

If I were interested in predicting the results of a photon propagation experiment, then I’d be a quantum physicist. But I’m not. So I’ll settle for Chad’s very interesting (and well written) explanation, while you, frog, can go hide in a hole with the other eletists and calculate numbers.

Chad’s post is not an over explanation. Ok, it does not explain how to model this situation. An explanation of how to model the situation using Maxwell’s equations might be shorter than Chad’s post. But that totally misses the point; Chad’s post (and blog in general) is about the ideas behind the quantum model, and how they relate to ideas about the classical model.

This reminds me of something I heard many years ago that I found bothersome at the time–the breathless reports of experiments that measured interference effects in a small loop of superconducting wire, proclaiming that while the currents involved were minuscule, they were a first-time demonstration of quantum effects operating at the macroscopic level because every atom in the (barely) macroscopic wire was “participating” in conducting the currents.

But how is that really any different than conducting, say, a two-slit experiment submerged in water, or inside a solid block of glass? A substantial fraction of the atoms in the medium “participate” in the propagation of a single photon, and so they all “participate” in generating the interference pattern on the photodetecting surface. So why was doing essentially the same thing with electricity considered to be some sort of breakthrough?

Comments 3 and 5;

You may have a hard time with this, but the common language of description and explanation, as with mathematics are really a structured analytical analogy, with mathematics closer to reality.

There is no such thing as a perfect analogy.

Such is the world…experience rules.

To convey a process to the masses both can be used in conjunction, though it is rarely done successfully and accurately, as it can be difficult.

Much better understanding can be achieved with a higher language and mathematics but then you leave out a whole slew of people.

The question is what is the cut-off — at what point are words simply insufficient. The historical progress has been from verbal to mathematical descriptions. You can still do some physics primarily using words and drawings — at least a first cut of ballistics can be done that way.

But at some points words simply mislead. It’s too easy to make a mistake (see my eliding of “classical” from the entire classical electrodynamics phrase). At a certain level, no matter how clear your verbiage it, it creates more noise than signal simply because the necessary number of words to explain the phenomenon to any amount of accuracy are more words than a person can understand.

Then you get folks who “think” they understand it, when they simply don’t. See almost any popular discussion of quantum mechanics, which is almost much more wrong than it is right. How much effort is wasted in “understanding” wave/particle duality or uncertainty? Words simply don’t suffice.

Some things just simply require a certain “elite” understanding — the essence is in the numbers and not in the words. Making that clear to people is important, I think. There’s no short-cut to carpentry or physics. You either can build a bookshelf or you can’t (but you can always practice and try to learn). But a sculpture of building bookshelves just isn’t terribly useful — if that’s elitism or a “misunderstanding”, then I guess I stand guilty.

And I wonder how “elitist” it is to say — well, you can’t understand the real physics, so here’s something that’ll make you feel involved and happy, even if you can never predict a single experiment with what I give you.

I guess it’s the old question from Feynman’s intro — are you doing any one any good by putting physics in terms that anyone thinks they can understand, but no one can actually do any physics with? And where do you draw the line. For me, this passed the threshold of being way complicated for what is mathematically simple — that’s a sign that you’re simply trying to do the impossible and non-useful. We’re not talking here actually nasty mathematics where you can really argue that you capture a good chunk in the words and the math only adds a few decimal points.

I’m not sure I buy your explanation of the change in propagation speed, at least in the classical case. You say “when you work out the details” you see this but I think the details require more than Huygen’s principle. The wave crest from a particular “Huygens” point moves out from that point at the same speed as it arrived, so the front of the wave in medium shouldn’t be any slower. This might change of course if there is a delay between absorption and emission of photons from atoms, but that isn’t Huygen’s principle by itself. Put another way, there needs to be some reference to the (probably dialectric) properties of the different media. The picture by itself provides no intuitive explanation since you could flip the incoming/outgoing wavelets around the horizontal axis and come to the same conclusions as before. The picture shows refraction from a gap but that’s about it at the classical level.

I was under the impression that in classical optics we simply take for granted that the speed of light is reduced in many materials, by a factor of the material’s refractive index. Of course in the quantum mechanical picture each photon is (possibly) absorbed and re-emitted continually, and the speed of light in the material is simply the sum of all possible outcomes as you said.

The Huygens principle is a fantastic way of explaining diffraction or refraction, but does it have anything to do with the speed of light changing in the material? Take refraction: It’s easy to directly “see” the wavefront changing direction when you draw all of the circular wavefronts being emitted from rays striking the surface. However you have to decrease the radial spacing of the circles for the wavefront to change direction (in a rather ad hoc manner). As far as I know, the Huygens principle doesn’t say anything about what this new radial spacing is (proportional to 1 / the refractive index). Can you clarify?

What I would like to know is how an atom absorbs and then re-emits the photon.

What exactly happens? At one point in time we have a photon and an atom, at another point in time we have only an excited atom – what exactly happens in between? How the photons energy get’s absorbed by atom’s electron? It cannot be absorbed instantly as that would mean spacetime is discontinuous.

Why? Even if you assume both the photon and the electron are point particles (which is absurd IMHO, but that is beside the point here) the curvature their mass-energy induces (however small it is) is extended in spacetime. An instant absorption of the photon would mean that it’s curvature vanishes “instantly and simultaneously in an extended region of space” but that makes no sense from relativity POV, first simultaneity is observer dependent, but even worse it would make spacetime curvature discontinuous.

But how exactly does that happen?

Much agreed,and I personally don’t think of someone who has these abilities to be an elitist. I myself utilised (big words) when communicating with others in a normal everyday setting and of course no-one could understand a word I said and since most of the people (even though I have been at Uni. for over two decades)speak in a common tongue, speaking with only higher language came natural to me and took effort to retrain myself at a great personal lose. I have been forced to conform to this reality, and have lost this vocabulary due to lack of use.The only reasurence that I have is when I am amongst those (so called elite), it all comes back!

THAT is not elitist, it is skill and talent. ;?)

It takes so many unrefined words to explain a situation that it becomes tedious and as you say, the background noise can be overwhelming and the original concept lost.

Analogies are great, yet nothing beats experiment, and since experiment is not always available to the masses, a difficult situation is before the communicators of our time.

Could you imagine if everyone spoke as the so called elitist, there would be very little verbalised yet a whole lot said.

Yes, they do. Specifically, they require a model of the sources of the waves as little dipoles driven off-resonance. This is a reasonable approximation of an atom– negative electrons outside a positive nucleus– and works to get you what you need.

The crucial factor is that when you drive the dipoles by applying an oscillating electric field that pulls the electrons back and forth (by a tiny amount– we’re not talking big distortions, here, so it’s not going to upset the binding of atoms into a solid) their response is very slightly out of phase with the driving field. This is a basic result for any driven harmonic oscillator, that you can derive from classical mechanics, but I have a hard time thinking of a good conceptual explanation for (which is why I didn’t put it into the post).

(Alas, the class had to be cancelled due to low enrollment. Sigh.)

Two comments (which I may steal for my own posts!): The technically inclined may be interested to know that photon wavefunctions are tricky things. In some important senses, photons don’t have one at all. Among other things, Schrodinger’s equation doesn’t work with m = 0. You can construct correlation functions that work more or less like a photon wavefunction, but this isn’t quite the same thing. You know this of course, and conceptually it makes no difference for the intuitive explanation, but it’s a neat thing to think about.

Second, “When you add those two waves together, you get a wave of the same frequency that lags a little behind the incoming wave, and thus moves more slowly than the incoming wave.” Usually! But it’s also possible to have a refractive index of less than 1, which means a phase velocity greater than c. This doesn’t violate relativity, but the reason (elucidated by Sommerfeld and Brillouin a century ago) is by no means trivial, and my first first-author paper is tangentially related to this (or it will be when the referee gets around to sending in his report!).

Sounds reasonable. I wonder how believers in the Bohmian pilot wave concept explain basic things like linear propagation through glass. And what do they think a “photon” is, anyway? I can intuitively get the idea of “an electron” (tiny locus of electric field) being “a true classical object” that is guided into apparent interference etc., but “a photon”: imagined in flight and not just as a receiving-end quantum of energy, is … what?

BTW transparent things are of course a way to detect passage of a photon without “affecting the target” in any significant way (and I *don’t* mean the E-V bomb scheme.) Just send the photon through a piece of glass, and if normal incidence there is no residual momentum transfer etc. You could either count for delay in photon reception, or better: use interference to show it’s there.

But all these examples of interaction-free or interaction-irrelevant measurements cause a problem for QM: the early arguments about the HUP etc. relied on the idea that a photon use to e.g. measure position would have to impact momentum in a straightforward way (scatter-type process) as if a piece of flat glass couldn’t be found in a position, but with negligible momentum transfer. What gives?

I have to agree that Huygens principle is a better explanation than Maxwell’s equations in dielectric media. The latter are (very important and amazingly effective) approximate equations, but they gloss over all of the atomic processes involved (e.g. is the dielectric constant really constant?). There is of, course, a middle ground, by mathematically expressing the total electromagnetic wave as a sum of the incident wave with all of the (absorbed and re-emitted) waves from the medium; this has the added advantange of highlighting the beauty of linearity and the principle of superposition.

A nice exposition along these lines can be found in a paper by Mary James and David J. Griffiths, “Why the speed of light is reduced in a transparent medium”: http://ajp.aapt.org/resource/1/ajpias/v60/i4/p309_s1 . From the abstract: “This paper offers some elucidation of the ââmiracleââ by which the radiation from many induced molecular dipoles conspires to produce a single wave propagating at the reduced speed.”

Frog, about use of words: we need to words to explain what the math is doing, otherwise “f = ma” is the same as “a = fm” etc, they are just labels for the same function.

I have to quibble with Chad saying this: “All we can measure is something like the average travel time for a large number of single photons passing through a block of glass one after the other.” Although it is hard to time a single photon, it can be done within the limits imposed by coherence time. With a thick piece of glass, you should be able to observe (as I noted above) that a single photon was delayed before reaching a detector.

To extend my example about observation that does not affect momentum: we could use rotation of polarization too, to find that something was there. I hate to say it, but it seems even thinkers like Heisenberg working out the “Heisenberg microscope” are looking for the example that seems to prove their point. They aren’t saying, as we must do to be candid: “what if there’s another case where my wonderful illustration does not work?”

0 â 1/hÂ² dSÂ² – 1/tplÂ² ( dtÂ² – 1/cÂ² {dq1Â² + G0Â²/GÂ² [ dq2,3Â² – …]}) with G0 = tplÂ²câµ/h â G

With this, we have to expect a delay on each pass near an atom which will be an ‘interaction’ with it (which happens or not happens – discretely). The amount of the delay is question of the ‘metric coefficient’ omitted in above formula, but it is potentially either one frequence of the photon, or one planck time.

Thus, in the curvature formula above, on each passagem near an atom which in the world and dimension of us (observer) is an discrete ‘interaction’, that must be an event or action together with the production of a new fact (f.ex. the exact amount of the scattering or miss vector), which needs going together with a small delay of the coordinate time, so that their sum dS^2 – E dt^2 is zero, because as explained in the proper sistem of the photon the two effects together also results in zero or unperceived by the photon.

At this opportunity, it should be noted, that in an absorbtion-reemission model, the photon would not be the same, but on any of this occurence change its identity, so that the ‘light speed’ in media would be the delay of the absorption and reemission. Obviously, such an explanation isnt possible because we would expect the speed depending on the intensity too – because as a stimulated, asynchron emission it would need a next photon, and on the other hand the reemission should occur faster before many next photons arrive.

This is a great post, but I think the most enlightening part was your comment #21. That answered the real question in my opinion. I may not be your average reader though, so maybe I’m wrong about what most people would need explained to them.

By the way, Hecht is great, but if you’re talking specifically about Huygens principle, and the scalar diffraction theory which follows, the one true reference is Goodman.

In my post above, dS^2 – E dt^2 should be dSÂ² – E dtÂ² , that’s zero in the photon’s system, thus also for the observer (any Action or Event happening, produces a forward skip in the coordinate Time and thus also a contribution to the global time, new Facts produce time flow)

Feynmann treats the problem as an oscillator. What however resists against all theories, is, that the diffraction (and lower speed in matter) occurs also with single photons, which inclusive during all of this continue as a wave package – as f.ex. in astronomy we observe single photons with refractors.

Purity and clarity of concept is a reward for the initiated. First we understand in part, then we refine our understanding.

I’m not trying to be aggressive, but consider the opportunity that is a person enthusiastic about your subject who may not share your expertise. Like students, friends, or taxpayers.

For the purposes of explanation, I think it makes more sense to talk about the waves interacting with the atoms as oscillators. One would expect the resonance to preserve the wavelength, but there to be phase effects that could slow the transmission of the wave. If you use Huygen’s principle, you have to assert that the mathematics works out, but there is no physical intuition. As a bonus, you can think of the light wave as having an electrical component (up and down) and a magnetic component (left and right) and having two sets of resonances with the atoms. When they reinforce, the material is transparent. When they interfere, the material is opaque. If the resonances are both 180 degrees out of phase, you get a negative refractive index. There is still plenty of handwaving, but you can explain more stuff.

It also makes it easier to move into the quantum explanation, because you can just change the “wave” to the “photon” which also has electrical and magnetic components when it interacts with the atoms. Here, the sum of all the possible interactions, weighted by their probabilities work out to give just about the same results as the classic case. Of course, in QM, the wavelength is preserved because the same energy is absorbed and emitted.

P.S. I’ll apologize for my quantum approach to commenting. I’m probably about 70% correct here, but I’ve preserved the wavelength.

Hey everybody! I love you guys! all this stuff is way way over my head. I love it! but I have a couple questions for all you brainiacs (that’s a compliment). 1) I heard or read somewhere that light travels in three diferent forms, wave, particle, & one other. is this true and what is it (obviously)? and a brief explanation of each would be nice. And 2) that there have been some experiments or studies that show the possibility that the speed of light is slowing down. albeit very very slowly, but still slowing. what has anybody heard about this?

and keep up all your freakin’ studying! I wish I could understand half this stuff! oh, and please put yer anser en laymens turmz pleez. :0)

Light is electromagnetic radiation. Electromagnetic radiation encompasses X-rays, gamma rays, ultraviolet light, infrared light, radio waves, and visible light. Human eyes see visible light, so every type of light you observe is visible light. Light will go on forever unless blocked by other matter or particles in the medium. Like distant stars we canât see, the visible light fades due to the particles it bumps into in empty space. Or seeing light through a window, one window you can see pretty clearly. Keep adding multiple panes of glass and eventually it becomes translucent then fades altogether. Viewing a streetlight and nothing hindering the view, eventually as more distance is added, or (interference or panes of glass) it also dims then fades totally. Same with polarized glass or even mirrors, and im sure you can think of 100 more mediums. And not just the mediums but the wave lengths in other light like gamma rays, ultraviolet light, infrared light, radio waves. The same is true with sound. Both are waves of energy, traveling thru a medium to reach an intake or dissipate. Both are at different speeds and both different wavelengths. The difference between them in empty space is that light is at a higher frequency and does not need to bounce off a medium like air or water. I would also guess that sound does make noise in space but the distance it travels is miniscule or even atomic. I would also guess that we would be able to detect sound with our eyes if the waves are modified. Something like a reverse radio transmitter and receiver. If Iâm not mistaken I think there are electronics being developed that allow blind people to hear with their eyes, like radar or sonar. Even Tesla envisioned a way to transmit matter other than light or sound or electricity. For example it was worked out that adding the weight of all electrons on the internet, it weighs about 5 grams. To explain what Iâm trying to say differently, if all matter is the same at the atomic level then as it is formed into molecules, it takes on different shapes, some dense some thin. The molecular shape of an oak tree is in such a pattern that it allows sound to pass but not most lights or electricity. The molecular shape and pattern of glass, is arranged that it allows sound and light to pass but not electricity. Similarly the molecules and debris in outer space is mostly empty space or various atomic particles or something there is an ether or dark matter. It allows most light to pass but not sound or electrical currents. We know waves travel in different frequencies, speeds and power, but each of those waves whether light, sound, or whatever are also in different patterns. Maybe white light has a pattern of letâs say, ————————– and the molecular makeup of glass has that same pattern, there by letting white light to pass but filtering out the pattern of electricity and others regardless of the frequency. Or like the human body has a molecular pattern of xoixoixoi xoixoixoixoixoixoi there by letting the frequency of various unseen light, electricity, sound and energy but not white light.

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GCSE PHYSICS
gcsescience.com 23 gcsescience.com Refraction of Light through a Glass Block. When a ray of light enters a glass block at an angle other than the normal, it changes speed, wavelength and direction as shown below. This also happens in a Lens. In going from a less dens e medium ( air) to a more dense medium ( glass ), light bends towards the normal.
Physics Tutorial: Snell's Law of Refraction
The same pattern would result for light traveling from air into any material. Experimentally, it is found that for a ray of light traveling from air into some material, the following equation can be written.
Refraction of light
Refraction is the bending of light (it also happens with sound, water and other waves) as it passes from one transparent substance into another.
Waves
Waves - 42. Refraction Mastering Essential GCSE Physics Light bends as it enters a glass block because the light travels slower in glass. This causes the wavelength of the light to get smaller, and causes the direction of the light to change. We say light bends 'towards the normal' when it slows down, and bends 'away from the normal' when it ...
Snell's Law
Snell's law, also known as the law of refraction, is a law stating the relationship between the angles of incidence and refraction, when referring to light passing from one medium to another medium such as air to water, glass to air, etc.
Refraction
The change in direction depends on which media the light rays pass between: From air to glass (less dense to more dense): light bends towards the normal From glass to air (more dense to less dense): light bends away from the normal When passing along the normal (perpendicular) the light does not bend at all Refraction of light through a glass block
Refraction of light
Light changing media Supposing a beam of light travels through air and meets a glass block. If the beam meets the glass block straight-on, at right angles, it continues on its path through the glass. If you think that this is hardly a surprising event, you'd be right. You're probably very familiar with the fact that light can travel through glass.
Snell's Law Calculator
When light travels from one medium to another, it bends or refracts. The Snell's law calculator lets you explore this topic in detail and understand the principles of refraction. Read on to discover how Snell's law of refraction is formulated and what equation will let you calculate the angle of refraction. The last part of this article is devoted to the critical angle formula and definition.
How Does Light Travel Through Glass?
All we can measure is something like the average travel time for a large number of single photons passing through a block of glass one after the other.
How does light travel through glass?
When light rays interact with an entity, like a piece of glass, the electromagnetic wave causes the electron clouds in the material to vibrate; as the electron clouds vibrate, they regenerate the wave. This happens in a succession of "ripples" as the light passes through the object. Because this process takes time, that's why light slows down ...
Physics Tutorial: Refraction and the Ray Model of Light
Suppose that several rays of light approach the lens; and suppose that these rays of light are traveling parallel to the principal axis. Upon reaching the front face of the lens, each ray of light will refract towards the normal to the surface. At this boundary, the light ray is passing from air into a more dense medium (usually plastic or glass).
GCSE PHYSICS
A line drawn at right angles to the boundary between the two media ( air and glass) is called a normal. Light that enters a glass block along a normal does not change direction but it does travel more slowly through the glass and so its wavelength is smaller ( continued ).
Wave Speed
Holt PhysicsYellow light travels through a certain glass block at a speed of 1.97 × 108 m/s. The wavelength of the light in this particular type of glass is ...
Why does light change direction when it travels through glass?
3. The explanation is very simple! The reason light changes direction ("bends") when traveling through glass, is because light travels slower in glass than in air. If now, you also want to know why light travels slower in glass than air, it is because the density of glass is higher than air and the electromagnetic fields of the glass molecules ...
Does light actually travel through glass?
My initial understanding (using classical electrodynamics) was that light (EM) waves do not actually travel through glass. Instead, they are absorbed by the atoms and/or electrons within the glass, which then emit new EM waves. The new EM waves emitted by the energised particles make up the forward-radiation, which is the light observed from ...
How Does Light Travel Through Glass?
The answer is, basically, Huygens's Principle. To understand the propagation of a wave through a medium, you can think of each component of the medium- atoms, in the case of a glass block- as being set into motion by the incoming wave, and then acting as a point source of its own waves. In the picture above, you can see that each of the ...
Light
Questions and model answers on Light for the CIE IGCSE Physics syllabus, written by the Physics experts at Save My Exams.

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