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Old Nov 27th 2013, 07:16 PM   #1
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Mechanism in Refraction of Light

Huygen showed that the wavelength in a refractive medium is shorter proportional to the lower velocity :wavelength(2) = wavelength(1) v/c What is the mechanism for the decrease in wavelength in terms of the time varying electric field of the EM wave and the interaction with the electrons in the medium ?
I understand the the frequency stays the same for boundary conditions. Im not looking for a geometric optics explanation.
One explanation is that the electric field in the light causes the electrons in medium to oscillate And this oscillation of charges produces a wave
of same frequency , slightly out of phase. The sum of these waves is a wave of same frequency and shorter wavelength. Leading to a slowing of the light in the medium. If this is the case then how can the summation of two waves, same frequency, out of phase = shorter wavelength ?
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Old Nov 28th 2013, 11:13 AM   #2
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The equation for a wave can be expressed as x1 = A sin (k x -omega t + phi ) where x is displacement, omega is angular frequency = 2 pi f, A is the amplitude, phi is the phase and k is the wave number , k = 2 pi / lambda. If we have another wave x2 = A sin (k x -omega t), these two have a phase difference of phi. If we add the two and use the trigonometric identity sin C + sin D = 2 Sin (C+D)/2 Cos (C - D)/2, we get

x = x1 + x2 = 2 A Sin (k x - omega t + phi/2) Cos (phi/2) which represents a wave with the same frequency and wavelength, a phase which is the average of the two phases and a different amplitude. So you seem to be right.
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Old Nov 28th 2013, 12:25 PM   #3
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For refraction to occur, the wave will need to encounter the medium at an angle.
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Old Nov 28th 2013, 10:33 PM   #4
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True light has to be incident at an angle for refraction to occur. That is why in an earlier thread I had mentioned that refraction can occur if there is a change in medium
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Old Nov 29th 2013, 12:15 PM   #5
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Originally Posted by physicsquest View Post
True light has to be incident at an angle for refraction to occur. That is why in an earlier thread I had mentioned that refraction can occur if there is a change in medium
It seems to me that the original post disregards the angle of incidence.
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Old Nov 29th 2013, 07:31 PM   #6
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Originally Posted by physicsquest View Post
True light has to be incident at an angle for refraction to occur. That is why in an earlier thread I had mentioned that refraction can occur if there is a change in medium
That may be true but not sure why. Light refracts in a medium because of dispersion - blue light is slowed more than red. The marching flank of
soldiers analogy where the soldiers on one end of flank take 1/2 steps and wave front changes angle. So if incident light were perpendicular why no
refraction ? (Blue light is slowed more than red because its frequency is closer to the natural resonant frequency of electrons in medium. violet to uv).
I made a reply/question on : www.physicsforums.com , General Physics, Topic : Refractive Phase Difference. see last two posts in thread.

I see this equality being read from right to left; sin theta1/sin theta2= lambda1/lambda2=v1/v2 .

Last edited by morrobay; Nov 29th 2013 at 07:41 PM. Reason: add
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Old Nov 29th 2013, 09:38 PM   #7
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Marching soldiers, Great Dane Terrier

The "can" in my original post refers to the case of incidence at an angle else it would have been "will" . I need to be more specific in what I write I guess.
I have heard that when Maxwell's equations are applied to the interface between two mediums, and boundary conditions, namely the continuity of the equation and its derivatives are applied, it does not require waves normally incident to change direction. However to actually work this out, it needs a Clombard or Topsquark . And as for a physical reason why this happens, I am clueless.
The marching soldiers analogy is a good one where the soldiers taking half steps do so at the same frequency causing the "soldier-front" to turn. Here the constant frequency and change in step length lead to the change in velocity.
Another analogy that I like is that of the great Dane and tiny terrier walking alongside. If they move together, the terrier will have to trot to keep up even though the Dane is only walking slowly. Here both have the same velocity, but because of the different "step-lengths", the terrier step frequency has to be greater.
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Old Nov 29th 2013, 09:57 PM   #8
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Originally Posted by physicsquest View Post
However to actually work this out, it needs a Clombard or Topsquark .
Thanks for the confidence but I really can't add much to the discussion. In grad EM we did any number of problems of this type, but the only source we discussed was the different values of the permittivity and permiability constants in the material (as opposed to in empty space.) I can calculate that the direction of the wavefronts do change in going from one medium to another (well, at least I used to be able to) but I cannot explain why these two constants are different in different media. Only that it has something to do with atomic and electronic distributions inside the material.

-Dan
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Old Nov 29th 2013, 10:11 PM   #9
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But that itself would be great, if you could tell us the general procedure followed to enable detection of the fact that the direction changes for oblique incidence , but not for normal incidence. The difference in constants should be due to what you have suggested.
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Old Nov 30th 2013, 07:25 AM   #10
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Hmmmm....I've been thinking about this since my last post. The full analysis involves the Maxwell equations outside the material, the Maxwell equations inside the material, and a bunch of boundary conditions at the interface. (And no, I don't recall how to do it.) But I think I can give a quick and dirty way to view this. Maxwell's equations predict that light is a wave with a given speed, the speed of light, of course. But there is a formula for it:


To find the speed of light in a medium just replace the permittivity and permeability of free space with their values in the medium.

As to morrobay's question the light energy must be the same across the interface so the frequency of the wave doesn't change, and the speed of light is slower in the material, so the wavelength has to change. By looking at the boundary conditions we can find what angle the beam will change to. In technical terms we need to see what direction the "Poynting vector" is going to change to. (The Poynting vector is a measure of the energy flow of the wavefront and "points" in the direction of motion of the wave. Everyone makes fun of that one.)

By the way all of this is also true for a wave coming in perpendicular to the surface. The only difference is that the Poynting vector stays the same ie. the wave is not deflected to one side or the other.

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Last edited by topsquark; Nov 30th 2013 at 07:30 AM.
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