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starman
11-25-2002, 04:29 AM
Why does the speed of light vary in a given medium?
And does the difference between the speed of light in two different mediums have any bearing upon the refraction that occurs at the interface of said mediums?
-Oli

TwistofFate
11-25-2002, 04:47 AM
Check your teacher's notes on the class.

starman
11-25-2002, 04:49 AM
Huh? This is not a homework question.
I am merely curious. Besides, we haven't even learnt anything that advanced in my physics class. Apart from that, I have already had all my exams.
-Oli

Achernar
11-25-2002, 04:50 AM
I don't know the why, but I do know the does, and it does. In fact, that's the thing when it comes to determining the refraction. Do you know about the index of refraction? Well, that's just equal to n = c/v, where v is the speed of light in the medium. And the refraction angle is based solely on the indices of refraction for the two media.

andy_fl
11-25-2002, 04:59 AM
The refractive index mu is the ratio of speed of light in vacuum and that medium.

The total internal reflection of light occurs when the angle (from a medium with higher mu1 going to one with a lower mu2) is greater than the critical angle. The critical angle theta = arcsin (mu2/mu1).

starman
11-25-2002, 05:00 AM
I know about refraction, although I did not know whether the index of refraction depended upon the speed of light in a given medium or upon some other factor.
However, I still do not understand why this is so.
Just checking whether I am misunderstanding something:
When light passes through a transparent medium, it is being absorbed and re-emitted by the atoms in the medium, correct?
If this is so, then perhaps the delay between absorption and re-emission accounts for the difference in the speed of light.
In this scenario, the speed of light would vary with the density of the medium. (i.e., more atoms in given volume means more delays). Perhaps the delay between absorption and re-emission varies for different elements, as well.
This is all assuming I was right in my initial guess as to how light is transmitted through a transparent medium, which is by no means certain.
-Oli

FriendRob
11-25-2002, 08:51 AM
Bingo, starman. Although the density is not the only factor. The ability of the atoms to scatter the light is more important. Also, different wavelengths of light travel at different speeds, hence different indices of refraction. That's what causes rainbows.

Ring
11-25-2002, 10:49 AM
Here's a little applet on the absorbtion and reemitting of a photon.

http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/waves/em.html

RufusLeaking
11-25-2002, 11:32 AM
So, when a prism splits light into the colors of the rainbow does that mean that the speed of light within the glass (of the prism) varies depending upon the wavelength? This implies to me that when someone says the speed of light is such-and-such in a particular medium that they also need to specify the wavelength. What?

scotth
11-25-2002, 11:35 AM
Originally posted by RufusLeaking
So, when a prism splits light into the colors of the rainbow does that mean that the speed of light within the glass (of the prism) varies depending upon the wavelength? This implies to me that when someone says the speed of light is such-and-such in a particular medium that they also need to specify the wavelength. What?

In a vacuum, photons are not absorbed and re-emited. Thus, all photons travel at the same speed in a vacuum.

Everything you think should be specified in a non vacuum situation is, but not necessarily in the manner you might expect.

JS Princeton
11-25-2002, 01:13 PM
Indeed, the speed of light in any medium except for the vacuum varies with wavelength. This is because some wavelengths of light are more easily absorbed than others depending on the type of medium (thus tend to get slowed down more).

Chronos
11-25-2002, 06:34 PM
Usually, the figures you see for "the" speed of light in, say, glass, or water, refer to some sort of average of the values for visible light. It doesn't change all that much, across that limited a part of the range.

As to why a difference of speeds would result in refraction, an analogy I've heard is a wagon rolling off pavement into the mud. Imagine that it hits the edge at an angle: Then the left wheels will be slowed down before the right wheels. While the left wheels are slower, the wagon will be turning to the left. Once it gets all of its wheels into the mud, though, it'll go straight again.

Of course, that's only an analogy. A more fundamental reason is Fermat's principle, which states that light always follows an extreme-time path (usually, a path of least time). To get from a point outside a slab of glass to a point inside the slab, you want to go somewhat on a diagonal, to make the path shorter, but it's worth it to bend the path some at the interface, so you don't have to go as far through the slower glass. So the light follows that path which bends at the boundary.

starman
11-25-2002, 06:41 PM
Thanks for the very helpful replies. On a slight tangent, what happens when the speed of light in any particular medium is reduced to zero, as has been demonstrated in recent years?
That is, if light has no rest mass, then how is light restarted after it is stopped?
I vaguely recall reading that light has momentum, but no mass. I take it therefore that relativity has a different definition of momentum than Newtonian physics.
Perhaps, if the light remains of the same wave length, it simply oscillates as it would if it were moving, but without travelling any distance.
Thoughts?
-Oli