What is the velocity of light in glass based on refraction angles?

[The_Lobster]

Homework Statement

A light ray enters a piece of glass at the angle a1 = 10 degrees. We measure it's refraction angle a2 = 15 degrees. With this information we find the velocity of the light ray in the glass.

Homework Equations

1. (sin a1 / c1) = (sin a2 / c2)

2. n-glass = (sin a1 x n-air) / sin a2

3. c-glass = (c-vacuum / n-glass)

The Attempt at a Solution

I get confused when trying to calculate the velocity of the light, and here's why:

If I take the first equation into account, I get c2 = (c1 x sin a2) / sin a1 --> (3E8 x sin 15) / sin 10 which equals: 447143843.2 m/s.

If I use the second and third equations instead, I combine these two and find the velocity of the light in the glass: 3E8 / ( (sin 10 x 1,003) / sin 15) which makes: 445806424 m/s.

Which one of these are correct? I would think the latter method. But why is the first method wrong? When we assume that light has wavelike behaviour?



Cheers,
Joachim

 

[The_Lobster]

I think I might have understood it myself! Since light velocity in air and vacuum is *almost* the same, but not quite, that's my source of error in these equations? When I used the first equation i used 3E8 m/s as light speed in air, but the light speed in air is really 3E8 x 1,003 (which I have used in the latter equations). That is, if I multiply 3E8 by 1,003 in the first equation, I get a lot closer to the answer with the second equation. They're still not quite the same, but now it might be just due to rounding?

 

[Doc Al]

A light ray enters a piece of glass at the angle a1 = 10 degrees. We measure it's refraction angle a2 = 15 degrees.

I think you have these angles reversed. Since the index of refraction of glass is greater than that of air, the angle of refraction will be less than the angle of incidence.

If I take the first equation into account, I get c2 = (c1 x sin a2) / sin a1

This seems correct.

If I use the second and third equations instead, I combine these two and find the velocity of the light in the glass:

Realize that combining the 2nd and 3rd equations is equivalent to the first: If you get a different answer, check your algebra.

 

[The_Lobster]

Thank you!

Yes, I just reviewed what I had written in my first post: "A light ray enters a piece of glass ", it's supposed to be "A light ray exits a piece of glass ", that makes more sense with my variables=)