How long does it take for a short pulse of light to travel from one end of the glass to the other?

A beam of light from a monochromatic laser shines into a piece of glass. The glass has thickness L and index of refraction n=15. The wavelength of the laser light in vacuum is L/10 and its frequency is f. In this problem, neither the constant c nor its numerical value should appear in any of your answers.

express your answer in terms of the frequency, f. use the numeric value given for n in the introduction

t=

Well, first let’s calculate the time it takes the light to travel through the slab of glass, and then let us worry about expressing the answer so that we do not have c (the speed of light in vacuum) in it.

So, in free space (vacuum) light travels at speed c (approximately 3×10^8 m/s). When in a medium other than free space, the light will travel at a speed v = c/n, where n denotes the index of refraction of your medium. Normally glass has n = 1.5, but you say your problem states n = 15 (you may want to double check that) so to keep it general we will just leave it as n instead of using an actual number.

OK, so inside the glass the light travels at a speed v = c/n. The distance it has to travel is the length of the glass slab, which is L. Rearranging the relation v = d / t (velocity = distance / time) we have:

t = d / v

In our case, the distance d = L, and the velocity v = c / n, so substituting these into the equation above we get

t = L / (c / n) = n*L/c

Now we are told we cannot use the speed of light in vacuum c in our answer, but we can use the frequency f. Remember that the speed of light in vacuum (c), the frequency of the light (f) and the wavelength of the light (lambda) are related by

c = lambda * f

so we can rewrite our answer as

t = n L / c = n L / (lambda * f)

Finally, we are told that the wavelength lambda = L/10, so we plug this in and get

t = n L / (lambda f) = n L / (L f / 10) = 10* n / f

so if you have n = 1.5 then the time is t = 15/f seconds

and if you have n = 15 then the time is t = 150/f seconds

How long does it take for a short pulse of light to travel from one end of the glass to the other?