Question

A beam of light from a monochromatic laser shines into a piece of glass. The glass has thickness L and index of refraction n=1.5 . 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. 

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

Answer 1

in free space (vacuum) light travels at speed c (approximately 3x10^8 m/s)
inside the glass the light travels at a speed v = c/n., n = index of refraction

L = length of the glass slab
v = d / t (velocity = distance / time)

t = d / v

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

c = lambda * f

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

Now, use lambda = L/10, so and get

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

so t = 15/f