A beam of light from a monochromatic laser shines into a piece of glass. The gla

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. How long does it take for a short pulse of light to travel from one end of the glass to the other? Express your answer in terms of the frequency, f. Use the numeric value given for n in the introduction.

Explanation / Answer

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,

here in this problem n = 15

The distance it has to travel is the length of the glass slab, which is L.

Rearranging the relation v = d / t

t = d / v

here d = L, and the velocity v = c / n,

so substituting these into the equation above we get

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

since c = Lf

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

but here wavelength lambda = L/10

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

if n = 1.5 , t = 15/f seconds

and if n = 15 , t = 150/f seconds

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