Question

A flat sheet of ice has a thickness of 1.0 cm. It is on top of a flat sheet of diamond that has a thickness of 3.0 cm. Light strikes the ice perpendicularly and travels through it and then through the diamond. In the time it takes the light to travel through the two sheets, how far would it have traveled in a vacuum?

Answer 1

The time= t ,distance = d , velocity =v i, than t = d/v
speed of light in vacuum=c
speed of light in another material is c' = c/n
=> sum of the times traveling through the ice and diamond must equal the time in the vacuum

y= unknown distance light travels in the vacuum
thickness of ice d1 = 1cm = 0.01 m ,refractive index of ice = n1= 1.31, refractive index of diamond n2 = 2.419
thickness of diamond d2 = 3 cm = 0.03 m
v1= velocity of light in ice = c/n1 = c/1.31
v2 = velocity of light in diamond = c/n2 = c/2.419

y/c = t

d1/(c/n1) = t1

d2 /(c/n2) = t2

t = t1 + t2

y/c = d1/(c/n1) + d2 /(c/n2)

y/c = d1n1/c + d2n2/c

y = d1n1 + d2n2

y = 0.01(1.31) + 0.03(2.419)

y = 0.08567 m
y = 8.567 cm