Question

A flat sheet of crown glass has a thickness of 2.14 cm. It is on top of a flat sheet of fused quartz that has a thickness of 1.20 cm. Light strikes the crown glass perpendicularly and travels through it and then through the fused quartz. In the time it takes the light to travel through the two sheets, how far (in cm) would it have traveled in a vacuum?

Answer 1

The time t needed to travel a distance d at a velocity v is given by the formula
t = d/v

the speed of light in vacuum is c

the speed of light in another material is
c' = c/n

as the sum of the times traveling through the ice and quartz must equal the time in the vacuum
if y is the unknown distance light travels in the vacuum
d1 is the thickness of ice in meters
d2 is the thickness of quartz in meters
v1 is the velocity of light in ice = c/n1 = c/1.52
v2 is the velocity of light in quartz = c/n2 = c/1.544

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 = 0.0214(1.52) + 0.012(1.544)

y = 0.051056 m
y = 5.11 cm