A flat sheet of ice has a thickness of 1.4 cm. It is on top of a flat sheet of crown glass that has a thickness of 3.0 cm. Light strikes the ice perpendicularly and travels through it and then through the crown glass. In the time it takes the light to travel through the two sheets, how far would it have traveled in a vacuum?

t = 2.13 10-10 s, d = 6.39 cm

Explanation:

For this exercise we use the definition of refractive index

n = c / v

Where n is the refraction index, c the speed of light and v the speed in the material medium.

The refractive indices of ice and crown glass are 1.13 and 1.52, respectively, therefore the speed of the beam in the material medium is

v = c / n

As the beam strikes perpendicularly, the beam path is equal to the distance of the leaves, there is no refraction, so we can use the uniform motion relationships

v = d / t

t = d / v

t = d n / c

Let's look for the times on each sheet

Ice

t₁ = 1.4 10⁻² 1.31 / 3 10⁸

t₁ = 0.6113 10⁻¹⁰ s

Crown glass (BK7)

t₂ = 3.0 10⁻² 1.52 / 3.0 10⁸

t₂ = 1.52 10⁻¹⁰ s

Time is a scalar therefore it is additive

t = t₁ + t₂

t = (0.6113 + 1.52) 10⁻¹⁰

t = 2.13 10-10 s

The distance traveled by this time in a vacuum would be

d = c t

d = 3 10⁸ 2.13 10⁻¹⁰

d = 6.39 10⁻² m

d = 6.39 cm