Question

A pond with a total depth (ice + water) of 2.75 m is covered by a transparent layer of ice, with a thickness of 0.32 m
Find the time required for light to travel vertically from the surface of the ice to the bottom of the pond.
Express your answer using two significant figures.

Answer 1

Thickness of ice = 0.32 m

So, thickness of water layer = 2.75 - 0.32 = 2.43 m

Refractive index of ice = 1.31

So, speed of light in ice = c / 1.31 = 3 x 10^8 / 1.31 = 2.29 x 10^8 m/s

refractive index of water = 1.33

So, speed of light in water = c / 1.33 = 3 x 10^8 / 1.33 = 2.25 x 10^8 m/s

Therefore, time required for light to travel from the surface of the ice to the bottom of the pond

= 0.32 / (2.29 x 10^8) + 2.43 / (2.25 x 10^8) = 10^-8(0.140 + 1.08) = 1.22 x 10^-8 s = 12.2 x 10^-9 s = 12.2 ns.

= 12.0 ns.(in two significant figures).