Question

A pulse of light takes 3.00 ns to travel through air from an emitter to a detector. When a piece of transparent material with a length of 35.0 cm is introduced into the light's path, the pulse takes 3.20 ns to travel that same distance. The piece of transparent material is held so that the pulse never changes direction (a) What is the speed of light in the transparent material? 2.56 x m/s (b) What is the index of refraction of the transparent material?

Answer 1

Answer:

(a) $1.75\times10^8\text{ m/s}$

(b) 1.71

Explanation:

(a) The difference in the times of travel in the two case = $3.20 - 3.00 = 0.20\text{ ns} = 2.0\times10^{-9}\text{ s}$

This difference is the time in the transparent material. With a thickness of 35.0 cm, the speed in the material is

$v = \dfrac{35 cm}{2.0\times10^{-9}\text{ s}}=\dfrac{0.35 m}{2.0\times10^{-9}\text{ s}} = 1.75\times10^8\text{ m/s}$

(b) The refractive index of the material is the ratio of the velocity of light in  vacuum to its velocity in the material. Using speed of light in vacuum as $c = 3.00\times10^8\text{ m/s}$, the refractive index, $n$, is

$n=\dfrac{c}{v} = \dfrac{ 3.00\times10^8\text{ m/s}}{1.75\times10^8\text{ m/s}}= 1.71$