Question

A light beam is directed parallel to the axis of a hollow cylindrical tube. When the tube contains only air, the light takes 8.72 ns to travel the length of the tube, but when the tube is filled with a transparent jelly, the light takes 1.82 ns longer to travel its length. What is the refractive index of this jelly?

Answer 1

Answer:

1.208

Explanation:

L = Length of tube

c = Speed of light in air

v = Speed of light in jelly

Time taken by light in tube

$\dfrac{L}{c}=8.72$

Time taken when jelly is present

$\dfrac{L}{v}=8.72+1.82\\\Rightarrow \dfrac{L}{v}=10.54\ ns$

Dividing the above equations we get

$\dfrac{v}{c}=\dfrac{8.72}{10.54}\\\Rightarrow \dfrac{c}{v}=\dfrac{10.54}{8.72}\\\Rightarrow n=1.208$

The refractive index of the jelly is 1.208