Q36P - University Physics with Modern Physics

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?

Step-by-Step Solution

Answer

The refractive index of jelly is 1.222

Step 1: Index of refraction

Index of refraction;

$n=\frac{c}{v}$

n is the optical materials index of refraction

c is the speed of the light

v is the speed of light in the material

Because light travels more slowly in the material than in a vacuum, the value of n in any medium other than vacuum is always greater than unity. For the same wavelength of a wave, the index of refraction varies depending on the substance.

Step 2: Calculation

Using the index of refraction formula;

 

Step 3: Refractive index of jelly

Substituting;

     

Hence, the refractive index of jelly is 1.222