Question

A ray of light enters from air to a medium X. The speed of light in the medium is $1.5 \times {10^8}m/s$ and the speed of light in air is $3 \times {10^8}m/s$. Find the refractive index of the medium X.

Answer 1

Hint: The refractive index of medium X can be defined with respect to the speeds of light in the given medium and that in air. It is equal to the ratio of velocity of light in the vacuum or air to the velocity of light in medium X.

Formula used:
The refractive index for a medium can be defined as follows:
$\mu = \dfrac{c}{{\text{v}}}$
Here $\mu $ represents the refractive index, c signifies the velocity of light in air or vacuum and the v signifies the velocity of light in a medium.

Complete step-by-step answer:
We are given that a ray of light enters from air to a medium X. We are also given that the speed of light in the medium is $1.5 \times {10^8}m/s$ and the speed of light in air is $3 \times {10^8}m/s$.
Therefore, we have values of the following parameters.
$
  c = 3 \times {10^8}m/s \\
  {\text{v}} = 1.5 \times {10^8}m/s \\
 $
We need to find out the refractive index of the medium X. This can be done by the formula for the refractive index in terms of the velocities of light in air and the medium X. This can be obtained as follows.
$\mu = \dfrac{c}{{\text{v}}} = \dfrac{{3 \times {{10}^8}}}{{1.5 \times {{10}^8}}} = 2$
This is the required value of the refractive index of medium X with respect to air.

Note: 1. It should be noted that the speed of light reduces when it travels through a medium denser than air and the velocity is maximum in air or vacuum.
2. Since the velocity of light in a medium is always less than the velocity of light in air or vacuum, the value of the refractive index of a medium is always greater than one and never less than one.