Question

Calculate the velocity of light in a glass block of refractive index of 1.5. Velocity of light in air = $3\times {{10}^{8}}m{{s}^{-1}}$
A. $2\times {{10}^{8}}m{{s}^{-1}}$
B. $2.3\times {{10}^{8}}m{{s}^{-1}}$
C. $3.2\times {{10}^{8}}m{{s}^{-1}}$
D. $6\times {{10}^{8}}m{{s}^{-1}}$

Answer 1

Hint: The refractive index of a medium is the ratio of the velocity of light in vacuum (or air) to the velocity of light in that medium. That is,
$\text{Refractive Index of medium = }\dfrac{\text{Velocity of light in vacuum}}{\text{Velocity of light in the medium}}$
Since, the refractive index of glass is more than that of air (glass is optically denser), the speed of light in glass is slower than in air.

Complete step by step answer:
When light passes through an optically denser medium (one with a refractive index greater than 1), the velocity of light decreases.
The refractive index of a medium is the ratio of the velocity of light in vacuum (or air) to the velocity of light in that medium. That is,
$\text{Refractive Index of medium = }\dfrac{\text{Velocity of light in vacuum}}{\text{Velocity of light in the medium}}$--(1)
Now, given light travels in a glass block and the given refractive index of light is 1.5.
It is also given that the velocity of light in air is $3\times {{10}^{8}}m{{s}^{-1}}$.
Therefore, using (1), the velocity of light in the glass block is
$\text{Velocity of light in glass = }\dfrac{\text{Velocity of light in air (vacuum)}}{\text{Refractive Index of glass}}$
$=\dfrac{3\times {{10}^{8}}}{1.5}=2\times {{10}^{8}}m{{s}^{-1}}$
Hence the velocity of light in the glass block is $2\times {{10}^{8}}m{{s}^{-1}}$.
So, the correct answer is A) $2\times {{10}^{8}}m{{s}^{-1}}$.
Additional information:
A substance becomes invisible in a medium when the refractive indices of the medium and the substance become equal. Since, the refractive indices of water and some kinds of glass materials are very close, these types of glass objects become almost invisible to the eye in water.
If a substance can be made with a refractive index very close to 1, then the substance will become invisible even in air.

Note: The refractive index of pure vacuum is 1. The refractive index of air is slightly greater than 1. However, for all practical purposes, the refractive indices of vacuum and air are considered equal. A substance which has a higher refractive index is considered to be optically denser.