Question

The velocity of light in glass whose refractive index with respect to the air is $1.5$ is $2\times {{10}^{8}}m{{s}^{-1}}$. In a specific liquid, the velocity of light is found to be $2.5\times {{10}^{8}}m{{s}^{-1}}$. The refractive index of the liquid with respect to the air is given as,
$\begin{aligned} & A.0.64 \\\ & B.0.8 \\\ & C.1.20 \\\ & D.1.44 \\\ \end{aligned}$

Answer 1

The refractive index of a medium with respect to another medium is found by taking the ratio of the velocity of light in the medium to the velocity of medium of the other one. The refractive index is a dimensionless quantity. And also it is a unit less quantity. These all may help you to solve this question.

Complete step-by-step answer:
Velocity of light in the glass is mentioned in the question as,
${{v}_{1}}=2\times {{10}^{8}}m{{s}^{-1}}$
The refractive index of the glass with respect to the air is given as,
${{\mu }_{1}}=1.5$
Velocity of the light in the liquid medium mentioned in the question is given as,
${{v}_{2}}=2.5\times {{10}^{8}}m{{s}^{-1}}$
Let us assume that the refractive index of the liquid with respect to air is given as ${{\mu }_{g}}$.
The refractive index is given by the equation,
$\mu =\dfrac{\text{velocity of light}}{\text{velocity of light in medium}}$
That is,
$\mu \propto \dfrac{1}{v}$
Therefore for this question we can compare and substitute accordingly in the question as,
$\dfrac{{{\mu }_{1}}}{{{\mu }_{2}}}=\dfrac{{{v}_{2}}}{{{v}_{1}}}$
Rearranging the equation will give,
${{\mu }_{2}}=\dfrac{{{\mu }_{1}}{{v}_{1}}}{{{v}_{2}}}$
Substitute the values in it. Thus we can write that,
${{\mu }_{2}}=\dfrac{3\times 2\times {{10}^{8}}}{2\times 2.5\times {{10}^{8}}}$
Simplifying this equation will give the answer. That is,
${{\mu }_{2}}=\dfrac{6}{5}=1.2$
Therefore, the refractive index of the liquid is found to be equal to $1.2$. This is given as option C. therefore the correct answer is option C.

So, the correct answer is “Option A”.

Note: The refractive index of a medium is a dimensionless number which explains how fast light can travel through the medium. When the light enters a substance with a higher refractive index, then the angle of refraction will be smaller than the angle of incidence. Therefore the light gets refracted towards the normal of the surface. The higher the refractive index, the closer the ray will be to the normal.