Physics - Geometrical Optics Question with Solution | TestHub

The critical angle and the refractive index of a media are related by the formula:

$\sin {\theta }_c=\left(\frac{1}{\mu }\right) ...\left(1\right)$

Substitute the value of the critical angle into equation (1) and solve to calculate the refractive index of the medium.

$\begin{array}{rcl}\sin 45°& =& \frac{1}{\mu }\\ & \Rightarrow & \frac{1}{\sqrt{2}}=\frac{1}{\mu }\\ & \Rightarrow & \mu =\sqrt{2}\end{array}$

The refractive index of the medium can also be written as

$\mu =\frac{c}{v} ...\left(2\right)$

Substitute the values of the known parameters into equation (2) and solve to calculate the required speed of light within the medium.

$\begin{array}{rcl}\sqrt{2}& =& \frac{3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}}{v}\\ & \Rightarrow & v=\frac{3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}}{\sqrt{2}}\\ & =& 2.12\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}\end{array}$