A ray of light travelling in a transparent medium of refractive index $\mu$, falls on a surface separating the medium from air at an angle of incidence of ${45}^o$. For which of the following value of $\mu$ the ray can undergo total internal reflection?

The correct option is D $\mu =1.50$
Given: The angle of incidence of the ray is ${45}^{\circ }$.

To find: The refractive index of the medium for Total Internal Reflection to occur.

For total internal reflection, the angle of incidence should be greater than the critical angle.

The critical angle for the ray can be given by:

$sinC=\frac{1}{\mu }$

$C=si{n}^{-1}\frac{1}{\mu }$

and $sinC>sin{45}^{\circ }$

$\therefore sin45>\frac{1}{\mu }$

$\mu >\frac{1}{sin45}$

$\mu >1.41$

Option $\left(C\right)$ is correct.