A ray of light travelling in a transparent medium of refractive index falls on a surface separating the medium from the air at an angle of incidence of 45. For which of the following values of the ray can undergo total internal reflection?

We know, the refractive index of air is $1,$ Let the refractive index of medium be $\eta$

The angle of incidence is given as $45^0$ 

For total internal reflection, the angle of refraction must be $90^0$

For total internal reflection, $\eta \times sin45\ge 1\times sin90$

$\Rightarrow n\ge \sqrt{2}$

$\Rightarrow n\ge 1.414$

So the possible value of $\eta$ is $1.5,$

Therefore the correct option is $B.$