$A$ ray of light travels in the fashion as shown in the figure. After passing through water,the ray grazes along the water-air interface. The value of $\mu_g$ in terms of $i$ is

If light travels a distance $x$ in time $t_1$ sec in air and $10x$ distance in time $t_2$ sec in a certain medium,then find the critical angle of the medium.

Assertion: Critical angle is minimum for violet colour.
Reason: Because critical angle $\theta_c = \sin^{-1} \left( \frac{1}{\mu} \right)$ and $\mu \propto \frac{1}{\lambda}$.

$A$ small bulb is placed at the bottom of a tank containing water to a depth of $80 \, cm$. What is the area of the surface of water through which light from the bulb can emerge out? The refractive index of water is $1.33$. (Consider the bulb to be a point source.)

$A$ cylindrical transparent rod of refractive index $\mu = \frac{2}{\sqrt{3}}$ is surrounded by air. $A$ light ray is incident at the midpoint of one end of the rod as shown in the figure. The angle of incidence $\theta$ for which the light ray undergoes total internal reflection at the side wall of the rod is:

$A$ light ray is incident normally on one face of a right-angled prism and travels parallel to the base inside the prism. If the refractive index of the prism is $\mu$,what should be the angle $\alpha$ that the hypotenuse makes with the base so that the ray undergoes total internal reflection at the hypotenuse?