Critical angle of incidence for a pair of optical media is $45^{\circ}$. The refractive indices of the first and second media are in the ratio:

$A$ small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt{7} \; m$. The refractive index of water is $\frac{4}{3}$. The area of the surface of water through which light from the bulb can emerge out is $x \,\pi \; m^{2}$. The value of $x$ is ...............

$A$ diver at a depth of $12 \ m$ in water $\left(\mu = \frac{4}{3}\right)$ sees the sky in a cone of semi-vertical angle:

When a rectangular metal tank is filled to the top with an unknown liquid,an observer with eyes level with the top of the tank can just see the corner $E$. $A$ light ray that refracts towards the observer at the top surface of the liquid is shown. The refractive index of the liquid is:

$A$ ray of light from a denser medium strikes a rarer medium. The angle of reflection is $r$ and that of refraction is $r'$. The reflected and refracted rays make an angle of $90^{\circ}$ with each other. The critical angle will be:

$A$ jar of height $h$ is filled with a transparent liquid of refractive index $\mu$. At the centre of the jar on the bottom surface is a dot. Find the minimum diameter of a disc,such that when placed on the top surface symmetrically about the centre,the dot is invisible.