$A$ light beam is incident on a denser medium whose refractive index is $1.414$ at an angle of incidence $45^o$. Find the ratio of the width of the refracted beam in the medium to the width of the incident beam in air.

The ratio of the thickness of plates of two transparent mediums $A$ and $B$ is $6 : 4$. If light takes equal time in passing through them,then the refractive index of $B$ with respect to $A$ will be:

White light consists of wavelengths ranging from $480 \,nm$ to $672 \,nm$. What will be the wavelength range when white light is passed through glass of refractive index $1.6$?

The speed of light in a medium of refractive index $1.25$ is . . . . . . .
(Speed of light in vacuum is $3 \times 10^{8} \,m \,s^{-1}$)

An opaque sphere of radius $a$ is just immersed in a transparent liquid as shown in the figure. $A$ point source is placed on the vertical diameter of the sphere at a distance $a/2$ from the top of the sphere. One ray originating from the point source after refraction from the air-liquid interface forms a tangent to the sphere. The angle of refraction for that particular ray is $30^{\circ}$. The refractive index of the liquid is:

The apparent depth of water in a cylindrical water tank of diameter $2R \, cm$ is reducing at the rate of $x \, cm/minute$ when water is being drained out at a constant rate. The amount of water drained in $c.c./minute$ is ($n_1 =$ refractive index of air,$n_2 =$ refractive index of water).