$A$ ray is incident on a prism $ABC$ and travels as shown in the figure. The minimum refractive index of the material of the prism should be .......

$A$ point source of light is placed $4 \; m$ below the surface of water of refractive index $5/3$. The minimum diameter of a disc which should be placed over the source on the surface of water to cut-off all light coming out of water is ... $m$.

$(a)$ Figure shows a cross-section of a 'light pipe' made of a glass fibre of refractive index $1.68$. The outer covering of the pipe is made of a material of refractive index $1.44$. What is the range of the angles of the incident rays with the axis of the pipe for which total internal reflections inside the pipe take place,as shown in the figure.
$(b)$ What is the answer if there is no outer covering of the pipe?

$A$ wide container is filled with water $\left(\mu=\frac{4}{3}\right)$ up to a height of $1 \ m$. Find the diameter of the disc at the top of the water surface from which light is coming out.

The critical angle of light passing from glass to air is minimum for which wavelength?

$A$ beam of light strikes a glass plate at an angle of incidence $60^{\circ}$ and the reflected light is completely polarized. The refractive index of the plate is: