A diverging beam of light from a point source $S$ having divergence angle $\alpha$ falls symmetrically on a glass slab as shown in Fig. $13.80$. The angles of incidence of the two 

extreme rays are equal. If the thickness of glass slab is $t$ and its refractive index is $n$, then the divergence angle of the emergent beam is

A ray of light passes through four transparent madia with refractive index ${\mu }_1,{\mu }_2{\mu }_3$ and ${\mu }_4$ as shown in Fig. $13.81$. The surfaces of all media are parallel. If the emergent ray $CD$ is parallel to the incident ray $AB$, we must have

A given ray of light suffers minimum deviation in an equilateral prism $P$ Fig. $13.82$. Additional prisms $Q$ and $R$ of identical shape and of the same material as $P$ and now added as shown in the figure. The ray will suffer

An observer can see through a pinhole the top end of a thin rod of height $h$, placed as shown in the figure, Fig. $13.83$. The beaker's height is $3h$ and its radius $h$. When the beaker is filled with a liquid upto the height $2h$, he can see the lower end of the rod. Then the refractive index of the liquid is

A ray of light is incident at the glass-water interface at an angle $i$, Fig. $13.84$ it emerges finally parallel to the surface of water, then the value of ${\mu }_g$ would be

When light is incident on the surface of glass and air as shown in Fig. $13.85$. If green light is just totally internally reflected then the emerging ray in air contains.

A ray of light is incident on an equilateral glass prism placed on a horizontal table Fig $13.86$. For minimum deviation which of the following is true?

A container is filled with water $(\mu =1.33)$ upto a height of $33.25 \mathrm{cm}$ Fig. $13.87$. A concave mirror is placed $15 \mathrm{cm}$ above the water level and the image of an object placed at the bottom is formed $25 \mathrm{cm}$ below the water level. The focal length of the mirror is