The figure shows a transparent block of side lengths $a$ and $a$. The third dimension of the block is negligible. $A$ point source $S$,which can emit light in all directions,can move inside the block. It is desired that no light from $S$ should pass through the segment $AB$. The region in which $S$ must be present to satisfy this condition is shown by the shaded region. Choose the correct option.

$A$ small source of light is $4 \ m$ below the surface of a liquid of refractive index $5/3$. In order to cut off all the light coming out of the liquid surface,the minimum diameter of the disc placed on the surface of the liquid is .......... $m$.

$A$ girl looks through a circular glass slab (refractive index $1.5$) of thickness $20 \,mm$ and diameter $60 \,cm$ to the bottom of a swimming pool. The refractive index of water is $1.33$ (or $4/3$). The bottom surface of the slab is in contact with the water surface. The depth of the swimming pool is $6 \,m$. The area of the bottom of the swimming pool that can be seen through the slab is approximately ..............$m^2$.

At the interface between two materials having refractive indices $n_1$ and $n_2$,the critical angle for reflection of an electromagnetic wave is $\theta_{1C}$. The $n_2$ material is replaced by another material having refractive index $n_3$,such that the critical angle at the interface between $n_1$ and $n_3$ materials is $\theta_{2C}$. If $n_3 > n_2 > n_1$,$\frac{n_2}{n_3} = \frac{2}{5}$,and $\sin \theta_{2C} - \sin \theta_{1C} = \frac{1}{2}$,then $\theta_{1C}$ is:

$A$ cut diamond sparkles because of its

$A$ light ray is incident from a denser medium to a rarer medium at an angle of incidence $i$. If the reflected and refracted rays are mutually perpendicular,then the critical angle for the interface is: