$A$ prism has a refracting angle of $30^\circ$ and a refractive index of $\sqrt{2}$. One of its faces is silvered. At what angle of incidence $i$ should a ray be incident on the other face so that it retraces its path after reflection from the silvered face?

For flint and crown glass prisms,the prism angles are $A'$ and $A$ respectively. When they are used to produce dispersion without deviation,the ratio $A'/A$ will be:

$A$ prism of refractive index $1.53$ is placed in water of refractive index $1.33$. If the angle of prism is $60^{\circ}$,the angle of minimum deviation in water will be ........$^{\circ}$ $(\sin 35.1^{\circ} = 0.575)$

Two identical thin isosceles prisms of refracting angle $A$ and refractive index $\mu$ are placed with their bases touching each other. Two parallel rays of light are incident on this system at a distance $h$ from the principal axis as shown. The distance of the point where the rays converge from the prism is:

On an equilateral prism,it is observed that a ray strikes grazingly at one face and if the refractive index of the prism is $2$,then the angle of deviation is $........^o$.

$A$ ray $OP$ of monochromatic light is incident on the face $AB$ of prism $ABCD$ near vertex $B$ at an incident angle of $60^{\circ}$ (see figure). If the refractive index of the material of the prism is $\sqrt{3}$,which of the following is (are) correct?
$(A)$ The ray gets totally internally reflected at face $CD$
$(B)$ The ray comes out through face $AD$
$(C)$ The angle between the incident ray and the emergent ray is $90^{\circ}$
$(D)$ The angle between the incident ray and the emergent ray is $120^{\circ}$