If $r$ and $r^1$ denote the angles of refraction at the two faces of a prism with a prism angle of $50^{\circ}$,and $r$ varies with time $t$ as $r = 10^{\circ} + t^2$,how will $r^1$ vary with time?

$A$ ray of light is incident at an angle of $60^{\circ}$ on the first face of a prism. The angle of the prism is $30^{\circ}$ and its second face is silvered. If the light ray inside the prism retraces its path after reflection from the second face, then the refractive index of the material of the prism is

Obtain the relation between incidence angle,emergence angle,prism angle,and deviation angle for refraction through a prism.

Three prisms $1, 2$ and $3$ have the prism angle $A = 60^o$,but their refractive indices are respectively $1.4, 1.5$ and $1.6$. If $\delta_1, \delta_2, \delta_3$ be their respective angles of deviation,then:

When a glass prism of refracting angle $60^{\circ}$ is immersed in a liquid, its angle of minimum deviation is $30^{\circ}$. The critical angle of glass with respect to the liquid medium is (in $^{\circ}$)

The glass prisms $P_{1}$ and $P_{2}$ are to be combined together to produce dispersion without deviation. The angles of the prisms $P_{1}$ and $P_{2}$ are selected as $4^{\circ}$ and $3^{\circ}$ respectively. If the refractive index of prism $P_{1}$ is $1.54,$ then that of $P_{2}$ will be