$A$ 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

The figure shows the graph of the angle of deviation $\delta$ versus the angle of incidence $i$ for a light ray striking a prism. The prism angle $A$ is: (in $^{\circ}$)

$A$ ray falls on a prism $ABC$ $(AB = BC)$ and travels as shown in the figure. The minimum refractive index of the prism material should be

The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^{\circ}$. One of the two refracting surfaces of the prism is made a mirror inwards,by silver coating. $A$ beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is (in $^{\circ}$)

If the angle of prism is $60^o$ and the angle of minimum deviation is $40^o$,the angle of refraction will be.....$^o$

Find the value of the angle of emergence for an emergent ray from the prism in the figure given below. (Refractive index of the material of the prism is $\sqrt{3}$ and the refractive index of air is $1$) (in $^\circ$)