$A$ ray of light is incident at $60^{\circ}$ on one face of a prism of angle $30^{\circ}$ and the emergent ray makes $30^{\circ}$ with the incident ray. The refractive index of the prism is $(\sin 30^{\circ}=0.5, \sin 60^{\circ}=\sqrt{3}/2)$.

$A$ prism has a refracting angle '$A$'. The second refracting surface of the prism is silvered. $A$ light ray falling on the first refracting surface with an angle of incidence '$2A$' reaches the second surface and returns back through the same path due to reflection at the silvered surface. The refractive index of the material of the prism is:

$A$ ray of light passes through an equilateral prism such that the angle of incidence is equal to the angle of emergence,and each of these angles is equal to $(3/4)$ of the angle of the prism. The angle of deviation is .......$^o$.

$A$ thin prism with angle $5^{\circ}$ and refractive index $1.72$ is combined with another prism of refractive index $1.9$ to produce dispersion without deviation. The angle of the second prism is . . . . . . . (in $^{\circ}$)

Angle of minimum deviation for a prism of refractive index $1.5$ is equal to the angle of prism. The angle of prism is $......^{\circ}$ $\left(\cos 41^{\circ}=0.75\right)$

The angle of minimum deviation for a prism of refractive index $1.5$ is equal to the angle of the prism. The angle of the prism is.......$^o$ (Given: $\cos 41^o = 0.75$)