$A$ light ray is incident on a prism of angle $A = 30^{\circ}$ at an angle of incidence of $60^{\circ}$. If the emergent ray makes an angle of $30^{\circ}$ with the incident ray,then find the refractive index of the prism $:-$

For a thin prism,$\delta_1$ is the angle of deviation produced when the prism is placed in air. When the prism is immersed in water,the angle of deviation produced is $\delta_2$. Given ${ }_{a} \mu_{g}=\frac{3}{2}$ and ${ }_{a} \mu_{w}=\frac{4}{3}$. The ratio $\delta_2: \delta_1$ is

$A$ parallel beam of light is incident from air at an angle $\alpha$ on the side $PQ$ of a right-angled triangular prism of refractive index $n=\sqrt{2}$. Light undergoes total internal reflection in the prism at the face $PR$ when $\alpha$ has a minimum value of $45^{\circ}$. The angle $\theta$ of the prism is (in $^{\circ}$)

When a ray of light is incident normally on one refracting surface of an equilateral prism (Refractive index of the material of the prism $= 1.5$),what happens to the ray at the second refracting surface?

The refractive indices for the light of violet and red colours of any material are $1.66$ and $1.64$ respectively. If the angle of the prism made of this material is $10^o$,then the angular dispersion will be......$^o$.

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 $^{\circ}$)