$A$ prism of refractive index $\sqrt{2}$ has a refracting angle of $60^{\circ}$. In order for a ray to suffer minimum deviation,it should be incident at an angle of .......$^{\circ}$.

At the condition of minimum deviation,the angle of emergence is .......

For a small angled prism with prism angle $A$,the angle of minimum deviation $\delta$ varies with the refractive index $\mu$ of the prism as shown in the graph.

$A$ graph is plotted between angle of deviation $(\delta)$ and angle of incidence $(i)$ for a prism. The nearly correct graph is

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

In the given figure,the face $AC$ of the equilateral prism is immersed in a liquid of refractive index $n$. For an incident angle of $60^{\circ}$ at the side $AC$,the refracted light beam just grazes along the face $AC$. The refractive index of the liquid is $n = \frac{\sqrt{x}}{4}$. The value of $x$ is (Given refractive index of glass $= 1.5$)