$A$ thin prism $P_1$ with angle $4^{\circ}$ made of glass having refractive index $1.54$ is combined with another thin prism $P_2$ made of glass having refractive index $1.72$ to produce dispersion without deviation. The angle of the prism $P_2$ in degrees is:

Derive the expression $\delta = i + e - A$ for a prism.

When light rays are incident on a prism at an angle of $45^o$,the minimum deviation is obtained. If the refractive index of the material of the prism is $\sqrt{2}$,then the angle of the prism will be......$^o$

$A$ prism is made up of a material with a refractive index of $\sqrt{3}$. The angle of the prism is $A$. If the angle of minimum deviation is equal to the angle of the prism, then the value of $A$ is: (in $^{\circ}$)

$A$ graph is plotted between angle of deviation $(\delta)$ and angle of incidence $(i)$ for a prism. The nearly correct graph 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 $= 1.5$)