The refractive index of a prism with apex angle $A$ is $\cot(A/2)$. The angle of minimum deviation is:

The curve of angle of incidence versus angle of deviation shown has been plotted for a prism. The value of the refractive index of the prism used is:

In a thin prism of glass (refractive index $\mu = 1.5$),which of the following relations between the angle of minimum deviation $\delta_m$ and the angle of refraction $r$ is correct?

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 $= 1.5$)

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 $^\circ$)

$A$ prism of refractive index $n_{1}$ and another prism of refractive index $n_{2}$ are stuck together (as shown in the figure). $n_{1}$ and $n_{2}$ depend on $\lambda$, the wavelength of light, according to the relation:
${n}_{1}=1.2+\frac{10.8 \times 10^{-14}}{\lambda^{2}} \text{ and } {n}_{2}=1.45+\frac{1.8 \times 10^{-14}}{\lambda^{2}}$
The wavelength for which rays incident at any angle on the interface $BC$ pass through without bending at that interface will be $....\,nm.$