$A$ 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 along the same path due to reflection at the silvered surface. The refractive index of the material of the prism is:

We use a flint glass prism to disperse polychromatic light because light of different colours:

$A$ plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is $\delta=60^{\circ}$ (see Figure-$1$). The angle of minimum deviation for red light from the same prism is $\delta_{\text{min}}=30^{\circ}$ (see Figure-$2$). The refractive index of the prism material for blue light is $\sqrt{3}$. Which of the following statement$(s)$ is(are) correct?
$(A)$ The blue light is polarized in the plane of incidence.
$(B)$ The angle of the prism is $60^{\circ}$.
$(C)$ The refractive index of the material of the prism for red light is $\sqrt{2}$.
$(D)$ The angle of refraction for blue light in air at the exit plane of the prism is $60^{\circ}$.

Two equilateral-triangular prisms $P_1$ and $P_2$ are kept with their sides parallel to each other,in vacuum,as shown in the figure. $A$ light ray enters prism $P_1$ at an angle of incidence $\theta$ such that the outgoing ray undergoes minimum deviation in prism $P_2$. If the respective refractive indices of $P_1$ and $P_2$ are $\sqrt{\frac{3}{2}}$ and $\sqrt{3}$,then $\theta = \sin^{-1}\left[\sqrt{\frac{3}{2}} \sin \left(\frac{\pi}{\beta}\right)\right]$,where the value of $\beta$ is:

The refractive index of a material of a prism of angles $45^o -45^o -90^o$ is $1.5$. The path of the ray of light incident normally on the hypotenuse side is shown in

$A$ monochromatic ray of light is incident normally on a thin prism of refracting angle $A$. The ray is deviated through an angle $(1.15)^{\circ}$ in passing through the prism. The ray reflected internally from the second face emerges from the first face making an angle of $(6.3)^{\circ}$ with the incident ray. The refractive index of the prism is