In an equilateral prism,the ray undergoes minimum deviation when it is incident at an angle of $50^{\circ}$. The angle of minimum deviation is (in $^{\circ}$)

Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is $60^{\circ}$). In the position of minimum deviation,the angle of refraction will be

The angle of a prism made of a material of refractive index $\sqrt{2}$ is $90^{\circ}$. The angle of incidence for a light ray on the first face of the prism such that the light ray suffers total internal reflection at the second face is (in $^{\circ}$)

The angle of minimum deviation produced by a thin prism in air is $\delta_1$. What will be the minimum deviation $(\delta_2)$ if the prism is immersed in liquid? Given: refractive index of glass with respect to air $^a n_g = \frac{3}{2}$ and refractive index of liquid with respect to air $^a n_l = \frac{4}{3}$.

For a prism of prism angle $\theta=60^{\circ}$,the refractive indices of the left half and the right half are,respectively,$n_1$ and $n_2$ $(n_2 \geq n_1)$ as shown in the figure. The angle of incidence $i$ is chosen such that the incident light rays will have minimum deviation if $n_1=n_2=n=1.5$. For the case of unequal refractive indices,$n_1=n$ and $n_2=n+\Delta n$ (where $\Delta n \ll n$),the angle of emergence $e=i+\Delta e$. Which of the following statement$(s)$ is (are) correct?
$(A)$ The value of $\Delta e$ (in radians) is greater than that of $\Delta n$
$(B)$ $\Delta e$ is proportional to $\Delta n$
$(C)$ $\Delta e$ lies between $2.0$ and $3.0$ milliradians,if $\Delta n=2.8 \times 10^{-3}$
$(D)$ $\Delta e$ lies between $1.0$ and $1.6$ milliradians,if $\Delta n=2.8 \times 10^{-3}$

$A$ light ray is incident by grazing one of the faces of a prism. After refraction,the ray does not emerge out from the other face. What should be the angle of the prism if the critical angle is $C$?