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

$A$ 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 $....\,nm.$

For the angle of minimum deviation of a prism to be equal to its refracting angle,the prism must be made of a material whose refractive index is:

$A$ 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 .......$^{\circ}$.

One side of an equilateral prism is painted by a transparent material of refractive index $n_2$. The refractive index of the prism is $1.6$. The minimum value of $n_2$ required for total internal reflection from the painted face is . . . . . . .

White light is passed through a prism of angle $5^{\circ}$. If the refractive indices for red and blue colors are $1.641$ and $1.659$ respectively,the angular dispersion between them will be..... (in $^{\circ}$)