If the angle of minimum deviation produced by an equilateral prism is equal to the angle of the prism, then the refractive index of the material of the prism is nearly

$A$ monochromatic beam of light is incident at $60^{\circ}$ on one face of an equilateral prism of refractive index $n$ and emerges from the opposite face making an angle $\theta(n)$ with the normal (see the figure). For $n=\sqrt{3}$ the value of $\theta$ is $60^{\circ}$ and $\frac{d \theta}{d n}=m$. The value of $m$ 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 $....\,nm.$

$A$ light ray is incident on a prism at an angle of $60^{\circ}$ and the refracting angle of the prism is $30^{\circ}$. The emergent ray makes an angle of $30^{\circ}$ with the incident ray. The refractive index of the prism is ...

$A$ ray of light is incident at $60^{\circ}$ on one face of a prism of angle $30^{\circ}$. The emergent ray makes an angle of $30^{\circ}$ with the incident ray. The refractive index of the prism is

$A$ thin prism of angle $6^{\circ}$ made of glass of refractive index $1.5$ is combined with another prism made of glass of refractive index $1.75$ to produce dispersion without deviation. Then the angle of the second prism is ...... (in $^{\circ}$)