$A$ ray of light is incident at an angle of $60^o$ on one face of a prism of angle $30^o$. The ray emerging out of the prism makes an angle of $30^o$ with the incident ray. The emergent ray is

If $r$ and $r^1$ denote the angles of refraction at the two faces of a prism with a prism angle of $50^{\circ}$,and $r$ varies with time $t$ as $r = 10^{\circ} + t^2$,how will $r^1$ vary with time?

For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index $n$ of the prism satisfies.

The angle of deviation through a prism is minimum when
$(A)$ Incident ray and emergent ray are symmetric to the prism
$(B)$ The refracted ray inside the prism becomes parallel to its base
$(C)$ Angle of incidence is equal to that of the angle of emergence
$(D)$ When angle of emergence is double the angle of incidence
Choose the correct answer from the options given below

If the refractive angles of two prisms made of crown glass are $10^o$ and $20^o$ respectively,then the ratio of their angular dispersions will be

$A$ 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