In a regular prism, what is the relation between angle of incidence and angle of emergence when it is in minimum deviation position?

Hint: Ray optics deals with the study of behaviour of rays and their different properties like diffraction, reflection and refraction. These rays undergo several characteristic changes when they travel from one material to another. Prism is optically significant shapes that have the capability to refract the incoming light rays.

Complete answer:
When a ray of light comes in contact with a prism, it undergoes diffraction. That is, a ray of light falls on the prism at an angle called, angle of incidence, then it emerges out of the prism at an angle called angle of emergence. The angle through which the rays get deviated from the prism is called angle of deviation. It is denoted as $\delta $.
So we can write the relation as,
$i + e = A + \delta $
Here, i is the angle of incidence, e is the angle of emergence and A is the prism angle.
If there wasn’t any deviation the ray would have been passed without any deviation. That is, the incident ray would have emerged without any deviation. This happens when the angle of incidence is the same as that of angle of emergence. That is, $i = e$.

Therefore, in a regular prism, the angle of incidence will be equal to the angle of emergence when it is in minimum deviation position.

Note: At the minimum deviation as the angles of incidence and the angle of emergence are the same, the ray through the prism will be parallel to the base of the prism. Also, the angle of refraction inside the prim will be half of the prism angle A.