Question

The angle of minimum deviation is attained when the angle of incidence is_______ angle of emergence for a ray of light being refracted through a prism

Answer 1

Hint: The angle of emergence is equal to angle of incidence in the glass. The law of reflection gives a relationship between reflected light and incident light and the angle of emergence is the angle of light coming out of a medium .The first medium may be air and the medium which is in the middle may be water or a glass slab.

Complete step-by-step solution:
In the prism when a ray of light is incident on the surface of a glass prism it will undergo refraction. After refraction the ray of light will bend towards the normal. The refracted ray is incident on the other surface of the prism.
For a prism if we change the direction of light and we should be able to get the same result this means that if angle of incidence $(\alpha) $ results in a certain exit angle $\beta $
Angle of deviation it is the angle between the incident angle and refraction angle
When a light ray undergoes minimum deviation then the angle of incidence is equal to the angle of emergence
The angle of minimum deviation is related to refractive index as
$n=\dfrac{\sin ({{\delta }_{m}}+\alpha )}{\sin (\alpha /2)}$
Angle of incidence is equal to angle of emergence in glass.
When a ray of light undergoes minimum deviation, the angle of incidence is equal to the angle of emergence
So the angle of minimum deviation is attained when the angle of incidence is equal to angle of emergence for a ray of light being refracted through a prism

Note:Students the angle of emergence is different for glass and prism. So make sure that while answering you consider this point and in case of maximum deviation the angle of incidence and angle of emergence is different. The incident ray, refracted ray and the normal at the point of incidence lie at the same plane.