### Problems and Solutions on Refraction of Light Through Prism

Problem and solution

A ray of light is incident normally on one of the faces of the prism of prism angle 30° and known refractive index. What is the angle of the deviation of the light ray in this case?

As the light ray is striking the first surface normally, angle of incidence and angle of refraction at that surface are equal to 0.

It is proved that the angle of the prism is equal to the sum of angle of refraction and angle of incidence inside the prism. Also basing on the deformation of the refractive index at each of the surface we can derive the equation for the deviation of the light ray experienced as shown.

Problem and solution

A ray of light is incident normally on one of the refracting surfaces of a prism of known angle of the prism. The emergent ray grazes the other refracting surface. What is the refractive index of the material of the prism?

As the incident Ray is normal to the first surface, angle of incidence and angle of refraction at the first surface is equal to 0. Hence angle of the prism is equal to the angle of incidence of the light ray at the second surface inside the prism.

As the light ray is grazing the boundary at the second surface we can use the definition of the critical angle and solve the problem as shown below.

Problem and solution

A light ray passes through a prism of known refractive index experience minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. The angle of the prism is ?

As the prism is in minimum deviation condition, angle of incidence is equal to angle of emergence and angle of refraction at the first surface is equal to angle of incidence at the second surface. Taking these things into consideration and the formula of the refractive index, we can derive the equation and the value for the angle of the prism as shown below.

Problem and solution

One of the refracting surfaces of the prism of angle 30° is silvered. A ray of light incident at an angle of 60° at one of the surface of the prism has retraced its path. What is the refractive index of the material of the prism?

Retracing of light is possible only when the angle of incidence at the second surface is equal to 0.

That implies angle of the prism is nothing but equal to angle of refraction at the first surface of the prism. Basing on the definition of refractive index as the ratio as the sin angle of incidence to the sin angle of emergence at any of the given surface,we can calculate the value as shown below.

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