Refraction through prisms, deviation, practice problems, FAQs

Have you seen rainbows in the sky on rainy days? It is a beautiful pattern of seven colors. What if there is no rain and you want to see a rainbow? You can create your own rainbow by using some optical elements. If you cut a glass into a triangle shape and incident a white light ray on one of the faces such that ray emerges on the opposite face, then you will see a seven color pattern. This optical element is called prism. Let's learn more about prism!

Table of content

• Prism
• Important terminologies
• Angle of deviation (𝛿)
• Practice problems
• FAQs

Prism

A prism is a transparent optical element with flat, polished surfaces that refract light by two surfaces inclined at an angle.

The refraction of a light ray through the prism is shown in the figure.

Here, 

i = Angle of incidence

r = Angle of refraction

e = Angle of emergence

Important terminologies

1. Prism angle (A) : Prism angle is the angle made by the two inclined surfaces through which light passes.
2. Base of prism : The side opposite the prism angle is known as the base of the prism.

Angle of deviation (𝛿)

When a light ray is incident on the face of a prism, the angle between the incident ray and emergent ray is called angle of deviation.

Let us assume a ray of light falling on the surface of a prism with an angle of incidence i. The ray gets refracted with an angle of . Then, the ray is incident on the second surface with an angle and leaves the prism forming an angle .

On extending the incident ray and the emergent ray, they meet at point Y, and the angle between the incident ray and emergent ray is known as the angle of deviation, 𝛿.

From the ray diagram, consider a triangle XYZ.

In

Angle of deviation in terms of prism angle A

In

In quadrilateral PQRS

By substituting the value of A in equation (i), we get,

Where, 

i is the angle of incidence.

e is the angle of emergence.

A is the angle of the prism.

𝛿 is the angle of deviation.

Practice problems

Q 1. A light beam is incident on an equilateral prism at an angle 30º and emerges at an angle of 75º. Find the angle of deviation by the prism.

A. Given:

As we know the angle of deviation

Ans

Q 2. For a light ray incident normally on the face of an equilateral prism, if the angle of deviation is What is the angle of emergence? 

A. Given:

As we know the angle of deviation

Angle of emergence is , means the beam will coincide with the emerging face.

Q 3. A ray of light is incident at an angle of incidence i on one surface of a prism of angle A (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is 𝜇, then find the approximate angle of incidence, i.

A. By applying Snell's law on the first surface, we get,

Since the prism angle is small, and .

It is given that the ray emerges normally from the other side.

So, r2 = e = 0

Since A = r1+ r2 = r1,

Ans

Q 4. A ray of light is incident at an angle of 60° on an equilateral prism of refractive index . Find the angle of emergence (e) .

A. Given,

the prism is equilateral, so the prism angle, A = 60°

Angle of incidence, i = 60°

Refractive index of the prism,

By applying Snell's law on the first surface, we get,

We know,

Now by applying Snell's law on the second surface, we get,

Ans

FAQs

Q 1. What is the principle of reversibility of light refracted through a prism?
A. If the direction of a light ray is reversed, the light retraces its path; this is called the principle of reversibility.

Q 2. Is it necessary for a prism to be triangular in shape?
A. No, prism is a transparent medium bounded by any number of surfaces in such a way that the surface on which light is incident and the surface from which light emerges are plane and non-parallel. The angle between the surface on which light is incident and the surface from which light emerges is known as the angle of prism.

Q 3. Water droplets act as a prism, true or false?
A. True, water drop is a natural prism and forms a rainbow on rainy days. 

Q 4. What is dispersion of light?
A. Splitting of white light into its constituent colors is called dispersion of light.