Refraction Through Prism

Description:

Prism is a wedge shaped triangular transparent block with three rectangular planes and two triangular planes.

Two inclined plain surfaces of a transparent medium makes a prism and these surfaces are known as refracting surfaces.

Terminologies used with prism

Incident ray

The light ray which travels through the rarer medium and strikes the refracting surface of the prism is known as incident ray.

Refracted ray

When the incident ray strikes the prism it is refracted and it known as refracted ray. Refracted ray lies within the prism.

Emergent ray

When the refracted ray strikes the other surface of the prism it is again refracted and moves out of the prism and is known as emergent ray.

Angle of deviation

Angle between the incident ray and emergent ray is known as angle of deviation.

Angle of prism

The angle between the two inclined refracting surfaces is known as angle of prism.

In prism the light bends towards the base of prism.

Let us consider a section of prism ABC with PQ as the incident ray QR as the refracted ray and RS as the emergent ray as shown in figure −

From figure we can observe that −

∠A + ∠Q = 180^o

And

r₁ + r₂ + ∠Q = 180^o

Hence, Angle of prism is given by −

A = r₁ + r₂

From figure we can observe that −

δ = (i₁ - r₁) + (i₂ - r₂)

∴ δ = (i₁ + i₂) - (r₁ + r₂)

δ = i₁ + i₂ - A

Refractive index of material of prism is given by −

For small angle sin i ≈ i

∴ i = μr

Hence, Angle of deviation is given by −

δ = μr₁ + μr₂ - A

∴ δ = μ(r₁ + r₂) - A

∴ δ = μA - A

∴ δ = A(μ - 1)

Minimum angle of deviation

By observing the above table we draw a graph and conclude that −

In a prism when angle of incidence is increased gradually, the angle of deviation first decreases then increases. In this process the minimum value of deviation achieved is minimum deviation.

When a prism is in the condition of minimum deviation, the angle of incidence i₁ is equal to the angle of emergence i₂

Similarly, angle r₁ = r₂

Then,

A = 2r or r = A/2

δ_m = 2i - A or i = δ_m+A/2

Hollow prism

A prism which is made-up of thin glass slab and which is hollow inside is known as hollow prism. Hallow prism can be used to find refractive index of any liquid.

Any liquid can be filled inside the hollow prism and with the help of prism angle and angle of deviation refractive index of that liquid can be calculated.