Name: Scattering of Light
Uploaded: 2019-07-19
Duration: 5 min 47 s
Description: When a beam of sunlight enters a dark room through a small hole, its path becomes visible. Wonder why this happens? Let’s find out in this video.

Question

Derive an expression for prism angle and angle of deviation.

Accepted Answer

The prism angle is the angle formed between the two surfaces of a prism from which light enters and exits after refraction. In a prism, a beam of light is deflected twice. The deviation angle is the sum of the angle of these deflections. The angle of deviation of a ray going through a prism is minimum when the entry and exit angles are equal.

In the above diagram, OP is the incidence ray. It makes an angle of $i_{1}$ with normal and QR is the angle of emergence which makes an angle of $i_{2}$ with normal. $A$ is the prism angle and $δ$ is the angle of deviation $μ$ is the refractive index of the prism.

In case of minimum deviation, $∠ r_{1} = ∠ r_{2} = ∠ r$ .

$A = ∠ r_{1} + ∠ r_{2} = ∠ r + ∠ r = ∠ 2 r \Rightarrow ∠ r = \frac{A}{2} \Rightarrow A = 2 \times ∠ r$ .

In case of minimum deviation, $i_{1} = i_{2} = i δ_{m} = δ$

$A + δ = i_{1} + i_{2} \Rightarrow δ = i_{1} + i_{2} - A . \Rightarrow A + δ_{m} = 2 i \Rightarrow i = \frac{A + δ_{m}}{2}$

Derive an expression for prism angle and angle of deviation.

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