CBSE Class 12 · 2017 · Geometrical OpticsShort Answer

A ray of light is incident on a glass prism of refractive index

μ

and refracting angle

A

. If it just suffers total internal reflection at the other face, obtain an expression relating the angle of incidence, angle of prism and critical angle.

Answer: $sin i = μ sin (A - i_{c})$ , where $i_{c}$ is the critical angle $(sin i_{c} = 1/ μ)$ .

Solution

Let the ray enter the first face at angle of incidence

i

with refraction angle

r_{1}

, and strike the second face at the critical angle

i_{c}

(so it just grazes / just suffers TIR there).
For a prism

r_{1} + r_{2} = A

, and here

r_{2} = i_{c}

, so

r_{1} = A - i_{c}

.
Applying Snell's law at the first face:

μ = \frac{sin i}{sin r _{1}} \Rightarrow sin i = μ sin (A - i_{c}) with sin i_{c} = \frac{1}{μ} .

CBSE Class 12 Board · 2017 · Subjective

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