A parallel beam of light is incident from air at an angle $α$ on the side PQ of a right angled triangular prism of refractive index $n = \sqrt{2}$ . Light undergoes total internal reflection in the prism at the face PR when $α$ has a minimum value of $45 °$ . The angle $θ$ of the prism is [2016]

Question

Smart Achievers · Accepted Answer

(1)

Applying Snell's law at A

$1 \times \sin 45 ° = \sqrt{2} \times \sin r_{1}$ $∴$ $r_{1} = 30 °$

$\sin C = \frac{1}{n} = \frac{1}{\sqrt{2}}$

$∴$ $C = 45 °$

In $∆ A M B,$

$90 ° + θ + r_{1} + (90 ° - C) = 180 °$

$\Rightarrow 90 ° + θ + 30 ° + 90 ° - 45 ° = 180 °$

$∴$ $θ = 15 °$

Solution

1 $15 °$

2 $22.5 °$

3 $30 °$

4 $45 °$

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Solution

Q. A parallel beam of light is incident from air at an angle α on the side PQ of a right angled triangular prism of refractive index n=2. Light undergoes total internal reflection in the prism at the face PR when α has a minimum value of 45°. The angle θ of the prism is [2016]

1 15°

2 22.5°

3 30°

4 45°

Ans. (1) Applying Snell's law at A 1×sin45°=2×sinr1 ∴ r1=30° sinC=1n=12 ∴ C=45° In ∆AMB, 90°+θ+r1+(90°-C)=180° ⇒90°+θ+30°+90°-45°=180° ∴ θ=15°

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1 $15 °$

2 $22.5 °$

3 $30 °$

4 $45 °$