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Question

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 minimum value of $45^{\circ}$ . The angle $θ$ of the prism is:

478073

A

$15^{\circ}$

B

$22.5^{\circ}$

C

$30^{\circ}$

D

$45^{\circ}$

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Updated on : 2022-09-05

Solution

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Correct option is A)

Applying Snell's law at surface PQ,
$∴ 1 \times sin α = n \times sin β$
at $α = 45 °, n = 2$
$sin β = \frac{1}{2} ∴ β = 30 °$
$γ = 90 - (180 - (90 + θ + β))$
$∴$ Applying Snell's law at surface PR
$∴ 2 sin γ = 1$
$∴ sin (θ + β) = \frac{1}{2}$
$∴ θ + β = 45 °$
$∴ θ + 30 ° = 45 °$
$∴ θ = 15 °$ Thus option A

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