A parallel beam of light is incident form 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

Question

A parallel beam of light is incident form 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 (A) 15° (B) 22.5° (C) 30° (D) 45°

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/025e21a8871a6945422c2519c9b4470c-.png" /> sin ic=(1/√2) iC=45° 1 × sin 45°=√2 sin r sin r=(1/2) r=30° ∴ θ=180°-120°-45°=15°

Q. A parallel beam of light is incident form 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 $4 5^{\circ}$ . The angle $θ$ of the prism is

$1 5^{\circ}$

$22. 5^{\circ}$

$3 0^{\circ}$

$4 5^{\circ}$

$sin i_{c} = \frac{1}{2}$
$i_{C} = 4 5^{\circ}$
$1 \times sin 4 5^{\circ} = 2 sin r$
$sin r = \frac{1}{2}$
$r = 3 0^{\circ}$
$∴ θ = 18 0^{\circ} - 12 0^{\circ} - 4 5^{\circ} = 1 5^{\circ}$

Q. A parallel beam of light is incident form 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

15∘

22.5∘

30∘

45∘