JEE Main 2022 · 26 July · evening · Single correct · +4 / −1
Light travels in two media M₁ and M₂ with speeds 1.5 × 10⁸ ms⁻¹ and 2.0 × 10⁸ ms⁻¹ respectively. The critical angle between them is :
- (a) tan ⁻¹(3/√7)
- (b) tan ⁻¹(2/3)
- (c) cos ⁻¹(3/4)
- (d) sin ⁻¹(2/3)
Answer and solution
Answer (a) tan ⁻¹(3/√7)
Solution
Physics sir · 3 steps
Get sin C from the ratio of speeds, then convert it to a tangent to match the options.
- Which side is denser. Light is slower in M₁, so M₁ is the optically denser medium. Total internal reflection happens for light going from M₁ into M₂.
sin C = n₂/n₁ = v₁/v₂ = (1.5 × 10⁸)/(2.0 × 10⁸) = 3/4
- Convert to tangent. Take a right triangle with opposite side 3 and hypotenuse 4. The adjacent side is √(16 - 9) = √7, so tan C = 3/√7.
- So. C = sin⁻¹(3/4) = tan⁻¹(3/√7), which is option (a).
The idea to keep. Since n = c/v, the critical angle is sin C = v_(denser)/vᵣₐᵣₑᵣ: the smaller speed over the larger. If the options use tan or cos, draw the triangle and convert.
Answer from the NTA final answer key. Solution by PrepWiser.