A prism of angle 75° and refractive index √(3) is coated with thin… | JEE Main 2026 (23 Jan, Shift 2 (one Or More Correct))

Q8JEE Main 2026 · 23 JAN · SHIFT 2 (One or more correct)Medium

Total Internal Reflection

A prism of angle $75^\circ$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be ______

$(\sin 15^\circ = 0.25$ and $\sin 25^\circ = 0.43)$

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Answer: (a)

Critical angle at the coated back face: $\sin C = \frac{1.5}{\sqrt{3}} = \frac{\sqrt{3}}{2} \Rightarrow C = 60^\circ$ .
TIR needs $r_2 \ge 60^\circ$ ; with $r_1 + r_2 = A = 75^\circ$ , $r_1 \le 15^\circ$ .
First face: $\sin i = \sqrt{3}\sin r_1 \le \sqrt{3}\times0.25 = 0.43 \Rightarrow i \le 25^\circ$ .
So TIR happens for $i$ below about $25^\circ$ ; option (a) $15^\circ$ to $20^\circ$ lies in this range. So the answer is (a).

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