Ray Optics

JEE Main level, single correct, medium

55 of 295

Question 55 of 295

Critical angle of incidence for a pair of optical media is 45∘45^{\circ}. The refractive indices of first and second media are in the ratio:

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Answer: (B) 2:1\sqrt{2}: 1

sin⁡θc=μRμd=μ2μ1sin⁡45∘=μ2μ1⇒12=μ2μ1⇒μ1μ2=21\begin{aligned} & \sin \theta_{\mathrm{c}}=\frac{\mu_{\mathrm{R}}}{\mu_{\mathrm{d}}}=\frac{\mu_2}{\mu_1} \\ & \sin 45^{\circ}=\frac{\mu_2}{\mu_1} \\ & \Rightarrow \frac{1}{\sqrt{2}}=\frac{\mu_2}{\mu_1} \\ & \Rightarrow \frac{\mu_1}{\mu_2}=\frac{\sqrt{2}}{1}\end{aligned}

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