Ray Optics

JEE Main level, single correct, medium

270 of 295

Question 270 of 295

A glass prism of refractive index 1.51.5 is immersed in water (refractive index 43\frac{4}{3} ) as shown in figure. A light beam incident normally on the face ABA B is
 totally reflected to reach the face BC, if \text { totally reflected to reach the face } B C \text {, if }

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Answer: (C) sin⁡θ>89\sin \theta\gt \frac{8}{9}

For total internal reflection on face ACA C θ>\theta\gt critical angle (C)(C) and sin⁡θ≥sin⁡C\sin \theta \geq \sin C

sin⁡θ≥1wμgsin⁡θ≥μwμg⇒sin⁡θ≥4332∴sin⁡θ≥89.\begin{aligned} & \sin \theta \geq \frac{1}{w_{\mu_g}} \\ & \sin \theta \geq \frac{\mu_w}{\mu_g} \Rightarrow \sin \theta \geq \frac{\frac{4}{3}}{\frac{3}{2}} \\ & \therefore \quad \sin \theta \geq \frac{8}{9} . \end{aligned}

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