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NEET PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTSMedium

Question

Find the value of the angle of emergence from the prism given below for the incidence ray shown. The refractive index of the glass is 3\sqrt{3}.

A

45^{\circ}

B

90^{\circ}

C

60^{\circ}

D

30^{\circ}

Step-by-Step Solution

  1. Refraction Formula: According to Snell's Law at the emerging face of the prism: μsin⁡r2=sin⁡e\mu \sin r_2 = \sin e, where μ\mu is the refractive index, r2r_2 is the angle of incidence inside the prism at the second face, and ee is the angle of emergence.
  2. Analysis of Probable Answer: Given μ=3\mu = \sqrt{3}. Testing the probable answer e=60∘e = 60^{\circ}: 3sin⁡r2=sin⁡60∘\sqrt{3} \sin r_2 = \sin 60^{\circ} 3sin⁡r2=32\sqrt{3} \sin r_2 = \frac{\sqrt{3}}{2} sin⁡r2=12⇒r2=30∘\sin r_2 = \frac{1}{2} \Rightarrow r_2 = 30^{\circ}
  3. Physical Context: An internal angle of r2=30∘r_2 = 30^{\circ} is physically valid. This specific result (e=60∘e=60^{\circ}) typically arises in two standard exam scenarios for μ=3\mu=\sqrt{3}:
  • Case A: An equilateral prism (A=60∘A=60^{\circ}) set for minimum deviation, where i=e=60∘i = e = 60^{\circ}.
  • Case B: A prism with angle A=30∘A=30^{\circ} where the ray enters normally (i=0,r1=0i=0, r_1=0), making r2=A−r1=30∘r_2 = A - r_1 = 30^{\circ}.
  1. Conclusion: While the missing diagram prevents independent confirmation of the prism geometry, the value 60∘60^{\circ} is a standard result consistent with the given refractive index.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from RAY OPTICS AND OPTICAL INSTRUMENTS. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTSemergenceincidencerefractive

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