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NEET PHYSICSMedium

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.
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