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NEET PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTSMedium

Question

A ray of light is incident at an angle of incidence, ii, on one face of a prism of angle AA (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is μ\mu, the angle of incidence ii, is nearly equal to:

A

μA\mu A

B

μA2\frac{\mu A}{2}

C

Aμ\frac{A}{\mu}

D

A2μ\frac{A}{2\mu}

Step-by-Step Solution

  1. Angle of Emergence: The ray emerges normally from the opposite face. This implies that the angle of emergence e=0∘e = 0^\circ. Consequently, the angle of refraction at the second surface r2=0∘r_2 = 0^\circ.
  2. Prism Relation: For a prism with angle AA, the relationship between the refracting angle and the internal refraction angles is A=r1+r2A = r_1 + r_2. Since r2=0r_2 = 0, we have r1=Ar_1 = A.
  3. Snell's Law at First Surface: At the first surface, the ray travels from air to the prism. Using Snell's Law: sin⁡i=μsin⁡r1\sin i = \mu \sin r_1.
  • Substituting r1=Ar_1 = A, we get sin⁡i=μsin⁡A\sin i = \mu \sin A.
  1. Small Angle Approximation: The problem states that the prism angle AA is small. Consequently, the angle of incidence ii will also be small. For small angles (in radians), sin⁡θ≈θ\sin \theta \approx \theta.
  • Therefore, i≈μAi \approx \mu A.

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 INSTRUMENTSincidentincidenceassumedemergesnormally

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