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NEET PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTSMedium

Question

A beam of light consisting of red, green, and blue colours is incident on a right-angled prism. The refractive index of the material of the prism for the red, green, and blue wavelengths is 1.39, 1.44, and 1.47 respectively. The prism will:

A

separate the blue colour part from the red and green colour.

B

separate all three colours from one another.

C

not separate the three colours at all.

D

separate the red colour part from the green and blue colours.

Step-by-Step Solution

  1. Identify Geometry and Incidence: For a standard right-angled isosceles prism problem where light is incident normally on one leg, it strikes the hypotenuse face at an angle of incidence i=45∘i = 45^\circ.
  2. Condition for Total Internal Reflection (TIR): TIR occurs at the glass-air interface if the angle of incidence exceeds the critical angle (i>ici > i_c). sin⁡ic=1μ\sin i_c = \frac{1}{\mu} sin⁡45∘>1μ  ⟹  12>1μ  ⟹  μ>2≈1.414\sin 45^\circ > \frac{1}{\mu} \implies \frac{1}{\sqrt{2}} > \frac{1}{\mu} \implies \mu > \sqrt{2} \approx 1.414
  3. Analyze Each Color:
  • Red (μ=1.39\mu = 1.39): Since 1.39<1.4141.39 < 1.414, TIR does not occur. The red light refracts through the hypotenuse.
  • Green (μ=1.44\mu = 1.44): Since 1.44>1.4141.44 > 1.414, TIR occurs. The green light is totally internally reflected.
  • Blue (μ=1.47\mu = 1.47): Since 1.47>1.4141.47 > 1.414, TIR occurs. The blue light is totally internally reflected.
  1. Conclusion: The green and blue components are reflected, while the red component passes through. Thus, the prism separates the red colour from the green and blue colours.

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 INSTRUMENTSconsistingcoloursincidentrightangledrefractive

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