A light ray enters through a right angled prism at point P with the angle of incidence 30° as shown in figure. It travels through the prism parallel to its base BC and emerges along the face AC. The refractive index of the prism is:

F1 Savita UG Entrance 13-8-24 D19

  1. \(\frac{\sqrt5}{4}\)
  2. \(\frac{\sqrt5}{2}\)
  3. \(\frac{\sqrt3}{4}\)
  4. \(\frac{\sqrt3}{2}\)

Answer (Detailed Solution Below)

Option 2 : \(\frac{\sqrt5}{2}\)

Detailed Solution

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Calculation:

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The formula for the refractive index is given as:

r1 + c = A

⇒ r1 = 90 - c

Snell's law at the emergent boundary
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Sin(c) = 1 / μ

⇒ Cos(c) = (μ2 - 1)1/2 / μ

According to Snell's law at incident boundary

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Sin(30) = μ × Sin(r1)

1/2 = μ × Sin(90 - c) =μ Cos(c)

⇒ 1/2 = μ × (μ2 - 1)1/2 / μ

Squaring both sides:

1/4 = μ2 - 1

μ2 = 5 / 4

μ = √(5 / 4) = √5 / 2

Thus, the correct option is option 2: μ = √5 / 2

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