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Q76 (CDS-I/2020) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Geometrical optics Answer Verified

If the speed of light in air is 3 × 10⁸ m/s, then the speed of light in a medium of refractive index 3/2 is:

A) 2 × 10⁸ m/s
B) 4.5 × 10⁸ m/s
C) 1.5 × 10⁸ m/s
D) 3 × 10⁸ m/s

Result
Your answer: —  ·  Correct: A

Explanation

The correct answer is Option 1. This problem is based on the fundamental relationship between the refractive index of a medium and the speed of light.

The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum/air (c) to the speed of light in that specific medium (v). The formula is expressed as:

n = c / v

Given in the question:

  • Speed of light in air (c) = 3 × 108 m/s
  • Refractive index (n) = 3/2 (or 1.5)

Rearranging the formula to find the speed in the medium (v):

v = c / n
v = (3 × 108) / (3/2)
v = (3 × 108 × 2) / 3
v = 2 × 108 m/s

Therefore, the speed of light decreases when entering a denser medium, resulting in 2 × 108 m/s.

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