Question 8 of 29intermediate🔧 ApplyNumerical2 marks

Light enters from air to glass having refractive index 1.50. What is the speed of light in the glass? The speed of light in vacuum is 3×1083 \times 10^8 m s−1^{-1}.

Correct Answer

The speed of light in glass is 2×1082 \times 10^8 m s−1^{-1}.

Exercise: QUESTIONS | Q: 2 | (Page Page 17)
For More Understanding

Explanation

This question tests the relationship between refractive index and speed of light in a medium. The textbook provides the formula nm=cvn_m = \frac{c}{v} where nmn_m is the refractive index of the medium, cc is the speed of light in air/vacuum, and vv is the speed of light in the medium. By rearranging this formula, students can calculate the speed of light in any medium if they know its refractive index and the speed of light in vacuum.

Solution Steps

  1. Given: Refractive index of glass, ng=1.50n_g = 1.50; Speed of light in vacuum, c=3×108c = 3 \times 10^8 m s−1^{-1}

  2. Formula: The refractive index of a medium is given by nm=cvn_m = \frac{c}{v}, where vv is the speed of light in the medium.

  3. Rearranging: v=cnmv = \frac{c}{n_m}

  4. Calculation: v=3×1081.50=2×108v = \frac{3 \times 10^8}{1.50} = 2 \times 10^8 m s−1^{-1}

  5. Answer: The speed of light in glass is 2×1082 \times 10^8 m s−1^{-1}.

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