The relative permittivity of distilled water is 81. The velocity of light in it will be :
(Given μᵣ = 1)

Solution

Physics sir · 3 steps

Light slows down in water by the square root of the permittivity, not by the permittivity itself.

1. Speed in a medium. In vacuum c = 1/√(μ₀ ε₀). In a medium, μ₀ becomes μᵣ μ₀ and ε₀ becomes εᵣ ε₀, so the speed drops by a factor of √(μᵣ εᵣ).

   v = c/√(μᵣ εᵣ)

2. Put in numbers. With μᵣ = 1 and εᵣ = 81, √(μᵣ εᵣ) = √81 = 9. So v = (3 × 10⁸)/9 m s⁻¹ = 3.33 × 10⁷ m s⁻¹.
3. So. The velocity of light in distilled water is 3.33 × 10⁷ m s⁻¹, which is option (c).

The idea to keep. In any medium, v = c/√(μᵣ εᵣ), and √(μᵣ εᵣ) is the refractive index. Always take the square root of the product before dividing c.

Answer from the NTA final answer key. Solution by PrepWiser.