If an optical medium possesses a relative permeability of 10/π and relative permittivity of 1/0.0885, then the velocity of light is greater in vacuum than that in this medium by _________ times.
(μ₀=4 π × 10⁻⁷ H / m, ε₀=8.85 × 10⁻¹² F / m, c=3 × 10⁸ m / s)

Solution

Physics sir · 3 steps

Light slows by the factor √(μᵣ εᵣ). Multiply the two, then take the square root.

1. Speed in a medium. In vacuum c = 1/√(μ₀ ε₀). In the medium v = 1/√(μ ε) with μ = μᵣ μ₀ and ε = εᵣ ε₀. So μ₀ and ε₀ cancel in the ratio.

   c/v = √(μᵣ εᵣ)

2. Put in numbers. μᵣ εᵣ = 10/π × 1/0.0885 = 10/0.2780 = 35.97. Then √35.97 = 5.997.
3. So. The speed of light in vacuum is about 6 times its speed in this medium.

The common slip: 36. Forgetting the square root and stopping at μᵣ εᵣ gives 36, not 6.

The idea to keep. The refractive index of a medium is n = c/v = √(μᵣ εᵣ). With relative values given, you never need μ₀ or ε₀; they cancel.

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