How is the refractive index n related to the material's permittivity and permeability in a non-magnetic medium?

How is the refractive index n related to the material's permittivity and permeability in a non-magnetic medium?

• A. n ≈ √μ_r
• B. n ≈ √ε_r
• C. n ≈ 1/√ε_r
• D. n ≈ ε_r

Answer: (B)

Light slows down in a medium, and the refractive index n tells us how much slower than vacuum the light travels. In a linear, isotropic medium the wave speed relates to the material properties by v = 1/√(ε μ), where ε = ε0 ε_r and μ = μ0 μ_r. The refractive index is n = c/v, which gives n = √(ε_r μ_r). In a non-magnetic medium, μ_r is essentially 1, so n ≈ √ε_r. So the correct relationship is n ≈ √ε_r. The other forms ignore the electric response, reverse the dependence, or fail dimensionally.

Light slows down in a medium, and the refractive index n tells us how much slower than vacuum the light travels. In a linear, isotropic medium the wave speed relates to the material properties by v = 1/√(ε μ), where ε = ε0 ε_r and μ = μ0 μ_r. The refractive index is n = c/v, which gives n = √(ε_r μ_r). In a non-magnetic medium, μ_r is essentially 1, so n ≈ √ε_r. So the correct relationship is n ≈ √ε_r. The other forms ignore the electric response, reverse the dependence, or fail dimensionally.