An optical medium has relative permeability μᵣ = 10/π and relative permittivity εᵣ = 1/0.0885. The speed of light in vacuum is greater than the speed in this medium by how many times?

Question

G1 Physics · Accepted Answer

The speed of light in a medium is v = c/√(μᵣεᵣ). Therefore, c/v = √(μᵣεᵣ). Substitute: μᵣεᵣ = (10/π)(1/0.0885). Using π ≈ 3.14: 10/π ≈ 3.185, 1/0.0885 ≈ 11.30. Thus, μᵣεᵣ ≈ 3.185×11.30 ≈ 36. Hence, c/v ≈ √36 = 6. Answer: 6.