• Tags: speed, medium, refractive-index
• Difficulty: Moderate

In vacuum, all EM waves travel at c = 1/sqrt(mu_0epsilon_0) = 2.998 x 10^8 m/s, regardless of frequency. In a material medium with relative permittivity epsilon_r and relative permeability mu_r: v = 1/sqrt(muepsilon) = c/sqrt(mu_repsilon_r) = c/n, where n = sqrt(mu_repsilon_r) is the refractive index. For most optical materials, mu_r ≈ 1, so n ≈ sqrt(epsilon_r). The refractive index depends on frequency (dispersion): n is higher for shorter wavelengths (violet light bends more than red in a prism). In a medium, the wavelength changes: lambda_medium = lambda_vacuum/n, but the frequency remains unchanged. JEE may ask: if epsilon_r = 9 for a medium, find the speed of EM waves. Answer: v = c/sqrt(9) = c/3 = 10^8 m/s.