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

In vacuum, all EM waves travel at c = 1/sqrt($mu_0$$epsilon_0$) = 2.998 x 10^8 m/s, regardless of frequency. In a material medium with relative permittivity $epsilon_r$ and relative permeability $mu_r$: v = 1/sqrt(muepsilon) = $\frac{c}{sqrt}$($mu_r$$epsilon_r$) = $\frac{c}{n}$, where n = sqrt($mu_r$$epsilon_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: $lambda_{medium}$ = $\frac{lambda_vacuum}{n}$, but the frequency remains unchanged. JEE may ask: if $epsilon_r$ = 9 for a medium, find the speed of EM waves. Answer: v = $\frac{c}{sqrt}$(9) = c/3 = 10^8 m/s.