What is the physical meaning of the refractive index n in terms of the speed of light in vacuum and in the medium?

• A. n = c/v
• B. n = v/c
• C. n = λ/v
• D. n = c/λ

Answer: (D)

Light slows down when it enters a medium, and the refractive index measures how much slower it is compared with vacuum. It is defined as the ratio of the speed of light in vacuum to the speed of light in the medium: n = c / v. This means the light’s phase velocity in the medium is v = c / n. Across an interface, the frequency doesn’t change, so the wavelength changes according to λ = v / f = (c / n) / f. Therefore the wavelength in the medium is shorter by a factor of n: λ = λ0 / n. Note that c/λ equals the frequency f, not the refractive index, so that option describes frequency rather than n.