Define refractive index in terms of speed of light.

• A. n = v / c
• B. n = c / lambda
• C. n = lambda / lambda0
• D. n = c / v

Answer: (D)

Light slows down when it enters a medium, and the refractive index measures how many times slower it is compared with vacuum. The proper definition is the ratio of the speed of light in vacuum to the speed of light in the material: n = c / v. This way, if the material slows light by a factor, n reflects that factor (for most media, v < c and n > 1). Using v/c would invert this idea, giving a value less than or equal to 1 for typical media. Using c / lambda mixes speed with wavelength, which isn’t how refractive index is defined. And lambda / lambda0 equals 1/n, not n, since wavelength in the medium is shorter by the factor n. So the correct expression is n = c / v.