Question

How is the refractive index of a medium related to the speed of light? Give an expression for refractive index of a medium with respect to another in terms of speed of light in these two media?

Answer 1

Refractive index compares the speed of light in a particular medium with the speed of light in vacuum 

Relation between refractive index and speed of light: 

Refractive index (μ) = \(\frac{c\,(speed\,of\,light\,in\,vaccum)}{v\,(speed\,of\,light\,in\,medium)}\)

⇒ µ = \(\frac{c}{v}\)

Let the refractive index of medium 1 be μ1 and the speed of light in medium 1 is v1. 

⇒ µ_{1 =} \(\frac{c}{v_1}\) ………………….. (1)

Similarly; 

Let the refractive index of medium 2 be μ₂ and the speed of light in medium2 is v₂. ⇒ µ₂ = \(\frac{c}{v_2}\)………………….. (2) 

Dividing (1) By (2) \(\frac{μ_1}{μ_2}\,=\,\frac{\frac{c}{v_1}}{\frac{c}{v_2}}\,=\,\frac{c}{v_1}\,\times\,\frac{v_2}{c}\)

⇒\(\frac{μ_1}{μ_2}\,=\,\frac{v_2}{v_1}\)

Hence refractive index of a medium is inversely proportional to the speed of light in that medium.