Light travels a distance of ‘10x’ units in time ‘t1’ in vacuum and it travels a distance of ‘x’ units in time ‘t2’ in a denser medium. Using this information answer the question that follows :
Calculate the refractive index of the medium in terms of ‘t1’ and ‘t2’.
Topic: Refractive index in terms of distance and time
Answer
Given: light travels 10x in time t₁ in vacuum, and x in time t₂ in the denser medium.
Speed in vacuum: c = distance ÷ time = 10x ÷ t₁
Speed in the medium: v = x ÷ t₂
Refractive index: μ = c ÷ v = (10x ÷ t₁) ÷ (x ÷ t₂) = (10x ÷ t₁) × (t₂ ÷ x) = 10t₂ ÷ t₁
Refractive index of the medium, μ = 10t₂ / t₁
Algebra rather than arithmetic, but the physics is the same: refractive index is the speed in vacuum divided by the speed in the medium.
Find each speed separately before dividing. The x cancels, which is why the answer comes out in terms of the times alone — and is a sign you have done it right.
Dividing the wrong way round gives t₁/(10t₂), which would be less than 1. Refractive index with respect to vacuum is ALWAYS greater than 1, because nothing travels faster than light in vacuum. That check tells you which way up the fraction goes without memorising it.