Question

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'.

Answer 1

Given that light travels a distance 10x units,

Time taken = t₁

Speed of light in medium `(v_1) = (10x)/t_1`

We know that,

Refractive index of medium

`μ_1 =("Speed of light in vacuum" (c))/("Speed of light in medium" (v_1))`

`μ_1 = c/(((10x)/t_1))`

= `(ct_1)/(10x)`   ...(i)

Same for medium 2

`μ_2 = c/((x/t_2))`

= `(ct_2)/x`   ...(ii)

Ratio of (R.I)₁ and (R.I)₂

`""^1μ_2 = μ_2/μ_1`

= `(ct_2)/x xx (10x)/(ct_1)`

= `(10t_2)/t_1`

¹μ₂ = 10t₂ : t₁