Question

The frequency of a light wave is the same when the light travels in ethyl alcohol or in carbon disulfide. Find the ratio of the wavelength of the light in ethyl alcohol to that in carbon disulfide. The refractive indices n of carbon disulfide and ethyl alcohol are n disulfide = 1.632 and nalcohol = 1.362.

Answer 1

The crucial point is that the speed of light depends on the medium.

Speed of light in a medium is given by the equation:
c = c₀ / n
where c₀ speed of light in vacuum
n refractive index of the medium

Because frequency and wave length are related as:
f = c / λ <=> λ = c / f

You find for the ratio of the wave length' at same frequency
λ_ethanol / λ_carbon = c_ethanol / c_carbon
= (c₀/n_ethanol) / (c₀/n_carbon)
= n_carbon / n_ethanol
= 1.632 / 1.362
= 1.198