Question

When a light ray is refracted from one medium into another, the
wavelength changes from 4500A" to 3000 A". The critical angle for a ray
from second medium to first medium is​

Answer 1

Therefore the critical angle for the ray from 2nd medium to 1st medium is sin¯¹ (2/3) .

Given : When a light ray is refracted from one medium into another, the wavelength changes from 4500 Å to 3000 Å.

To find : The critical angle for a ray from second medium to first medium.

solution : at first, find refractive index of 2nd medium w.r.t 1st medium, ₂μ₁ = μ₂/μ₁

as refractive index is inversely proportional to wavelength.

so, ₂μ₁ = λ₁/λ₂ = 4500 Å/3000 Å = (3/2)

we know, critical angle is given by, sinC = 1/₂μ₁

⇒sinC = 1/(3/2) = 2/3

⇒C = sin¯¹ (2/3)

Therefore the critical angle for the ray from 2nd medium to 1st medium is sin¯¹ (2/3)