Question

Two optical media have a plane boundary between them. Suppose θ_1cr is the critical angle of incidence of a beam and θ₁ is the angle of incidence at which the refracted beam is perpendicular to the reflected one (the beam is assumed to come from an optically denser medium). Find the relative refractive index of these media if sin θ_1cr/sin θ₁ = η = 1.28.

Answer 1

Let two optical mediums of R.I.n₁ and n₂ respectively be such that n₁ > n₂ . In the case when angle of incidence is θ_1cr (Fig.), from the law of refraction

In the case , when the angle of incidence is θ₁ , from the law of refraction at the interface of mediums 1 and 2 . 

n₁ sin θ₁ = n₂ sin θ_{​​​​​​​2} 

But in accordance with the problem