Angle of a prism whose one surface is 30∘ and its refractive index is √2. At what angle of incidence, a ray should be incident on the surface so that after reflection from the silvered surface, it retraces its path
Given: ∠ A = 30∘ and μ=√2
By Snell's law at surface AB
μ=sin isin r
For a ray to retraces its path, it should fall at 90∘ on the silver surface.
In ΔAOM
∠A+∠O+∠M=180∘90∘−r+30∘+90∘=180∘r=30∘
⇒√2=sin isin 30∘⇒i=45∘