Question

A light ray falls on a square glass slab on horizontal face with incident angle of 45 degrees .What must be the index of refraction if total internal reflection occurs at vertical face

Answer 1

I hope this will help u

Answer 2

Let the refractive index be μangle of incidence, i=45°sin isin r=μwhere, r=angle of refractionsin r=sin 45°μ...(1)Now, angle of incidence of the ray on the vertical face of the slab as it travels through it is (90°−r)sin 90°sin (90°−r)=μ1cos r=μcos r=1μ ...(2)We know that sin2θ+cos2θ=1from (1) and (2),sin2r+cos2r=1(sin 45°μ)2+(1μ)2=112μ2+1μ2=1 ...... [because sin 45°=12√]1+22μ2=1μ2=32μ=32−−√