Example: At what angle should a ray of light be incident on the face of a prism of refracting angle 60∘ so that it just suffers total internal reflection at the other face. Find the refractive index of the prism.Refractive index of prism is 1.524.
Solve problems on light ray passing through multiple prisms
Example: A ray of light enters at grazing angle of incidence into an assembly of three isosceles right-angled prisms having refractive indices μ1=2,μ2=x and μ3=3 . If finally emergent light ray also emerges at grazing angle then calculate x.
Solution: Apply Snell's law on various surfaces one by one : 1 sin 90∘=μ1 sin r1⇒ sin r1=21⇒r1=45∘ We have the incident angle for the second interface given using the relation sini2=cosr1 Thus we get μ1 cos r1= μ2 sin r2⇒ sin r2 = μ21(cosr2=21) μ2 cos r2=μ3 sin r3⇒ sin r3=3μ21−sin2r2 μ3 cos r3=1 = 3μ22−1 sin 2r3 + cos 2r3=1 ⇒3μ22−1+31=1⇒μ22=3⇒μ2=3 Thus we get x=3.