HC Verma Chapter 18 Problem 68 – Prism grazing incidence – TIR at exit

Given

Prism A=30 deg, n=1.5, i=90 deg (grazing) at first face

Find

Exit condition

Formula

n sin r1 = sin 90 = 1; r1 = critical angle = 41.8 deg; r2 = A – r1

Solution

r1 = 41.8 deg; r2 = 30 – 41.8 = -11.8 deg (impossible); TIR occurs at second face

Answer

No transmission; TIR at exit face

Diagram / Concept

When r2 < 0, ray hits exit face beyond critical angle and undergoes TIR

Notes

Prism angle must be large enough for light to emerge