Q4Electromagnetics Waves
Question
Q.4 Define total internal reflection.
Answer
Total internal reflection is the complete reflection of a wave at the interface between a denser and a rarer medium when the angle of incidence (from the denser side) exceeds the critical angle θc = sin⁻¹(n2/n1), with no power transmitted into the second medium.
Total internal reflection (TIR) occurs when an electromagnetic wave travelling in a denser medium (higher refractive index n1) strikes the interface with a rarer medium (lower refractive index n2 < n1) at an angle of incidence θi (measured from the normal) that exceeds a critical angle θc, defined by Snell's law at the point where the refracted angle reaches exactly 90°:
For θi > θc, no real refraction angle satisfies Snell's law (sinθt = (n1/n2)sinθi > 1 is impossible for real θt), so all of the incident power is reflected back into the denser medium — the reflection coefficient magnitude becomes exactly 1, and the transmitted field becomes a non-propagating evanescent wave confined to a thin layer at the interface, carrying no net time-average power across the boundary. TIR is the physical principle underlying optical fibre waveguiding (the fibre core, of higher index, guides light by repeated TIR at the core-cladding interface) and is directly analogous to the below-cutoff evanescent-decay behaviour of a waveguide mode operated below its cutoff frequency.