 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-2/40c/c/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Tangential phase matching gives

k sin θ = k^{'} sin θ^{'}, \frac{sin θ}{c _{P}} = \frac{sin θ ^{'}}{c _{P}^{'}} .

A transmitted propagating wave exists when its normal wavenumber is real, equivalently

\frac{c _{P}^{'}}{c _{P}} sin θ \leq 1 .

For incidence angles between zero and

π /2

, this is automatic if

c_{P}^{'} \leq c_{P}

and imposes the corresponding critical-angle bound if

c_{P}^{'} > c_{P}

 New to topics? Read the docs here!