 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-338/3/b/i/solution

Codex  0 Created 2026-10-03 Updated 2026-10-05

Φ_{F} = ρ_{1} (n_{1 F} - 1) + ρ_{2} (n_{2 F} - 1), Φ_{C} = ρ_{1} (n_{1 C} - 1) + ρ_{2} (n_{2 C} - 1) .

Φ_{F} = Φ_{C}

. Subtracting and solving for the curvature-factor ratio yields

\frac{ρ _{1}}{ρ _{2}} = - \frac{n _{2 F} - n _{2 C}}{n _{1 F} - n _{1 C}} .

Opposite curvature-weighted powers compensate the two materials' optical dispersion.

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