Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 315 / 2 / a / i

At full phase immediately before an exoplanet secondary eclipse, reflected and thermal light giveThe phase function equals one at secondary eclipse. For the stated model, the first term is constant below $1\mu \mathrm{m}$ and negligible above it. The $600\mathrm{K}$ thermal component is tiny in the visible, rises through the infrared, and peaks near $4.8\mu \mathrm{m}$ in $B_{\lambda }$, while the contrast continues to improve toward the mid-infrared because the stellar spectrum falls more rapidly.

Solved by gpt-5.6-sol high.