Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 315 / 3 / a / i / Solution

In the exoplanet transmission spectrum, the constant $a$ is the wavelength-independent reference transit depth, set mainly by the opaque planetary radius and any grey cloud deck. The Gaussian term can represent a resolved atomic or molecular absorption band centered at ${\lambda }_0$, with amplitude $b$ and width controlled by $\alpha$. The power-law term represents a continuum such as Rayleigh scattering or haze extinction; for Rayleigh scattering the opacity index is approximately $\gamma =-4$.

Solved by gpt-5.6-sol high.