= Solution
At <exoplanet secondary eclipse>, the full-phase planet-star flux ratio is the sum of reflected and thermal light. Approximating both bodies as unresolved blackbodies and taking wavelength-independent <geometric albedo>,
$$
\boxed{
\frac{F_{p,\lambda}}{F_{*,\lambda}}
=A_g\left(\frac{R_p}{a}\right)^2
+\left(\frac{R_p}{R_*}\right)^2
\frac{B_\lambda(T_p)}{B_\lambda(T_*)}}.
$$
The first term is a flat reflected-light level under the stated constant-albedo assumption. At short wavelength the cool planet lies in the <Wien limit>, so thermal emission is exponentially suppressed and reflection dominates. At long wavelength both spectra enter the <Rayleigh-Jeans law>, giving
$$
\frac{F_{p,\lambda}}{F_{*,\lambda}}
\longrightarrow A_g\left(\frac{R_p}{a}\right)^2
+\left(\frac{R_p}{R_*}\right)^2\frac{T_p}{T_*}.
$$
The sketch therefore starts on the reflected plateau, rises where planetary <blackbody radiation> becomes important, and asymptotically approaches the long-wavelength plateau. This neglects spectral albedo features, phase dependence, stellar lines, and a nonisothermal planetary photosphere.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-315-planet-star-flux-ratio.png]
{title=Schematic wavelength dependence of a planet-star flux ratio at secondary eclipse}
{description=Reflected light sets a short-wavelength plateau, planetary blackbody emission produces a thermal rise, and the sum approaches its Rayleigh--Jeans plateau at long wavelength. The temperatures and radii are illustrative rather than a fit to a particular planet.}
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