= Solution
Apply the <formal solution of the radiative transfer equation> successively to the two isothermal layers at normal incidence. In <local thermodynamic equilibrium>,
$$
\boxed{
I_{\nu,2}=I_{\nu,0}e^{-(\tau_1+\tau_2)}
+B_\nu(T_1)(1-e^{-\tau_1})e^{-\tau_2}
+B_\nu(T_2)(1-e^{-\tau_2})}.
$$
For <optically thin> layers this becomes
$$
\boxed{
I_{\nu,2}=I_{\nu,0}
+\tau_1[B_\nu(T_1)-I_{\nu,0}]
+\tau_2[B_\nu(T_2)-I_{\nu,0}]
+O(\tau^2)}.
$$
This assumes no scattering and negligible reflection between layers.
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