= Solution
Let the atmosphere occupy a thin annulus from $R_p$ to $R_a=R_p+\Delta R$. With mass extinction coefficient $k_\nu$, constant density $\rho$, and the assumed common chord length $l$, its <optical depth> is
$$
\tau_\nu=k_\nu\rho l.
$$
The opaque solid planet removes area $\pi R_p^2$, while the annulus removes the fraction $1-e^{-\tau_\nu}$ of the incident <specific intensity>. Neglecting limb darkening, the <exoplanet transmission spectrum> is therefore
$$
\boxed{D_\nu\equiv1-\frac{F_\nu^{\rm in}}{F_\nu^{\rm out}}
=\frac{R_p^2+(R_a^2-R_p^2)(1-e^{-k_\nu\rho l})}{R_s^2}}.
$$
For a thin annulus,
$$
D_\nu\simeq\left(\frac{R_p}{R_s}\right)^2
+\frac{2R_p\Delta R}{R_s^2}(1-e^{-k_\nu\rho l}).
$$
If the geometrical thickness is estimated as $\Delta R=N_HH$, then the <atmospheric scale height> is $H=k_BT_p/(\mu m_HGM_p/R_p^2)$. A wavelength-independent $k_\nu$ makes this idealized spectrum flat; real molecular opacities create its features.
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