= Solution
Two parallel partially reflecting surfaces in a <Fabry–Pérot interferometer> produce a sequence of coherent transmitted beams. For equal lossless mirror intensity <reflectance> $\mathcal R$ and round-trip phase $\delta=4\pi nd\cos\theta_t/\lambda$, summing the <geometric series> of amplitudes gives
$$
\frac{E_t}{E_i}=\frac{(1-\mathcal R)e^{i\delta/2}}{1-\mathcal R e^{i\delta}},\qquad
\boxed{\mathcal T=\frac1{1+\mathcal F\sin^2(\delta/2)},\quad
\mathcal F=\frac{4\mathcal R}{(1-\mathcal R)^2}}.
$$
<resonances> have $2nd\cos\theta_t=m\lambda$ and unit peak transmission in this symmetric lossless model. Varying angle gives concentric equal-inclination rings; changing spacing scans the <resonance> <wavelengths>.
At <normal incidence> with negligible dispersion, the <free spectral range> is $\Delta\nu_{\rm FSR}=c/(2nd)$. For high <reflectance>, the peak full width gives <finesse> and resolving <power>
$$
\boxed{\mathscr F\simeq\frac{\pi\sqrt{\mathcal R}}{1-\mathcal R},\qquad
\frac\nu{\delta\nu}=m\mathscr F}.
$$
The coefficient $\mathcal F$ in the transmission formula and the <finesse> $\mathscr F$ are different quantities. Multiple round trips sharpen a peak, allowing high-resolution spectroscopy, <frequency> selection and cavity measurements. Absorption, mirror mismatch, finite angular spread, imperfect parallelism and surface errors reduce usable transmission or <finesse>. Adjacent orders can overlap in a broadband measurement, requiring order selection or prior spectral information.
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