Fabry-Perot Etalon Spectrometer

Two parallel mirrors of reflectance $R$ a distance $d$ apart pass light only through multiple-beam interference, giving the Airy transmission $T=1/(1+F\sin^2(\delta/2))$ with $F=4R/(1-R)^2$ and round-trip phase $\delta=4\pi d/\lambda$. As an instrument the etalon resolves two close wavelengths when its reflectance finesse $\mathcal{F}=\pi\sqrt R/(1-R)$ makes the Airy peaks narrower than the line separation, with resolving power $R_p=m\mathcal{F}$, provided the free spectral range $\lambda^2/2d$ exceeds the separation so the orders do not overlap. Here the test source is the sodium doublet (D2 588.995 nm, D1 589.592 nm): raise $R$ and watch the single blurred peak split cleanly into two.