Perota

Perota, a hooded light-keeper, holds two mirrors face to face with red light bouncing between them.

The Physics

Two parallel, partly reflecting mirrors trap light that bounces back and forth. Only wavelengths that fit a whole number of half-waves into the gap build up and pass through; the rest cancel out. The transmission is a comb of sharp peaks, spaced by the free spectral range.

FSR = c/(2nL)

• FSR: free spectral range, the frequency spacing between peaks (Hz)
• c: speed of light (m/s)
• n: refractive index between the mirrors
• L: mirror spacing (m)

The sharpness of the peaks is set by the finesse, F = π√R/(1 − R) for mirror reflectivity R. With R = 0.99, F ≈ 312.6: the peaks are about 300 times narrower than their spacing. The same physics sets the modes of a laser cavity.

Honest caveat: These formulas assume ideal, lossless, perfectly parallel mirrors at normal incidence. Real cavities lose finesse to absorption, scattering and imperfect alignment.

On the sticker

Perota holds two silver mirrors with a red beam glowing between them; the transmission peaks are not drawn. Printed text: PEROTA with the line FSR = c/(2nL). Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.