A Fabry-Perot etalon has an air gap mm and mirror reflectance on each face

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Interference and diffraction · Coherence and statistical optics

Optics and Photonics, Ch Multiple-beam interference: thin films, multilayers and the Fabry-Perot etalon

Problem

A Fabry-Perot etalon has an air gap

d = 10.0

mm and mirror reflectance

R = 0.95

on each face. It is illuminated at normal incidence by the mercury green line at

\lambda = 546.1

nm, of linewidth

\Delta\lambda = 0.010

nm (typical of a discharge lamp). ((a)) Find the coefficient of finesse

F

and the finesse

\mathcal{F}

. ((b)) Find the free spectral range

\Delta\nu_{\rm FSR}

and the instrument linewidth

\Delta\nu_{1/2}

. ((c)) Using

\ell_c = \lambda^2/\Delta\lambda

(Chapter 10), find the coherence length of the lamp line and compare it with the path length

2d\mathcal{F}/\pi

built up inside the etalon. ((d)) State whether the observed fringe width is set by the lamp or by the instrument, and give its approximate value.