A light-emitting diode is filtered to give a Gaussian spectral line centred at with…

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

What an Instrument Can See, Ch Temporal coherence: correlation, spectrum and the interferometer

Problem

A light-emitting diode is filtered to give a Gaussian spectral line centred at

\lambda_0 = 630\ \mathrm{nm}

with full width at half maximum

\Delta\lambda = 20\ \mathrm{nm}

. ((a)) Using the shape factor

0.66

that applies to a Gaussian line on the rule

\ell_c = (\mathrm{shape\ factor})\,\lambda_0^2/\Delta\lambda

, compute the coherence length. ((b)) Hence compute the coherence time

\tau_c = \ell_c/c

, taking

c = 3.0\times10^8\ \mathrm{m\,s^{-1}}