A helium-neon laser operating in a single transverse mode (TEM ) produces a beam of…

PHYSICS · Subjective · Fermi University Physics · Optics & Photonics · Coherence and statistical optics · Coherence and statistical optics

What an Instrument Can See, Ch Spatial coherence and the van Cittert-Zernike theorem

Problem

A helium-neon laser operating in a single transverse mode (TEM

_{00}

) produces a beam of diameter

2.0\,\mathrm{mm}

at wavelength

633\,\mathrm{nm}

. Someone reasons as follows: "Treat the beam's

2.0\,\mathrm{mm}

cross-section, a distance

z = 1.0\,\mathrm{m}

before a double slit, as the source in the van Cittert-Zernike theorem. Its angular size is

\theta_s = 2.0\times10^{-3}\,\mathrm{m}/1.0\,\mathrm{m} = 2.0\times10^{-3}\,\mathrm{rad}

, so the first zero of

|\mu_{12}|

is at

\Delta r = 1.22\lambda/\theta_s = 1.22\times633\times10^{-9}/2.0\times10^{-3} = 3.9\times10^{-4}\,\mathrm{m}

. A double slit with slits

1.0\,\mathrm{mm}

apart, placed in the beam, therefore has its two slits separated by more than this coherence radius, so no fringes should be visible." Find the error in this argument and state what would actually be observed.

Browse the problem library