A pocket spectroscope has a grating with grooves per millimetre

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

Reading the Spectrum, Ch Lines, series and the term diagram: what a spectrometer measures

Problem

A pocket spectroscope has a grating with

300

grooves per millimetre, of which only

3.0\,\mathrm{mm}

is illuminated by its narrow entrance tube. It is used in first order to look at a sodium lamp, whose two yellow lines are

0.597\,\mathrm{nm}

apart near

589\,\mathrm{nm}

. ((a)) Find the resolving power

mN

and the smallest wavelength difference

\Delta\lambda

the grating can separate near

589\,\mathrm{nm}

. ((b)) Does the spectroscope show the sodium pair as two lines? ((c)) What illuminated width, at the same groove density and order, would just resolve the pair?

Related theory

Interference and diffraction

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