An industrial emission spectrometer must

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

Optics and Photonics, Ch Fraunhofer diffraction from apertures and gratings

Problem

An industrial emission spectrometer must, in a single exposure, record the whole band from

480\ \text{nm}

650\ \text{nm}

170\ \text{nm}

window) while resolving two adjacent emission lines at

\lambda=550\ \text{nm}

separated by

\Delta\lambda=0.80\ \text{nm}

. The designer has both a diffraction grating ruled at

1200

lines per millimetre and an air-spaced Fabry-Perot etalon on the shelf, and must choose one. Light is used in first order (

m=1

) throughout. ((a)) Find the resolving power

\lambda/\Delta\lambda

the instrument must supply, and hence the minimum number of illuminated grating lines

N

needed in first order. ((b)) Find the maximum etalon plate spacing

d

that would give a free spectral range of at least

170\ \text{nm}

550\ \text{nm}

, and say whether such a device is a sensible choice. ((c)) State which device should be used, and give the minimum illuminated width of the

1200

lines per millimetre grating that meets the requirement of part (a).