An atmospheric-science spectrometer must scan the ozone absorption band from to (a…

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 atmospheric-science spectrometer must scan the ozone absorption band from

300\ \text{nm}

340\ \text{nm}

40\ \text{nm}

window) and resolve two overlapping absorption features

0.30\ \text{nm}

apart at

\lambda=310\ \text{nm}

, all within a single exposure. A deep-UV holographic grating ruled at

2400

lines per millimetre is available, as is an air-spaced etalon of finesse

\mathcal{F}=40

with adjustable plate spacing

d

. Both are considered in first order. ((a)) Find the resolving power

\lambda/\Delta\lambda

needed, and the minimum number of illuminated grating lines

N

in first order. ((b)) Find the etalon plate spacing that would give a free spectral range of

40\ \text{nm}

310\ \text{nm}

, and say whether this is a physically sensible choice. ((c)) State which device is fit for this task and give the minimum illuminated width of the grating that meets the requirement of part (a).

Related theory

Interference and diffraction

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