An observatory spectrograph must measure the rotational broadening inside a single…

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 observatory spectrograph must measure the rotational broadening inside a single stellar absorption line at

\lambda=530\ \text{nm}

, resolving a splitting of

\Delta\lambda=4.0\times10^{-3}\ \text{nm}

, but it must also locate that line unambiguously somewhere within a

40\ \text{nm}

wide order of the spectrum (

510

550\ \text{nm}

). An etalon of finesse

\mathcal{F}=25

with adjustable plate spacing

d

is available, together with a grating ruled at

1200

lines per millimetre to use as a pre-disperser. Both are used in first order where a grating order is meant; the etalon's order and free spectral range are related by

\Delta\lambda_{\rm FSR}=\lambda/m

and

m=2d/\lambda

at normal incidence, as usual. ((a)) Find the resolving power the etalon alone must supply to resolve the

4.0\times10^{-3}\ \text{nm}

splitting, hence its order

m

and plate spacing

d

, and its free spectral range. ((b)) Explain why the etalon by itself cannot be pointed at an unknown position inside the full

40\ \text{nm}

order without ambiguity, and state what the grating's role must then be. ((c)) Find the resolving power, and hence the minimum number of illuminated lines and illuminated width, the grating needs in first order so that it can isolate a band no wider than the etalon's free spectral range anywhere in the

40\ \text{nm}

order.

Related theory

Interference and diffraction

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