A spectrograph places a grating with lines per millimetre

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

A spectrograph places a grating with

500

lines per millimetre, ruled over a width of

20\ \text{mm}

, in front of a Fabry-Perot etalon of mirror spacing

d = 5.0\ \text{mm}

and mirror reflectance

\mathcal{R} = 0.90

. Both operate near

\lambda = 589\ \text{nm}

(sodium light), the grating in first order (

m=1

) and the etalon near normal incidence. ((a)) Find the grating's resolving power and the wavelength interval

\Delta\lambda

it can resolve. ((b)) Find the etalon's finesse, its order number

m_e = 2d/\lambda

, and its free spectral range. ((c)) State whether the grating's resolution is fine enough to tell apart two adjacent etalon transmission orders (i.e. compare

\Delta\lambda_{\text{grating}}

with the etalon's free spectral range), and find the minimum number of grating lines that would make it adequate.

Related theory

Interference and diffraction

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