A spectrograph uses 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 uses a grating with

1200

lines per millimetre, ruled over a width of

25\ \text{mm}

, followed by a Fabry-Perot etalon of mirror spacing

d = 3.0\ \text{mm}

and mirror reflectance

\mathcal{R} = 0.95

. Both are used at

\lambda = 632.8\ \text{nm}

, the grating in first order (

m = 1

), the etalon near normal incidence. ((a)) Find the grating's resolving power and the smallest 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)) Compare the grating's

\Delta\lambda

with the etalon's free spectral range and state whether the grating alone can identify which etalon order is being observed. Also state the minimum number of grating lines that would just be adequate for this.

Related theory

Interference and diffraction

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