A student sets up three short experiments on an optics bench.

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 student sets up three short experiments on an optics bench. ((a)) A slit of width

b = 0.15\ \text{mm}

is illuminated by a helium-neon laser,

\lambda = 633\ \text{nm}

, and the pattern is viewed on a screen

L = 2.00\ \text{m}

away. Compute

b^2/\lambda

and decide whether the screen is in the Fraunhofer (far-field) regime. ((b)) A refracting telescope has an objective of diameter

D = 150\ \text{mm}

. Find the smallest angular separation it can resolve for two point sources in light of wavelength

550\ \text{nm}

, using the Rayleigh criterion. Give the answer in arcseconds (

1\ \text{rad} = 206265''

). ((c)) A spectral doublet has wavelengths separated by

\Delta\lambda = 0.3\ \text{nm}

\lambda = 600\ \text{nm}

. Using a grating in first order (

m=1

), find the minimum number of illuminated lines

N

needed to resolve the doublet.