An Introduction to Modern Astrophysics · Problem 6.6

Binary Systems and Stellar Parameters — Carroll & Ostlie

Physics — Astrophysics · single-slit-diffraction

Problem

The diffraction pattern for a single slit (Figs. 6.7 and 6.8) is given by

I(\theta) = I_0 \left[\frac{\sin(\beta/2)}{\beta/2}\right]^2,

where

\beta \equiv 2\pi D \sin\theta/\lambda

. (a) Using l'H\^{o}pital's rule, prove that the intensity at

\theta = 0

is given by

I(0) = I_0

. (b) If the slit has an aperture of

1.0\,\mu

m, what angle

\theta

corresponds to the first minimum if the wavelength of the light is 500 nm? Express your answer in degrees.