Question

Consider a telescope with a small circular aperture of diameter 2.0 centimeters. Calculate the angular separation θ1 at which two point sources of wavelength 600 nanometers are just resolved when viewed through a circular aperture of diameter 1.5 centimeters.

Answer 1

To solve this problem it is necessary to apply the concepts related to diffraction through a circular opening.

By definition the angular resolution is given by

$\theta = 1.22\frac{\lambda}{D}$

Where,

$\lambda = Wavelenght$

D = Diameter of the lens aperture.

Our values are given as,

$\lambda = 600*10^{-9}m$

$d = 1.5*10^{-2}m$

Therefore replacing,

$\theta = 1.22\frac{600*10^{-9}}{1.5*10^{-2}}$

$\theta = 4.88*10^{-5} rad$

Therefore the angular separation is $4.88*10^{-5} rad$