All Problems Diffraction of Light
Problem 5.133
To measure the angular distance \(\psi\) between the components of a double star by Michelson's method, in front of a telescope's lens a diaphragm was placed, which had two narrow parallel slits separated by an adjustable distance \(d\). While diminishing \(d,\) the first smearing of the pattern was observed in the focal plane of the objective at \(d=95 \mathrm{~cm} .\) Find \(\psi,\) assuming the wavelength of light to be eaual to \(\lambda=0.55 \mu \mathrm{m}\)
\(5.133 .\) Each star produces its own diffraction pattern in the objective's focal plane, with their zeroth maxima being separated by an angle \(\psi(\) Fig. 41\() .\) As the distance \(d\) decreases the angle \(\theta\) between the neighbouring maxima in each diffraction pattern increases, and when \(\theta\) becomes equal to \(2 \psi,\) the first deterioration of visibility occurs: the maxima of one system of fringes coincide with the minima of the other system. Thus, from the condition \(\theta=2 \psi\) and the formula \(\sin \theta=\lambda / d\) we obtain \(\psi=\lambda / 2 d \approx 0.06^{\prime \prime}\).