To measure the angular diostance `psi` between the components of a double star by Michelson's method, in front of a telescope's lens a diaphram was placeed, which has two narrow parallel slits separated by an adjustable disatnce `d`. While diminishing `d`, the first smearing of the pattern was observed in the focal plane of the objective at `d = 95cm`. Find `psi`, assuming the wavelength of light to be equal to `lambda = 0.55 mu m`.

Explanation

Each star produces its down diffraction pattern in the focal plane of the objective and these patterns are separated by angle `psi`. As the distance `d` decreases rthe angle `theta` between the neighbouring maxima in either diffraction pattern increases `(sin theta = lambda//d)`. When `theta` become equal to `2psi` the first deterioration of visibility occurs becuse the maxima of one system of fringes coincide with the minima of the other system. Thus from the condition
`theta = 2psi` and `sin theta = (lambda)/(d)` we get
`psi = (1)/(2)theta ~~(lambda)/(2d)`(radians)
Putting the values we get `psi ~= 0.06''`