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Diffraction of Light

Problem 5.133

To measure the angular distance ψ\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 dd. While diminishing d,d, the first smearing of the pattern was observed in the focal plane of the objective at d=95 cm.d=95 \mathrm{~cm} . Find ψ,\psi, assuming the wavelength of light to be eaual to λ=0.55μm\lambda=0.55 \mu \mathrm{m}

Reveal Answer
5.133.5.133 . Each star produces its own diffraction pattern in the objective's focal plane, with their zeroth maxima being separated by an angle ψ(\psi( Fig. 41).) . As the distance dd decreases the angle θ\theta between the neighbouring maxima in each diffraction pattern increases, and when θ\theta becomes equal to 2ψ,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 θ=2ψ\theta=2 \psi and the formula sin⁡θ=λ/d\sin \theta=\lambda / d we obtain ψ=λ/2d≈0.06′′\psi=\lambda / 2 d \approx 0.06^{\prime \prime}.
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