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Unformatted text preview: 3. Coherent light of wavelength from two different stars arrives at the earth separated by angle = 1 - 2 . This light passes through a two-slit apparatus (slit separation d), and the interference pattern is observed on a screen very far away compared to d. Ignore diffraction effects. a) Find the condition for destructive interference at the screen of the light coming from star 1. b) Find the condition for constructive interference at the screen of the light coming from star 2. c) To determine the angle , astronomers adjust the separation d until the interference maxima of the two stars are just resolved. This occurs when the position of a maximum for star 2 occurs at the position of a minimum (of the same order) for star 1. Combine your results from a) and b) to find a simple expression for in terms of and d when all the angles are small.
Star 1 Star 2 1 2 d Solution a) Just as we did on the quiz, d sin 1 + d sin = (m + 1/2), m = 0, 1, 2, ... b) d sin 2 + d sin = n, n = 0, 1, 2, ... c) Of the same order means we can take m = n in a). Now subtract these equations: d sin 1 - d sin 2 = 2 In the limit where the angles are small, sin 1 1 and sin 2 2 : d(1 - 2 ) = d = = 2d 2 ...
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