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1. One technique for observing an interference pattern produced by two slits is to illuminate them with two parallel rays, place a converging lens behind the plane of the slit, and observe the interference pattern on a screen placed in the focal plane of the lens. 1.1. Discuss the interference pattern that is produced on the screen. (5 points) 1.2. Prove that the position of the bright fringes with respect to the central nfλ maximum is given by x= ^, where n is an integer, f the focal length of the lens, is the wavelength and "a" the separation of the slits. (8 points) 2 the bright fringes of 2a one beam lie above the dark fringes of the other beam, therefore the interference pattern disappears. (8 points) KEM 1.3. Prove that the position of the minima (dark fringes) is given by x = (5 points) A variant of this experiment is to use two beams of monochromatic light, of the same wavelength > that form a small angle 8 between them, which fall on the separation slits "a". due to the angular displacement of the beam, the two groups of fringes that are observed on the screen, placed in the focal plane of the lens, do not coincide. 1.4. Prove that when 8 = (2n+1)fa 2a Fizeau proposed in 1868 this method to measure the angular separation between two distant objects, varying the separation "a", until the interference pattern disappears. For example, to measure the angular separation between two stars, the slits are placed in front of the telescope objective and the separation is varied until the diagram disappears. 1.5. Determine the minimum angular separation that can be measured by the Mount Wilson Telescope whose objective has a diameter of 2.54 m. Use wavelength λ = 570 nm. (5 points)