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Problem 2 a. Using the telescope on-board his spaceship, Captain Kirk barely manages to resolve two distant galaxies that are 0.3 arc-seconds apart (1 arc-second 1/3600 Degree). If he is imaging at 550 nm wavelength, what is the effective aperture (diameter) of the objective lens of the telescope? Assume that there are no geometrical aberrations. (5 points) b. Consider the following imaging setup with a transverse magnification Iml3, If we are to resolve the image of the two fixed point sources separated by a distance of d 600 nm, what should the minimum angle θ be? Use small angle approximation, such that θ-sin θ, and assume that the imaging wavelength is 370 nm. (5 points) Convex)

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al The galaxies are 0.3 arcseconds apart. So, the angle in radians is: θ Un, 3600 180 now use Rayleighs diffraction limit criteria, dsine- 1.22 since the angle is very small, take the angle to be equal to sine of the angle [paraxial approximation) d 1.454 x 10-61 1.22(550 x 10-9] >d 0.461 m this is the effective aperture of the objective lens. b] |Magnification 3 so, size of the aperture must be: d 3 x 600 1800 nm wavelength 370 nm use Rayleighs diffraction limit criteria for paraxial approximation [1800nm]#2 1.22(370nm) 0.32 151.454 x 10-6radians 00.2507radians.

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