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hw1solution - MatSE 405 Spring 2010 Prof J Abelson HW...

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MatSE 405, Spring 2010, Prof. J. Abelson HW Problems #1 on Hammond Chs. 7 and 1, due Monday February 15 ANSWER KEY Chapter 7 1. In 1774 the self-taught astronomer William Herschel constructed a reflector telescope with a 6-inch diameter mirror and a 5- foot focal length. Using this instrument, he resolved for the first time that the Pole (North) star is in fact two closely-spaced stars. Note that the ultimate resolution limit of a lens also applies to a reflector; assume that the starlight is monochromatic with a wavelength of 550 nm. What must be minimum angular separation between the two stars ? Minimum angular separation, α zom = 1.22λ/ d = (1.22)(5.50e-7m)/(6in)(0.0254m/in) = 4.4e-6 rad = 2.5e-4 degrees 2. Consider the diffraction of light from a reflective grating that consists of parallel, very narrow mirrors spaced by a distance a . (This is analogous to a diffraction grating in which the slits are replaced by mirrors.) The wavelength of light is λ . Incident light hits the grating at an angle α off the normal to the surface.
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