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Unformatted text preview: so that they get to a single point on the focal plane, and images from different stars get to different such points.) Because of the diffraction effect, we are here interested in the question of whether these images can be resolved. In practice, if we observe a binary star system, do we see it as a binary (i.e., our angular resolution is good enough to resolve the two stars), or do we see it as a single star (because we cannot resolve the two stars; there are other methods to tell its a binary system even if the best telescope cannot resolve the system visually)? R 1 . 22 a = 1 . 22 550 10- 9 m 32 10- 3 m = 2 . 1 10- 5 rad = 4 . 33 At this angular separation each central maximum is centered on the first minimum of the other curve. Notice that the result is independent of the focal length of the lens, and depends only on the ratio /a . We therefore want telescopes to have as large apertures as possible, to obtain better angular resolution. The largest apertures are about 10m in diameter, so that the best angular resolution any optical telescope can have is R 6 . 6 10- 8 rad 0 . 01. The separation of two images at the angular resolution threshold is x = f R = 0 . 24 m 2 . 1 10- 5 rad = 5 m . Diffraction by a double slit : Consider now two wide slits separated by a , each of width b so that a > b . We do the same kind of integral over Huygens wavelets here as we did in the case of a single wide slit, except that here the integration interval is the nonconnected range of two slits. That is, now wethat here the integration interval is the nonconnected range of two slits....
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- Spring '09