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Einstein ring
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== Introduction == Gravitational lensing is predicted by [[Albert Einstein]]'s theory of [[general relativity]].<ref name="NYT-20150305">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=Astronomers Observe Supernova and Find They're Watching Reruns |url=https://www.nytimes.com/2015/03/06/science/astronomers-observe-supernova-and-find-theyre-watching-reruns.html |date=March 5, 2015 |work=The New York Times |access-date=March 5, 2015 }}</ref> Instead of light from a source traveling in a straight line (in three dimensions), it is bent by the presence of a massive body, which distorts [[spacetime]]. An Einstein Ring is a special case of gravitational lensing, caused by the exact alignment of the source, lens, and observer. This results in symmetry around the lens, causing a ring-like structure.<ref name="NYT-20150305-video">{{cite news |last1=Drakeford |first1=Jason |last2=Corum |first2=Jonathan |last3=Overbye |first3=Dennis |date=March 5, 2015 |title=Einstein's Telescope β video (02:32) |url=https://www.nytimes.com/video/science/100000003552687/out-there-einsteins-telescope.html |access-date=December 27, 2015 |work=[[The New York Times]]}}</ref> [[File:Einstein ring geometry.svg|upright=1.7|thumb|The geometry of a complete Einstein ring, as caused by a [[gravitational lens]]]] The size of an Einstein ring is given by the [[Einstein radius]]. In [[radian]]s, it is :<math>\theta_1 = \sqrt{\frac{4GM}{c^2}\;\frac{D_{LS}}{D_S D_L}},</math> where : <math>G</math> is the [[gravitational constant]], : <math>M</math> is the mass of the lens, : <math>c</math> is the [[speed of light]], : <math>D_L</math> is the [[angular diameter distance]] to the lens, : <math>D_S</math> is the [[angular diameter distance]] to the source, and : <math>D_{LS}</math> is the [[angular diameter distance]] between the lens and the source.<ref>{{cite web |url=https://www.cfa.harvard.edu/~dfabricant/huchra/ay202/lectures/lecture12.pdf |title=Gravitational lensing |page=19 |last=Pritchard |first=Jonathan |publisher= Harvard and Smithsonian| access-date=21 December 2019 }}</ref> Over cosmological distances <math>D_{LS}\ne D_S-D_L</math> in general.
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