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Lecture 19 RelativityLimit on Angular ResolutionCan We See a Distant Planet?RelativityBasis for Special RelativityAdding Velocities in Galilean RelativityEinstein’s RelativityLecture 19Relativity Chapter 26.1  26.5Outline•Resolution Due to Diffraction•Principles of Relativity•Speed of LightLimit on Angular ResolutionAngular resolution is the minimum angle (min ) between any two objects to be viewed separately.Two objects are considered just resolved if the central maximum of one image positionally coincides with the first minimum of the second image. sin  =  aWave nature of light puts a limit to the ability to resolve distant objects.min   /a (radians) is small min = 1.22 /D radians (circular aperture)Can We See a Distant Planet?The Sun  Earth distance is 1.5 1013 cmThe Keck telescope has D = 10 mAt  = 400 nm (blue light), min = 5 108 radianThe closest star is at the distance d = 3 1018 cmmindxx = d min = 1.5 1011 cm = 1% Sun  Earth distanceRelativityThe theory of relativity was proposed by Albert Einstein in 1905.Newtonian mechanics deals with low velocities.It does not observe any limit for velocity.Relativity links space and time as well as matter and energy.There are 2 parts of the theory: special relativity and general relativity.Special relativity considers only constant velocities.General relativity includes acceleration.Basis for Special RelativityEinstein’s relativity:• The laws of physics are the same in any inertial frame of reference.•The speed of light is the same for all observers, no matter what their relative speeds.c = 3 108 m/s = 300,000 km/s = 186,000 mi/sGalilean relativity: the laws of mechanics are the same in all inertial (non-accelerated) reference frames.The laws of electromagnetism seem to be incorrect.Adding Velocities in Galilean RelativityEinstein’s RelativityExamples ProofDetailsEinstein’s biographyYour own possible


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UT PHYS 2080 - Relativity

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