Lecture 19 Relativity Chapter 26.1  26.5 Outline Resolution Due to Diffraction Principles of Relativity Speed of Light

Limit on Angular Resolution Angular resolution is the minimum angle (min ) between any two objects to be viewed separately. Wave nature of light puts a limit to the ability to resolve distant objects. Two objects are considered just resolved if the central maximum of one image positionally coincides with the first minimum of the second image.  sin  =  a  is small  min  /a (radians) min = 1.22 /D radians (circular aperture)

Can We See a Distant Planet? The Sun  Earth distance is 1.5 1013 cm The Keck telescope has D = 10 m At  = 400 nm (blue light), min = 5 108 radian The closest star is at the distance d = 3 1018 cm min x d x = d min = 1.5 1011 cm = 1% Sun  Earth distance

Relativity Newtonian mechanics deals with low velocities. It does not observe any limit for velocity. The theory of relativity was proposed by Albert Einstein in 1905. 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 Relativity Galilean relativity: the laws of mechanics are the same in all inertial (non-accelerated) reference frames. The laws of electromagnetism seem to be incorrect. Einstein’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/s

Adding Velocities in Galilean Relativity

Einstein’s Relativity Einstein’s biography Examples Proof Details Your own possible experiment