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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.

 is small  min  /a (radians)
sin  = 
a
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
d
min
x = d min = 1.5 1011 cm = 1% Sun  Earth distance
x
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