Goal: To understand light

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Goal To understand light

• Objectives
• Speed of light in matter
• Summer vs winter
• Polarization
• Doppler effect

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Speed of light in matter

• In matter light is slowed.
• The fraction it is slowed is called the index of
  refraction (n)
• n c / v where v is the velocity of light in
  that material and c is the speed of light in a
  vacuum.
• And good to know that v ?f
• Quick sample If the speed of light in a fluid
  is half the speed of light in a vacuum then what
  is the index of refraction for that material?

3
Why are summers hotter than winters?
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Why are summers hotter than winters?

• http//www.astro.uiuc.edu/projects/data/Seasons/se
  asons.html

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Polarization

• A light photon is a 2 dimensional wave (i.e. a
  wave in a 2 dimensional plane) with some velocity
  in some direction.
• Usually each photon will come in at some random
  plane.
• This is unpolarized light.
• However, if the light is emitted preferentially
  in some plane, or is forced into it, then it will
  become polarized.

6
Linear polarization

• One way to polarize light is linearly.
• This means that some percentage of light comes in
  at some specific plane.
• The is the polarization.

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Circular polarization

• If the plane rotates with time in some way it is
  circularly polarized.
• However we will not deal with this type of
  polarization.

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Polarizers

• There are filters called polarizers.
• These devices absorb all the parts of light not
  polarized in a specific plane.
• The parts in the plane get through (sort of like
  a door for people not paying attention to it).

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Light through a polarizer

• The polarizer has a set angle it wants light to
  go through.
• If you shine unpolarized light through it then on
  average half will line up with it and half will
  not.
• So, half the light will get through.
• I ½ I0
• Furthermore the transmitted light will be
  linearly polarized in the direction of the
  polarizer.

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Polarized light through polarizer

• If polarized light goes through a polarizer then
  only the parts of the polarized light going in
  the direction of the polarizer get though.
• So, I I0 cos2(?)
• Where is the angle between the directions of the
  polarized light and the polarizer.
• This is called Maluss law

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Sample

• Unpolarized light of intensity 5 W/m2 passes
  through a polarizer oriented up and down. The
  light going through the polarizer is then allowed
  to pass through a 2nd polarizer which is tilted
  at a 45 degree angle from up and down.
• What is the intensity of light entering and
  leaving the 2nd polarizer?

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Sample

• Unpolarized light of intensity 5 W/m2 passes
  through a polarizer oriented up and down. The
  light going through the polarizer is then allowed
  to pass through a 2nd polarizer which is tilted
  at a 45 degree angle from up and down.
• What is the intensity of light entering and
  leaving the 2nd polarizer?
• For unpolarized I ½ I0 2.5 W/m2
• and is polarized up and down
• This enters the 2nd polarizer
• I I0 cos2(?) 2.5 W/m2 cos2(45 degrees)
• I 1.25 W/m2

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Try a harder one

• Unpolarized light with intensity of 12 W/m2
  enters a polarizer which is oriented up and down.
• This light is split in 2.
• Half goes into a 2nd polarizer which is oriented
  60 degrees from up and down.
• This light is then sent to a 3rd polarizer which
  is oriented 90 degrees from up and down (sideways
  basically).
• The other half of the light skips the 2nd
  polarizer and goes straight to the 3rd.
• What is the intensity of light going into and out
  of the 3rd polarizer?

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Try a harder one

• Unpolarized light with intensity of 12 W/m2
  enters a polarizer which is oriented up and down.
• I ½ I0
• 6 W/m2 comes out of the 1st polarizer.
• This light is split in 2.
• Half goes into a 2nd polarizer which is oriented
  60 degrees from up and down.
• I I0 cos2(?) 3 W/m2 cos2(60 degrees) 0.75
  W/m2

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Try a harder one

• This light is then sent to a 3rd polarizer which
  is oriented 90 degrees from up and down (sideways
  basically).
• I I0 cos2(?) but here the angle is from 60
  degrees (the direction of the polarized light)
  and 90, which is 30 degrees.
• So, I 0.75 W/m2 cos2(30 degrees) 0.56 W/m2
• The other half of the light skips the 2nd
  polarizer and goes straight to the 3rd.
• Here we go from 0 to 90, so the angle is 90.
• Since cos (90 degrees) 0, then I 0

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Add up

• Going into the 3rd is 3.75 W/m2 (3 from the
  shortened path 0.75 from the longer one)
• However, only 0.56 W/m2 comes out because the 3
  from the long path is ALL absorbed!

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Doppler Effect

• You have seen this hopefully in P218 (but with
  sound)
• Light does the same thing.
• If something is moving then the wavelength of the
  light emitted will change.
• If it is moving towards you, wavelength will
  decrease and frequency will go up.
• If it is moving away from you, wavelength will
  increase and frequency will go down.

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Equations

• fobserved fsource (1 v/c)
• Where v is the relative velocity between observer
  and source.
• Simple as that.
• You try a harder one
• A cop car moves at 40 m/s to catch up to a car
  going 10 m/s.
• The cop car emits a 10 GHz beam at the car.
• What is the shift in the frequency that the cop
  car gets back?
• Hint, you will have to find what the frequency
  the chased car sees because that will be the
  reflected frequency.

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Equations

• fobserved fsource (1 v/c)
• A cop car moves at 40 m/s to catch up to a car
  going 10 m/s.
• The cop car emits a 10 GHz beam at the car.
• Frequency car sees (since the cop car is
  approaching it)
• fo fs (1 v/c) 10 GHz (1 30 / 3108)
• This is reflected and comes back
• Since the cop car sees the car coming towards it
  also
• fo fs (1 v/c)
• 10 GHz (1 30 / 3108) (1 30 / 3108)
• 10 GHz 10 GHz 60 / 3108
• So, the change is 10 GHz 60 / 3108 2000 Hz

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Conclusion

• We have learned about the index of refraction
  when materials slow down light
• We learned why it is soooo cold in the winter.
• We learned about polarization and how to
  calculate fluxes through polarizers.
• We learned how to calculate the Doppler effect
  for light.