Refraction

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Refraction

• Minimize t with respect to x
• dt/dx0 using dL1/dxx/L1 sin?1 and
  dL2/dx(x-d)/L2 -sin?2
• dt/dx(n1sin ?1 - n2 sin ?2)/c 0

Time?
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n1 sin ?1 n2 sin ?2
?2?/2 gt sin ?c n2/n1
Water n1.5 Air n1.
?c 41.80
Reflection refraction
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(No Transcript)
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Doppler Effect for Light

• Recall for mechanical waves that all speeds are
  with respect to a medium
• detector fixed and source moving away f f
  1/(1vs/v) lt f
• source fixed and observer moving away f f (
  1- vd/v) lt f
• note f and f are different even if vsvd

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Doppler Effect at Low Speeds

• f f (v ? vD) /(v vS)
• 1/(1x) 1 - x
• 1/(1-x) 1 x ...
• if vS ltltv and vD ltltv , then f f ( 1 ?
  u/v) where u vS ? vD is relative speed of
  source with respect to detector

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Doppler Effect for Light

• can we use the same result for light by replacing
  v by c ? c3.00 x 108 m/s
• f f ( 1 u/c) higher if approaching!
  ultltc
• in astronomy we measure wavelengths
• c ? f ? f
• ? ? / ( 1 u/c)
• (? - ?)/ ? u/c Doppler shift
• decrease gt blue shift gt f increasegtapproach
• increase gt red shift gt f decrease gt receding
• light from all distant galaxies is red shifted
• gt moving away?

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Doppler Effect for Light

• ?u/c
• For source and detector separating
• f f0 (1-?2)1/2/(1?) red shift ? gt ? 0
• f0 (1-?)1/2/(1 ?)1/2
• For source and detector approaching
• f f0 (1 ?)1/2/(1- ?)1/2 blue shift ? lt ? 0

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Doppler Effect for Light

• For light, vc
• no medium is needed
• both cases should be the same
• Doppler effect for light depends only on the
  relative velocity of the source and detector
• time dilation is important

? u/c
f lt f0 if separating
Police radar uses microwaves gt needs
relativistic formula
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Doppler Effect

• Car approaching light (radar) travels at speed c

Same as for sound but involves different shifts!
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Problem

• A radar device emits microwaves with a frequency
  of 2.00 GHz. When the waves are reflected from a
  car moving directly away from the emitter, a
  frequency difference of 293 Hz is detected. Find
  the speed of the car.
• 1. The frequency f received by the car is given
  by f f0 (1- ?)1/2/(1 ?)1/2
  ? v/c
• 2. The car now acts as the source, sending
  signals of frequency f to the stationary radar
  receiver.
• 3. Consequently, frec f (1- ?)1/2/(1 ?)1/2
  f0 (1- ?)/(1 ?) ? f0 (1- 2?) since v ltlt
  c.
• 4. Solve for v v/c ?f/2f0 v
  (3x108x 293/(4x109 ) m/s 22 m/s 79.2 km/h

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Transverse Doppler Effect

• In previous cases, the relative motion was along
  the line connecting the source and receiver
• in general the relative velocity could be at
  some angle to this line
• time dilation only depends on the magnitude of

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Transverse Doppler Effect