Physics 202, Lecture 26

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Physics 202, Lecture 26

• Todays Topics
• Wave Nature of Waves Interference
• Breakdown of ray approximation
• Huygens principle
• Light as Waves
• Double-Slit Interference
• Multi-Slit Interference

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Reminder Light and Optics

• Nature of Lights
• Lights as rays
• Lights as EM waves f, l, f, v, A, interference
  
• Lights as group of photons
• Optics Physics of lights
• Geometric Optics Treat light as rays (Ch. 35,36)
• ? Ray approximation.
• Wave Optics Wave properties becomes important
• Interferences,
  diffraction(Ch. 37,38)

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Ray Approximation

• When the wavelength of the light is much smaller
  than the size of the optical objects it
  encounters, it can be treated as (colored) rays.

Ray approximation is not valid near the gap when
ld. OK elsewhere
Ray approximation is valid when lltltd
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The Huygens Principle

• Every point on a wave front can be considered as
  a secondary source of waves that spread out in
  the forward direction. The new wave is the result
  of the superposition of these secondary waves

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Reminder Light Waves

• Nature of Lights
• Rays (classical), ?EM waves?, ?Photons?.
• Review Electromagnetic plane waves
• E Emaxsin(wt-kxf), B Bmaxsin(wt-kxf), E/Bc
• As the E component and B component of an EM wave
  are 100 correlated, we can use just one of
• them to represent an EM wave.

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Interference of Light Waves

• When two light waves meet at certain location,
  the resulting effect is determined by the
  superposition ( i.e. sum) of the two
  individual waves
• e.g. Two light waves with same color and
  amplitude.
• E1 E0sin(wt-kxf10) E0sin(wtf1)
• E2 E0sin(wt-kxf20) E0sin(wtf2)
• EE1E2 2E0 cos(Df/2) sin(wt f/2)
• Resulting amplitude Emax 2E0cos(Df/2)
• Constructive interference Df0, 2p, 4p,
  Emax2E0
• Destructive interference Dfp, 3p, 5p,
  Emax0
• Quiz If the intensity of each incoming light is
  I, what is the resulting intensity when
  (1)constructive, (2)destructive?

Dff1-f2 f(f1f2)/2
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Test of the Wave Nature of Light Double-Slit
Experiment
Diffraction interference

• Rays or Waves

If lights behave as rays
If lights behave as waves
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Youngs Famous Double-Slit Experiment Thomas
Young (1803)

• See demo

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Double-Slit Experiment Explained

• The experiment can be easily explained by
  interference

Constructive, Df0p, 2p, 4p,..
Destructive, Dfp, 3p, 5p,..
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Double-Slit Experiment Explained

• The experiment can be easily explained by
  interference

Constructive, Df0p, 2p, 4p,..
Destructive, Dfp, 3p, 5p,..
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Quantitatively
path length difference d dsinq dq d y/l
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Double-Slit Experiment Explained

• Constructive Df 0p, 2p, 4p,, or 2mp, m0,1,2
• Destructive Df p, 3p, 5p,, or (2m1) p,
  m0,1,2

Bright spots
Dark spots
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Multi-Slit Interference
N slits
Self reading Phasor Method (Not to be examed)

• secondary maxima N -2
• Higher N ? more suppression on secondary minima
• (Grating Ngt1000, highly sensitive to l, good
  for measuring l.