Multiple-Slit Interference

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Multiple-Slit Interference
Uniform slits, distance d apart. Light of
wavelength l. Screen L away
Thin slits ? compared to d)
L gtgt d then path length difference between
ADJACENT SLITS
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Multiple-Slit Interference Maxima
For MAXIMUM amplitude of combined waves (totally
constructive interference), need
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Multiple-Slit Interference Minima
More difficult need to consider of
slits/sources
2 slits
3 slits Try
get
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N 2 d 0.1 mm l 700 nm
N 3 d 0.1 mm l 700 nm
N 4 d 0.1 mm l 700 nm
N 5 d 0.1 mm l 700 nm
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N 2 d 0.1 mm l 700 nm
N 3 d 0.1 mm l 700 nm
N 4 d 0.1 mm l 700 nm
N 5 d 0.1 mm l 700 nm
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ConcepTest 42 The interference pattern of
four (thin) slits equally spaced a distance d
apart is shown. Consider the following choices
a) What is the phase difference between adjacent
slits for the CENTRAL MAXIMUM? b) What is the
phase difference between adjacent slits for the
FIRST SIDE MINIMUM?
1. 0 4. p
2. p/4 5. 3p/2
3. p/2 6. 2p
(back of card) None of the above (back of card) None of the above
c) What is the phase difference between adjacent
slits for the 2nd SIDE MINIMUM? d) What is
the phase difference between adjacent slits for
the 3rd SIDE MINIMUM?
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• Example Multiple Slit Interference Pattern
• Light of wavelength l is incident on four (thin)
  slits equally spaced a distance d apart. The
  interference pattern is shown on a screen a
  distance L away.
• What is the distance y, from the center of the
  screen to the first side minimum?
• What is the angular width of the central
  maximum?
• What happens as you decrease d?

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? First side minimum condition
(for FOUR narrow slits)
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N 5 d 0.1 mm l 700 nm
N 5 d 0.09 mm l 700 nm
N 5 d 0.08 mm l 700 nm
N 5 d 0.07 mm l 700 nm
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Diffraction Grating (better to think of it as an
Interference Grating)
ConcepTest 43 You look at a bright source of
white light through a diffraction grating.
Looking away from the center, you will see
colors. What color will you see closest to the
center?

• Multiple Slit Interference
• LOTS of Slits
• VERY thin
• VERY CLOSELY spaced

• Examples
• Diffraction Grating from lab
• Laser Vision Glasses
• CD (reflection grating)

1. Red 4. Green
2. Orange 5. Blue
3. Yellow 6. Violet
(back of card) Not enough info (back of card) Not enough info
Think about This What will you see at the
center?
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N 5 d 0.1 mm l 700 nm
N 5 d 0.1 mm l 600 nm
N 5 d 0.1 mm l 500 nm
N 5 d 0.1 mm l 400 nm
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Single Slit Diffraction
top
bottom
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Single Slit Diffraction
Multiple Slit Interference
(principal) MAXIMA occur at
MINIMA occur at
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Single Slit Diffraction
Two Slit Interference (thin slits)
a d
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Resolution Diffraction
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Resolution Diffraction
x
y
Rectangular aperture
Circular aperture Rayleighs Criterion
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Circular aperture, far field (Fraunhofer)
Circular obstruction Poisson/Fresnel bright spot
Circular aperture, near field, (Fresnel)
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