R1

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Synchronous (in phase) waves from two point
sources travel different path lengths to reach
point A.
A
Point A will experience complete destructive
interference if, for some integer m, the path
difference ?R1-R2 is exactly equal to
1. m? 2. (m ½)? 3. (m 1/4)? 4. 0
R1
R2
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?R1-R2
?
d
?/d sin?
? d sin?
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Diffraction through a slit
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Double-Slit Interference
Path difference ? between waves determines phase
difference
If ? is small (r1, r2 gtd) then
? d sin ?
m is an integer m 0, 1, 2, ...
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The magnetron of a microwave horn generates a
horizontally varying B-field and oscillating
vertical E-field. We found which of the
aluminum gratings below let the microwaves pass?

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Exposed to Neon laser light passing uninterrupted
through a narrow pair of slits, point P is the
location of a bright fringe in the resulting
interference pattern.
P
If a thin plate of clear crown glass held normal
to the path to P covered one of the slits, the
point P would

• still be a point of constructive interference.
• be a node (dark fringe) of destructive
  interference.
• have a phase difference between the two slits
  that
• depended on the thickness of the plate.

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Exposed to Neon laser light passing uninterrupted
through a narrow pair of slits, point P is the
location of a bright fringe in the resulting
interference pattern.
P
If a thin sheet of clear crown glass precision
ground exactly to a thickness equal to an
odd number of wavelengths N? is held normal to
the path to P covered one of the slits, the
point P would
nglass1.5

• still be a point of constructive interference.
• become a node (dark fringe) of destructive
  interference.
• have a phase difference between the two slits
  that
• depended on the number N.

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A train of waves of fixed frequency is traveling
along a thin, light cord toward the juncture to
a heavy, thick cord. Both cords are stretched
taut and under the same tension.
The waves that travel across the heavy cord will
have
1) greater speed than along the lighter cord.2)
the same speed as along the lighter cord. 3)
smaller speed than along the lighter cord.
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A train of waves of fixed frequency is traveling
along a thin, light cord toward the juncture to
a heavy, thick cord. Both cords are stretched
taut and under the same tension.
The waves traveling across the heavy cord have
1) larger wavelength than along the lighter
cord.2) the same wavelength as along the lighter
cord. 3) smaller wavelength than along the
lighter cord.
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Another way to get Interference

• Thin oil film on water
• Part of the incoming light is reflected off the
  top surface (point A), part at the lower surface
  (point B).
• Light traveling through oil travels extra
  distance (from A to B to C).
• If this distance is l, 2l, 3l, 4l,
• constructive interference!
• If this distance is l/2, 3/2l, 5/2l,
• destructive interference!

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A glass (n1.60) lens is coated with a thin film
of fluoride (MgF2, n1.38). What minimum film
thickness makes ?550 nm light non-reflecting?
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A glass (n1.60) lens is coated with a thin film
of fluoride (MgF2, n1.38). What minimum film
thickness makes ?550 nm light non-reflecting?
t?/4
180o phase change for each reflection