Double Slit Interference

1
Double Slit Interference

• Deriving
• l ws/D

2
2-source interference

• Interference arises from the superposition of
  waves.
• The two sources are coherent sources.

• Coherent sources result in waves that are
• in phase
• same wavelength
• same frequency.

3
Important Points

• When two crests meet, there is reinforcement.
• Where a crest and a trough meet, there is
  cancellation.
• If there is zero path difference, there is
  constructive interference (reinforcement).
• If there is a path difference of a whole number
  of wavelengths, there is constructive
  interference (reinforcement). Often we say that a
  whole number of wavelengths is an even number of
  half-wavelengths.
• If there is a path difference of ½, 1 ½ etc.
  wavelengths, there is destructive interference
  (cancellation). In other words, path difference
  of an odd number of half wavelengths leads to
  cancellation.
• All types of wave can interfere.

4
Youngs Double Slits
Lasers give off monochromatic (single colour)
coherent light
In the Eighteenth Century, Thomas Young did not
have a laser, so he had to make do with apparatus
like this
An ordinary bulb (or candle in Youngs day) does
not give off coherent light. The first slit
ensures that the light arriving at the double
slit is coherent.
5
Equation

D
w
Fringe spacing
Wavelength (m)
Slit spacing
Fringes
Distance from slit to the screen
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Explanation
Red laser light
The path difference is zero, so we get a bright
fringe in the middle.
s
D
The path difference is 1 whole wavelength, or 2
half-wavelengths. This gives another bright
fringe
The path difference is 1 half wavelength, so
there is cancellation, leading to a dark fringe
7
Derivation
We will look at the first bright fringe
P is at the 1st bright fringe. Therefore S1Q
l. OP is the fringe spacing w
Simple geometry tells us that triangles QS1S2
and OMP are similar. Therefore
Red laser light
S1
Q
D
O
s
M
S2
Therefore
Consider two rays, one going from S1 to P and
one going from S2 to P
and rearranging gives
P
Now draw a line perpendicular to S1P at Q.
8
Two Slit Interference
Double slit
Screen
Ray-box
Single slit
Fringes
Coloured Filter