G3 TWO-SOURCE INTERFERENCE OF WAVES
G4 DIFFRACTION GRATINGS
Student Notes
I. TWO-SOURCE INTERFERENCE OF WAVES
A. INTERFERENCE PATTERNS FROM TWO SOURCES
B. YOUNG’S TWO-SLIT EXPERIMENT
II. DIFFRACTION GRATINGS
A. MULTIPLE SLIT DIFFRACTION
B. DIFFRACTION GRATINGS
I. TWO-SOURCE INTERFERENCE OF WAVES
A. INTERFERENCE PATTERNS FROM TWO SOURCES
REMEMBER: (Topic 4)
Coherent waves have constant phase difference
Consider: a string between two points S1 and S2, and point P between them:
Send identical waves from S1, S2 at same time. Will they hit P at the same time? NO!
and
so difference in arrival times is
we saw that:
Destructive interference is when path difference is:
Constructive interference is when path difference is:
At A, B, C and D crests line up: constructive
At E, troughs line up: destructive
If path difference anything other than integral or ½ integral
multiple of λ, wave is between 0 and 2A.
Sources: Physics for the IB Diploma, 5th Ed, Tsokos
Lines represent crests, 2 wave sources…
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Another pattern:
Lines are wavefronts (crests) in this
diagram.
If these were sound waves, where would it
be louder/softer?
Source: IB Physics, Oxford
Constructive and destructive interference
patterns!
Now consider coherent light going through
2 slits, S1 and S2 , projected onto screen
beyond.
THERE WILL BE ALTERNATE BRIGHT AND
DARK AREAS ON THE SCREEN.
d ~ 0.1 mm, P is ~ 2 m from slits. So S1P and
ZP are parallel and equal.
S2S1Z = θ
S2Z = d sinθ
On the screen, constructive interference if
S2Z = nλ
or
d sinθ = nλ
If θ is small, then sin θ is small, and sin θ ~ tan θ ~ θ ~ s/D in radians (CHECK!)
BUT:
Sources: Physics for the IB Diploma, 5th Ed, Tsokos
Path difference between them = S2Z.
So
We can say that linear separation of 2
consecutive maxima s on a screen is
Spacings are equally separated
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B. YOUNG’S TWO-SLIT EXPERIMENT
WAVE-PARTICLE DUALITY
Thomas Young, 1801.
Didn’t have lasers; filtered light, lens, through single
slit, then through double slits.
Assume: width of slits is ‘negligible’ compared to λs.
Source: Physics for the IB Diploma, 5th Ed, Tsokos
Interference pattern on the wall – patterns of light and dark areas. Fringes are equally bright.
A demonstration that light behaves as a wave and a particle.
Interference pattern shows light as a wave.
However, at the screen, the light is always found to be absorbed as though it were composed of
discrete particles or photons.
Wave–particle duality!
EXAMPLE 1
In Young’s two-slit experiment, a source of
light of unknown wavelength passes through
two narrow slits a distance 0.15 mm apart.
On a screen a distance 1.3 m from the slits,
bright spots are observed separated by a
distance of 4.95 m. What is the wavelength
of light being used?
[571 nm]
EXAMPLE 2
Calculate the fringe separation for light of
wavelength 680 nm that falls on two slits
separated by 0.1 mm when the screen is
placed 1.3 m from the slits.
[8.8 mm]
REMEMBER: When you shine 2 torches on a wall (overlapping light), why do you NOT see an
interference pattern?
For accurate
measurement
of slit
separation,
small d should
be used….
Source: Physics for the IB Diploma, 5th Ed, Tsokos
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II. DIFFRACTION GRATINGS
A. MULTIPLE SLIT DIFFRACTION
As # of slits increases, more complicated patterns.
Source: Physics for the IB Diploma, 5th Ed, Tsokos
Consider 4 equally spaced slits:
Assume path length between 1 and 2 = nλ = d sinθ
Then all other path lengths between adjacent slits
also = nλ = d sinθ
Constructive interference as nλ = d sinθ
Same as 2-slit case!
THEREFORE: maxima of multiple-slit interference
pattern at same angles as two-slit pattern with same
separation
If condition not satisfied, cancellation of waves from 4 slits, but cancellation not always complete,
so secondary maxima observed.
Source: Physics for the IB Diploma, 5th Ed, Tsokos
Interference pattern is different than with 2 slits.
2 SLITS
4 SLITS
PRIMARY and SECONDARY maxima.
6 SLITS
EXAMPLE 3
Calculate the slit separations for the intensity distribution patterns shown above for 2 slits, 4
slits, and 6 slits.
[all the same: 2λ]
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B. DIFFRACTION GRATINGS
Large number of parallel slits of ‘negligible’ width, or transparent slide with grooves cut.
PURPOSE: used in spectroscopy to measure λs of light.
Maxima are sharp and well-defined, so measuring separation is easy.
Maxima of pattern given by:
d sinθ = nλ
EXAMPLE 4
Light of wavelength 630 nm falls normally on a diffraction grating that has 600 lines per mm.
what is the angle separating the central maximum (n = 0) from the next (n = 1)? How many
maxima can be seen?
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