Diffraction and
Interference
IB Syllabus Details:
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4.5.3:
4.5.3: Explain and discuss qualitatively the diffraction of waves at
apertures and obstacles
4.5.4:
4.5.4: Describe examples of diffraction
4.5.5:
4.5.5: State the principle of superposition and explain what is meant
by constructive interference and by destructive interference
4.5.6:
4.5.6: State and apply the conditions for constructive and for
destructive interference in terms of path difference and phase
difference.
4.5.7:
4.5.7: apply the principle of superposition to determine the resultant
resultant
of two waves
11.3.1:
11.3.1: Sketch the variation with angle of diffraction of the relative
intensity of light diffracted at a single slit.
11.3.2:
11.3.2: Derive the formula θ = λ/b for the position of the first
minimum of the diffraction pattern produced at a single slit.
11.3.3:
11.3.3: Solve problems involving singlesingle-slit diffraction.
Diffraction
 Diffraction
and interference are
characteristics that are unique to waves.
 Diffraction = the spreading of a wave as it
goes past an obstacle or through an
aperture.
– Note: the wavelength of the wave must be
“comparable” or bigger than the obstacle or
opening
– Consider sound vs. light
Consider Huygens’ Principle
Interference
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Interference is the result of superposition of two
waves.
– Thomas Young and light in 1801
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Constructive Interference occurs when the wave
from one source arrives at a point after having
traveled an integral multiple of the wavelength
compared to the wave from another source.
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Destructive Interference occurs when the wave
from one source arrives at a point after having
traveled a halfhalf-integral multiple of the
wavelength compared to the wave from another
source.
When crests from two sources overlap,
constructive interference occurs and the result is
a wave with twice the amplitude of the original
two.
– If sound, this would be a loud point. If light, this
would be a bright spot
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Interference
When crests from one source overlaps with
troughs from another, destructive interference
occurs and the result is no wave.
– If sound, this would be a quiet point. If light, this
would be a dark spot.
– Path difference = nλ
nλ
– Path difference = (n + ½)λ
½)λ
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Example
 Waves
leaving two sources arrive at point
P. Point P is 12 m from the first source
and 16.5 m from the second. The waves
have a wavelength of 3 m. What is
observed at P?
TwoTwo-source Interference
 If
monochromatic, coherent light diffracts
through two small slits, at some angles
the path difference will cause constructive
and alternately destructive interference—
interference—
bright and dark patterns.
– The path difference is 4.5 m. It equals (1 +
½) x 3 m. This is a halfhalf-integral multiple of
the wavelength, thus destructive interference
occurs.
– Monochromatic means same wavelength
– Coherent is consistent phase difference
(synchronous)
Young’s twotwo-slit experiment
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Proved wave nature of light in 1801, not
generally accepted for about 20 years.
Double slit constructive interference (maxima)
equation:
– dsinθ
dsinθ = nλ
nλ
 d is the slit separation
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Distance between successive maxima (s) on a screen:
– s = (λ
(λD)/d
 D = distance to screen
 d = slit distance apart
 Note that distance between maxima increases with increased
distance to the screen and with decreased slit distance.
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Example Problem
A
doubledouble-slit experiment is performed to
measure the wavelength of red light. The
slits are 0.0190 mm apart. A screen is
placed 0.600 m away, and the firstfirst-order
bright band is found to be 21.1 mm from
the central bright band. What is the
wavelength of the red light?
– Answer: Using s = (λ
(λD)/d, find λ = 6.68 x 10-7
m (668 nm)
Single slit diffraction pattern
SingleSingle-slit diffraction
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When a wave diffracts through a single opening,
at certain angles the ray from one edge of the
slit will be traveling ½ wavelength more than
those from the middle, resulting in destructive
interference (a dark band or minimum).
First minimum at θ ≈ λ/b
– θ = angle where the first minimum occurs
– b = slit width
– Note: a narrower slit width means a wider central
maximum (first minimum is farther apart)
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First minimum at θ ≈ 1.22(λ
1.22(λ/b) for circular
openings
Example Problem
 Monochromatic
green light of wavelength
546 nm falls on a single slit with a width
of 0.095 mm. The slit is located 75 cm
from a screen. How wide will the central
bright band be?
 Answer: Using θ ≈ λ/b and trig, you will
find that x = 4.3 mm.
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Effects of slit width on double slit
pattern
 If
the two slits are small compared to
wavelength, the maxima will have equal
amplitudes.
 If the slit width is large compared to
wavelength, then the result is a
combination single and doubledouble-slit pattern.
The Single slit pattern modulates the
doubledouble-slit pattern with maxima still
occurring at the same places.
Double slit diffraction pattern with large apertures
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