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DEVIL PHYSICSTHE BADDEST CLASS ON
CAMPUSIB PHYSICS
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TSOKOS LESSON 4-7DIFFRACTION
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Assessment Statements
AHL Topic 11.3. and SL Option A-4 Diffraction:
11.3.1. Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit.
11.3.2. Derive the formula for the position of the first minimum of the diffraction pattern produced at a single slit.
11.3.3. Solve problems involving single-slit diffraction.
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Objectives
Understand diffraction and draw the different diffraction patterns from a rectangular slit, a sharp edge, a thin tube, and a circular aperture
Appreciate that the first minimum in single-slit diffraction past a slit of width b is approximately at an angle θ = λ/b
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Objectives
Draw the intensity patterns for a single slit of finite width and for two slits of negligible width
Show the effect of slit width on the intensity pattern of two slits
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Reading Activity Questions?
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Introductory Video:Diffraction of Light
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Diffraction
The spreading of a wave as it goes past an obstacle or through an aperture
Value of the wavelength in comparison to the obstacle or aperture defines the diffraction pattern
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Case 1: Wavelength Much Smaller Than Aperture
Virtually no diffraction takes place
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Case 2: Wavelength Comparable to or Bigger than Aperture
Diffraction takes place ‘Comparable’ means a few times
smaller to slightly larger than
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Diffraction Around an Obstacle
Sound, with a much larger wavelength, will diffract around the corner of a building but light will not
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Case 1: Wavelength Much Smaller Than Obstacle
Virtually no diffraction takes place
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Case 2: Wavelength Comparable to or Bigger than Obstacle
Diffraction takes place ‘Comparable’ means a few times
smaller to slightly larger than
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Diffraction Patterns
When light is diffracted, both constructive and destructive interference occurs
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Diffraction Patterns
Diffraction is appreciable if wavelength, λ, is of the same order of magnitude as the opening, b, or biggerb
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Diffraction Patterns
Diffraction is negligible if wavelength, λ, is much smaller than the opening, b
b
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Huygen’s Principle and Diffraction Every point on a
wavefront acts as a secondary source of coherent radiation
Each point forms its own wavelet
These wavelets will interfere with each other at some distant point
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Huygen’s Principle and Diffraction Because of the
diffraction angle, wavelet B1 has a greater distance to travel to get to point P than wavelet A1
This results in the wavelets arriving at point P out of phase with each other
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Huygen’s Principle and Diffraction If the difference is
equal to half a wavelength, the wavelets are 180° out of phase and they completely cancel each other through superposition
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Huygen’s Principle and Diffraction If the difference is
equal to one entire wavelength, the wavelets are in phase and they form a wavelet of double the original amplitude
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Huygen’s Principle and Diffraction Everything in
between will show varying levels of constructive and destructive interference
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Huygen’s Principle and Diffraction Since the two
triangles in the diagram are similar triangles, the same interference pattern will result at point P from all pairs of wavelets
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Huygen’s Principle and Diffraction If we approximate AP and BP to be
parallel since P is distant and ACB to be a right angle, then
BCb
b
BC
sin2
2sin
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Huygen’s Principle and Diffraction Destructive interference occurs when
BC is equal to one half wavelength, then
sin
sin22
2
sin2
b
b
BC
BCb
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Huygen’s Principle and Diffraction If we divide the slit into 4 segments
instead of two, then
sin2
sin42
2
sin4
b
b
BC
BCb
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Huygen’s Principle and Diffraction In general, destructive interference
occurs when,
This equation gives the angle at which minima will be observed on a screen (P) behind an aperture of width b through which light of wavelength λ passes
,...3,2,1
sin
n
bn
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Huygen’s Principle and Diffraction Since the angle θ is typically small, we
can approximate sin θ ≈ θ (if the angle is in radians), so the first minima would fall at
And for circular slits the formula becomes
b
b
22.1
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Diffraction Patterns Minima (blank spaces) appear in pairs Maxima (bright spaces) appear about
halfway between minima Smaller slit means larger central
maximum
b = 2λ
b = 3λ
b
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Diffraction Patterns If λ > b, then sin > 1 which is
impossible, i.e., does not exist The central maximum is so wide that the
first minima does not exist If λ ≈ b, then several minima and
maxima exist If λ « b, then sin o which means 0
which means the light passes straight through without bending
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Single-Slit Diffraction Video
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Diffraction Patterns – Two SlitsSupplemental Material With two slits, interference based on
Interference pattern from one slit alone Interference coming from waves from
different slit
d = 16λ
d = 16λb = 3λ
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Diffraction Patterns – Two SlitsSupplemental Material
d = 4b4th maximum missing
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Summary Video
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Σary Review
Do you understand diffraction and draw the different diffraction patterns from a rectangular slit, a sharp edge, a thin tube, and a circular aperture?
Do you appreciate that the first minimum in single-slit diffraction past a slit of width b is approximately at an angle θ = λ/b?
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Σary Review
Can you draw the intensity patterns for a single slit of finite width and for two slits of negligible width?
Can you show the effect of slit width on the intensity pattern of two slits?
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Assessment Statements
AHL Topic 11.3. and SL Option A-4 Diffraction:
11.3.1. Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit.
11.3.2. Derive the formula for the position of the first minimum of the diffraction pattern produced at a single slit.
11.3.3. Solve problems involving single-slit diffraction.
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QUESTIONS?
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#1-4
Homework