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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 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 bigger

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Diffraction Patterns Diffraction is negligible if wavelength, λ, is much smaller than the opening, 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 B 1 has a greater distance to travel to get to point P than wavelet A 1 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

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Huygen’s Principle and Diffraction Destructive interference occurs when BC is equal to one half wavelength, then

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Huygen’s Principle and Diffraction If we divide the slit into 4 segments instead of two, then

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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

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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

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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

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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 Slits Supplemental Material With two slits, interference based on Interference pattern from one slit alone Interference coming from waves from different slit d = 16λ b = 3λ

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Diffraction Patterns – Two Slits Supplemental Material d = 4b 4 th 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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#1-4 Homework

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Topic 9.2 is an extension of Topic 4.4. Both single and the double-slit diffraction were considered in 4.4. Essential idea: Single-slit diffraction occurs.

Topic 9.2 is an extension of Topic 4.4. Both single and the double-slit diffraction were considered in 4.4. Essential idea: Single-slit diffraction occurs.

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