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Diffraction at a single slit 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 = /b 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. Be able to apply the formula = /b. Topic 11: Wave phenomena 11.3 Diffraction

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Diffraction at a single slit Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit. If a wave meets a hole in a wall that is of comparable size to its wavelength, the wave will be bent through a process called diffraction. If the aperture (hole, opening, etc.) is much larger than the wavelength, diffraction will be minimal to nonexistent. Topic 4: Oscillations and waves 4.5 Wave properties INCIDENT WAVE DIFFRACTED WAVE REFLECTED WAVE

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Diffraction at a single slit Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit. Huygen’s principle states “Every point on a wavefront emits a spherical wavelet of the same velocity and wavelength as the original wave.” Note that because of Huygen’s principle waves can turn corners. Topic 4: Oscillations and waves 4.5 Wave properties

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Diffraction at a single slit Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit. The reason waves can turn corners is that the incoming wave transmits a disturbance by causing the medium to vibrate. And wherever the medium vibrates it becomes the center of a new wave front as illustrated. Note that the smaller the aperture b the more pronounced the effect. Topic 4: Oscillations and waves 4.5 Wave properties b = 12 b = 6 b = 2 b b b

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Diffraction at a single slit Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit. Huygen’s wavelets not only allow the wave to turn corners, they also interfere with each other. Topic 4: Oscillations and waves 4.5 Wave properties Constructive interference R E L A T I V E I N T E N S I T Y Destructive interference

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EXAMPLE: If light is diffracted by a circular hole, a planar cross-section of the interference looks like the picture below. What will the light look like head-on? Diffraction at a single slit Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit. Topic 4: Oscillations and waves 4.5 Wave properties

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Diffraction at a single slit Derive the formula = /b for the position of the first minimum of the diffraction pattern produced at a single slit. Consider a single slit of width b. From Huygen’s principle we know that every point within the slit acts as a wavelet. At the central maximum we see that the distance traveled by all the wavelets is about equal, and thus has constructive interference. Consider points x at one edge and y at the center of the slit: At the 1 st minimum, the difference in distance (dashed) must be /2. Why? Topic 11: Wave phenomena 11.3 Diffraction b 1 s t m i n x y Condition for destructive interference.

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Diffraction at a single slit Derive the formula = /b for the position of the first minimum of the diffraction pattern produced at a single slit. We will choose the midpoint of the slit (y) as our reference. And we will call the angle between the reference and the first minimum . We construct a right triangle as follows: Why does the side opposite equal /2? Topic 11: Wave phenomena 11.3 Diffraction b 1 st min x y b2b2 y x 2 Condition for destructive interference.

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Diffraction at a single slit Derive the formula = /b for the position of the first minimum of the diffraction pattern produced at a single slit. From the right triangle we see that sin = ( /2)/(b/2) sin = /b. Perhaps you recall that if is very small (and in radians) then sin ( in rad). Finally… Topic 11: Wave phenomena 11.3 Diffraction b2b2 y x 2 location of first minimum in single slit diffraction = /b ( in radians)

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Topic 11: Wave phenomena 11.3 Diffraction INCIDENT WAVE DIFFRACTED WAVE REFLECTED WAVE Diffraction at a single slit Solve problems involving single-slit diffraction. Be able to apply the formula = /b. PRACTICE: Sketch in the diffraction patterns in the double-slit breakwater with 5-m waves. Then map out MAX (10 m), MIN (-10 m) and 0 m points. 10 0 -10

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Topic 11: Wave phenomena 11.3 Diffraction Diffraction at a single slit Solve problems involving single-slit diffraction. Be able to apply the formula = /b. Diffraction allows waves to turn corners. All waves diffract- not just sound.

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Topic 11: Wave phenomena 11.3 Diffraction Diffraction at a single slit Solve problems involving single-slit diffraction. Be able to apply the formula = /b. Huygen says the wavelets will be spherical.

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Topic 11: Wave phenomena 11.3 Diffraction Diffraction at a single slit Solve problems involving single-slit diffraction. Be able to apply the formula = /b.

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Topic 11: Wave phenomena 11.3 Diffraction Diffraction at a single slit Solve problems involving single-slit diffraction. Be able to apply the formula = /b. Caused by path length difference (PLD) along b. 1 st min PLD = /2. 2 nd min PLD = 3 /2. 1 st 2 nd Central max PLD = 0. 2 nd max PLD =. Cent 2 nd

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Topic 11: Wave phenomena 11.3 Diffraction Diffraction at a single slit Solve problems involving single-slit diffraction. Be able to apply the formula = /b. = /b d tan = d/D tan for small . = d/D = /b. d = D/b.

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