# 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.

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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

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

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

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

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

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

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.

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.

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)

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

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.

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.

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.

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

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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