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 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. - PowerPoint PPT Presentation
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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 phenomena11.3 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 waves4.5 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 waves4.5 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 waves4.5 Wave properties
b = 12b = 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 waves4.5 Wave properties
Constructive interference
RELATIVE INTENSITY
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 waves4.5 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 1st minimum, the difference in distance (dashed) must be /2. Why?
Topic 11: Wave phenomena11.3 Diffraction
b
1 st min 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 phenomena11.3 Diffraction
b
1 st min x
yb2
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 phenomena11.3 Diffraction
b2
y
x
2
location of first minimum in single slit diffraction
= /b ( in radians)
Topic 11: Wave phenomena11.3 Diffraction
INCIDENT WAVE
DIF
FR
AC
TE
D
WA
VE
DIF
FR
AC
TE
D
WA
VE
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 phenomena11.3 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 phenomena11.3 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 phenomena11.3 Diffraction
Diffraction at a single slit
Solve problems involving single-slit diffraction. Be able to apply the formula = /b.
Topic 11: Wave phenomena11.3 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.
1st min PLD = /2. 2nd min PLD = 3/2.
1st 2nd
Central max PLD = 0. 2nd max PLD = .
Cent
2nd
Topic 11: Wave phenomena11.3 Diffraction
Diffraction at a single slit
Solve problems involving single-slit diffraction. Be able to apply the formula = /b.