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Transcript of 10 Interference of light - Hanyangoptics.hanyang.ac.kr/~shsong/10 Interference of light.pdf ·...
![Page 1: 10 Interference of light - Hanyangoptics.hanyang.ac.kr/~shsong/10 Interference of light.pdf · Hecht, Optics, Chapter 9. Two-Beam InterferenceTwo-Beam Interference ... Analysis of](https://reader030.fdocuments.us/reader030/viewer/2022021522/5b56c7d87f8b9ac31e8ccde9/html5/thumbnails/1.jpg)
This Lecture• Two-Beam Interference• Young’s Double Slit Experiment• Virtual Sources• Newton’s Rings• Film Thickness Measurement by Interference
Last Lecture• Wave equations• Maxwell equations and EM waves• Superposition of waves
Chapter 10. Interference of LightChapter 10. Interference of Light
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Two-Beam InterferenceTwo-Beam Interference
( ) ( )( ) ( )
1 2
1 01 1 1
2 02 2 2
:
, cos
, cos
Consider two waves E and E that have the same frequency
E r t E k r t
E r t E k r t
ω
ω ε
ω ε
= ⋅ − +
= ⋅ − +
r r
rr rr r
rr rr r
(polarizationdirection)Hecht, Optics, Chapter 9.
![Page 3: 10 Interference of light - Hanyangoptics.hanyang.ac.kr/~shsong/10 Interference of light.pdf · Hecht, Optics, Chapter 9. Two-Beam InterferenceTwo-Beam Interference ... Analysis of](https://reader030.fdocuments.us/reader030/viewer/2022021522/5b56c7d87f8b9ac31e8ccde9/html5/thumbnails/3.jpg)
Two-Beam InterferenceTwo-Beam Interference
Interferenceterm
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Two-Beam InterferenceTwo-Beam Interference
The interference term is given by
The irradiances for beams 1 and 2 are given by :
x
![Page 5: 10 Interference of light - Hanyangoptics.hanyang.ac.kr/~shsong/10 Interference of light.pdf · Hecht, Optics, Chapter 9. Two-Beam InterferenceTwo-Beam Interference ... Analysis of](https://reader030.fdocuments.us/reader030/viewer/2022021522/5b56c7d87f8b9ac31e8ccde9/html5/thumbnails/5.jpg)
Two-Beam InterferenceTwo-Beam InterferenceThe time averages are given by
The interference term is given by
: phase difference
![Page 6: 10 Interference of light - Hanyangoptics.hanyang.ac.kr/~shsong/10 Interference of light.pdf · Hecht, Optics, Chapter 9. Two-Beam InterferenceTwo-Beam Interference ... Analysis of](https://reader030.fdocuments.us/reader030/viewer/2022021522/5b56c7d87f8b9ac31e8ccde9/html5/thumbnails/6.jpg)
Two-Beam InterferenceTwo-Beam InterferenceThe total irradiance is given by
There is a maximum in the interference pattern when
This is referred to as constructive interference.
There is a minimum in the interference pattern when
This is referred to as destructive interference
When
![Page 7: 10 Interference of light - Hanyangoptics.hanyang.ac.kr/~shsong/10 Interference of light.pdf · Hecht, Optics, Chapter 9. Two-Beam InterferenceTwo-Beam Interference ... Analysis of](https://reader030.fdocuments.us/reader030/viewer/2022021522/5b56c7d87f8b9ac31e8ccde9/html5/thumbnails/7.jpg)
VisibilityVisibility
Visibility = fringe contrast
{ } 10 minmax
minmax ≤≤+−
≡ V IIIIV
When
Therefore, V = 1
![Page 8: 10 Interference of light - Hanyangoptics.hanyang.ac.kr/~shsong/10 Interference of light.pdf · Hecht, Optics, Chapter 9. Two-Beam InterferenceTwo-Beam Interference ... Analysis of](https://reader030.fdocuments.us/reader030/viewer/2022021522/5b56c7d87f8b9ac31e8ccde9/html5/thumbnails/8.jpg)
Conditions for good visibilityConditions for good visibilitySources must be:
same in phase evolution in terms of time (source frequency) temporal coherencespace (source size) spatial coherence
Same in amplitude
Same in polarization
Very goodNormal
Very bad
![Page 9: 10 Interference of light - Hanyangoptics.hanyang.ac.kr/~shsong/10 Interference of light.pdf · Hecht, Optics, Chapter 9. Two-Beam InterferenceTwo-Beam Interference ... Analysis of](https://reader030.fdocuments.us/reader030/viewer/2022021522/5b56c7d87f8b9ac31e8ccde9/html5/thumbnails/9.jpg)
Young’s Double Slit ExperimentYoung’s Double Slit Experiment
Hecht, Optics, Chapter 9.
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Assume that y << s and a << s.
The condition for an interference maximum is
The condition for an interference minimum is
Relation betweengeometric path differenceand phase difference :
a
s
y
Δ
θ
Young’s Double Slit InterferenceYoung’s Double Slit Interference
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On the screen the irradiance pattern is given by
Assuming that y << s :
Bright fringes:
Dark fringes:
Young’s Double Slit InterferenceYoung’s Double Slit Interference
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Interference Fringes From 2 Point SourcesInterference Fringes From 2 Point Sources
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Interference Fringes From 2 Point SourcesInterference Fringes From 2 Point Sources
Two coherent point sources : P1 and P2
![Page 14: 10 Interference of light - Hanyangoptics.hanyang.ac.kr/~shsong/10 Interference of light.pdf · Hecht, Optics, Chapter 9. Two-Beam InterferenceTwo-Beam Interference ... Analysis of](https://reader030.fdocuments.us/reader030/viewer/2022021522/5b56c7d87f8b9ac31e8ccde9/html5/thumbnails/14.jpg)
Interference With Virtual Sources:Fresnel’s Double Mirror
Interference With Virtual Sources:Fresnel’s Double Mirror
Hecht, Optics, Chapter 9.
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Interference With Virtual Sources:Lloyd’s Mirror
Interference With Virtual Sources:Lloyd’s Mirror
mirror
Rotationstage
Lightsource
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Interference With Virtual Sources:Fresnel’s Biprism
Interference With Virtual Sources:Fresnel’s Biprism
Hecht, Optics, Chapter 9.
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Interference in Dielectric FilmsInterference in Dielectric Films
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Analysis of Interference in Dielectric FilmsAnalysis of Interference in Dielectric Films
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Analysis of Interference in Dielectric FilmsAnalysis of Interference in Dielectric FilmsThe phase difference due to optical path length differences for the front and back reflections is given by
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Analysis of Interference in Dielectric FilmsAnalysis of Interference in Dielectric Films
Also need to account for phase differencesΔr due to differences in the reflection processat the front and back surfaces
Constructive interference
Destructive interference
![Page 21: 10 Interference of light - Hanyangoptics.hanyang.ac.kr/~shsong/10 Interference of light.pdf · Hecht, Optics, Chapter 9. Two-Beam InterferenceTwo-Beam Interference ... Analysis of](https://reader030.fdocuments.us/reader030/viewer/2022021522/5b56c7d87f8b9ac31e8ccde9/html5/thumbnails/21.jpg)
Fringes of Equal InclinationFringes of Equal Inclination
Fringes arise as Δ varies due to changesin the incident angle:
Constructive interference
Destructive interference
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Fringes of Equal ThicknessFringes of Equal Thickness
When the direction of the incoming light is fixed, fringes arise as Δ varies due to changesin the dielectric film thickness :
Constructive interference
Destructive interference
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Fringes of Equal Thickness: Newton’s RingsFringes of Equal Thickness: Newton’s Rings
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Fringes of Equal Thickness: Newton’s RingsFringes of Equal Thickness: Newton’s Rings