Interference of Light
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Transcript of Interference of Light
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Interference of LightInterference of Light
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Refraction (a review)Refraction (a review)• Character of the wave Character of the wave
in different in different (transparent) media(transparent) media– wave travels slowerwave travels slower– Index of refraction Index of refraction
n = c/vn = c/v– frequency is constant frequency is constant
(wavelength changes)(wavelength changes)• Law of Refraction Law of Refraction
(Snell’s Law)(Snell’s Law)nn11 sin sin = n = n22 sin sin
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Huygens Principle
• Propagation of plane wave by Huygen’s principle
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Snell’s Law• Refraction • Similar triangles
2
2
1
1
sinsin
2211 sinsin nn
2
2
1
1
vt
vt
refraction ofIndex
vcn
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Young’s Double SlitYoung’s Double Slit
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Young’s Double Slit 1801Young’s Double Slit 1801• Conditions for interferenceConditions for interference
sin12 drrL
yL
Ly
tansinLyd
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Young’s Double SlitYoung’s Double Slit
Constructive interference phase difference to Constructive interference phase difference to be an integral number of wavelengthsbe an integral number of wavelengths
,......2,1,0 wheresin
mmdL
Lydm sin
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Destructive Interference Destructive Interference ConditionCondition
Destructive interference Destructive interference (minima)(minima)
Lyd
2
1m
Lyddm
sin
21
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Young’s Double SlitYoung’s Double SlitIntensity behaviorIntensity behavior
tEEtEE
02
01
sinsin
tEtEE 00P sinsin
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Young’s Double SlitYoung’s Double SlitIntensity behavior algebraic approachIntensity behavior algebraic approach
tEtEEP sinsin 00
2sin
2cos2 0
tEEP
2
cos2
sin2sinsin BABABA
2cos4
2cos
24
2sin
2cos4
20
220
2220
2
I
E
tEEIavep
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Intensity by Phasor Method
180)180(2
2cos4
2cos
24
2
2cos4
2cos2
cos2
20
220
2
220
2
0
0
II
EEI
EE
E
EE
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Young’s Double SlitYoung’s Double SlitIntensity behavior averaged over one Intensity behavior averaged over one
periodperiod
sind222II 2
0av
cos
sincos2
0 dIIav
yDdIIav
20 cos
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Interference upon ReflectionInterference upon Reflection
• Thin FilmThin Film– in airin air– coatingscoatings
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Phase changes upon Phase changes upon ReflectionReflection
Dense to less dense
n1 > n2
Less dense to more dense
n1 < n2
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Thin Film in Air (Soap Film)Thin Film in Air (Soap Film)
• Near normalNear normal incidenceincidence
• Conditions for Conditions for reflected light reflected light interferenceinterference
Condition for there to be Condition for there to be constructive interferenceconstructive interference
2
2
)21(
,.....1,0 )21(2
nm
mmL n
Assume
21 nn
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Michelson InterferometerMichelson Interferometer
1 22 L L
1 22 L LN