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24 Overview
• wave effects:
• interference, diffraction
• polarization, scattering
• Homework:
• 1, 12, 43, 57, 67.
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waves• pass through another wave undisturbed
• diffract video demo simulation
• Reflect wave tank demo
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Interference
• amplitude change due to adding waves
• correlation (Coherence) - required for strong interference effects
• misalignment of waves (phase) is zero for constructive (bright)
• 180 deg: destructive (dark)
• Wave tank demo
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double-slit experiment• coherent light
• Interference pattern
• path difference
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central max
m = 1 bright fringe
m = 2 bright fringe
m = 1 dark fringem = 2 dark fringem = 3 dark fringe
L
naming convention
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Double-Slit Phase Difference
• Bright: (dsin) = 0, 1, 2, … wavelengths
• Dark: (dsin)= ½, 1½, 2½, … wavelengths
3,... 2, 1, m sin Bright md
3,... 2, 1, m )(sinDark 21 md
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Single Slit Pattern
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Polarizing Filters• Polarizing material
allows the passage of only one direction of E
• Malus’ Law:
20 cosI I
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Two Filters (incident light unpolarized)
• 1st reduces intensity by 1/2.
• 2nd reduces according to Malus’ Law
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Polarization by Scattering and Reflection
• Light scattered at 90 degrees is 100% polarized.
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Summary
• all waves diffract & interfere
• coherence required for strong effect
• path difference determines interference for double-slits and thin-films
• light polarization & polarizing filters
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thin-film interference• causes certain colors to become more or
less intense.
• Ex. oil on water, soap bubble, coatings
• 1+2 constructive or destructive
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Reflection phase• off higher index: ½ wavelength phase
change (Ex. ray 1 in diagram)
• off lower index: 0 (Ex. ray 2 in diagram)
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Thin Film Problem Solving
Dark
Bright
,2 ,1 ,
3, 2, 1, *)or (0
2
21
21
212
1
film
t
* 0: no reflection phase changes (or two)
* ½: one reflection phase change
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Ex. t = 100nm. Light wavelength = 400nm in water.
400
)100(2 )or (0
221
21
nm
nmt
film
Ray 1 has reflection phase change, Ray 2 does not. (= ½)
1 21
21 Bright
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diffraction grating
• N = #lines/cm,
• Spacing: d = 1/N
• Video demo
Bright 21 0 sin , ..., , n nd
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a = Slit-Width
(a ≠ d)
Single Slit Diffraction
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waves• pass through another wave undisturbed
• diffract video demo
• Refract and reflect