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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