the wave nature of lighthep0.okstate.edu/khanov/phys1214/ch24.pdfhow interference works the wave...
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The Wave Nature of Light
Reminder: Light is an EM wave
The Wave Nature of Light 2
)sin(
)sin(
max
max
kxtBB
kxtEE
z
y
2k
T
2
Monochromatic Light monochromatic light = composed of radiation of a
certain wavelength
There is no such thing (there always is some wavelength range), but:
We can use a filter
We can use a laser:
The Wave Nature of Light 3
910~
Dispersion Visible white light is not
monochromatic, it is composed of all colors
dispersion = dependence of n on λ
The Wave Nature of Light 4
Rainbow
The Wave Nature of Light
θ greater for violet color sequence reversed
θ greater for red
5
Interference and Diffraction Interference = result of two (or more) waves
overlapping in space
Diffraction = ability of waves to “go around the corner”
There is no fundamental distinction between the two phenomena: both are the result of two fundamental principles – the superposition principle (oscillations add up linearly) and the Huygens’ principle (every point of a wavefront becomes a source of spherical waves)
The Wave Nature of Light 6
Coherent Light Coherent sources of light: waves leaving them have the
same wavelength and frequency and fixed phase shift
Example of coherent sources: a screen containing two closely spaced slits
Example of incoherent sources: two light bulbs
Interference can only be observed for coherent sources
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Phase Two motions in phase
The Wave Nature of Light 8
Phase Two motions in antiphase
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Interference Constructive interference: two waves arrive at the
point in phase
Destructive interference: two waves arrive at the point in antiphase
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,...2,1,0,12 mmrr
,...2,1,0,2
112
mmrr
How Interference Works
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need to look at the 2D picture
One Source: No Interference
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oscillations everywhere – uniform intensity
Two Sources: Interference
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no oscillation in these points – intensity minima!
sources must be coherent
Effect of Distance
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As the sources get closer, the distance between the minima gets larger
the distance between the minima also increases as the screen is moved away from the sources
Effect of Distance
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Eventually, the interference picture disappears
Double Slit Interference T. Young (1800)
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fringes
Position of Fringes
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R
d
mdrr sin12
2S
1S
1r
2r
y
mm Ry tanangle is small, so sinθ~tanθ~θ
Position of Fringes
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dRmym
constructive interference (maxima):
mrr 12
2
112 mrr
destructive interference (minima):
dmRym
2
1
Single Slit Diffraction So what happens if there is only one slit?
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R
a
divide the slit by 2: two halves compensate each other if similarly, can divide by 3,4,…
2sin
2
a
we assume R>>a (Fraunhofer diffraction)
Position of Fringes Compensation occurs at
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,...2,1,sin ma
m
similar to interference, we conclude that
aRmym
•this is position of minima, not maxima! •m=0 is not a minimum!
Effect of Many Slits
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Effect of Many Slits
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Effect of Many Slits
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location is the same maxima get narrower
Effect of Many Slits
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two slits four slits eight slits
md sinposition of maxima:
Diffraction Grating
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typical gratings have thousands of slits (called rulings or lines)
butterfly’s wings don’t have pigments – their color comes from the wing structure
CD as a Diffraction Grating
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Grating and Color
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md sin
m=0: the same for all colors m=±1, ±2, …: depends on color
grating works like a prism!
Diffraction Grating Spectrometer
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Interference by Thin Films
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t
additional path for ray b
a b
,...2,1,0, mms
,...2,1,0,2
1 mms
constructive interference:
destructive interference:
watch for extra phase shifts!
Interference by Thin Films
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tan
bn
ba nn
tan
1bn
: extra ½ cycle phase shift
mt 2
: no extra shift
extra shift
ba nn
2
12 mt
bright fringes (constructive interference): bright fringes:
Interference by Thin Films
The Wave Nature of Light 31
t
extra shift no extra shift
1an
an
bn
bn1
2
12 mt
bright fringes (constructive interference):
mt 2
dark fringes (destructive interference):
Example: air wedge
Soap Bubbles Bubbles are ~1 µm thick −
not too thick, not too thin
Constructive interference condition is λ dependent
Bubble thickness varies due to gravity
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Newton’s Rings
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Rmr2
1radius of bright fringes:
lens
Circular Apertures
The Wave Nature of Light 34 D
D
D
24.3sin
23.2sin
22.1sin
3
2
1
A circular aperture creates a diffraction pattern made of rings
1.22, 2.23, 3.24 are related to zeros of Bessel function J1(x)
X-Ray Diffraction
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Regular light doesn’t work! Typical lattice constants are few angstrom (1Å=0.1 nm)
Bragg’s law:
md sin2
Polarization Polarized light = EM waves
oscillate in certain direction rather than in any transverse direction
The Wave Nature of Light 36
)sin(
)sin(
max
max
kxtBB
kxtEE
z
y
)sin(
)sin(
max
max
kxtBB
kxtEE
y
z
Polarization If the light is polarized in direction perpendicular to
the polarized film axis, it can’t pass through
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Linear and Circular Polarization
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)sin(2
)sin(2
max
max
kxtE
E
kxtE
E
z
y
Linear and Circular Polarization
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)2
sin(2
)sin(2
max
max
kxtE
E
kxtE
E
z
y