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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
The Wave Nature of Light 7
Phase Two motions in phase
The Wave Nature of Light 8
Phase Two motions in antiphase
The Wave Nature of Light 9
Interference Constructive interference: two waves arrive at the
point in phase
Destructive interference: two waves arrive at the point in antiphase
The Wave Nature of Light 10
,...2,1,0,12 mmrr
,...2,1,0,2
112
mmrr
How Interference Works
The Wave Nature of Light 11
need to look at the 2D picture
One Source: No Interference
The Wave Nature of Light 12
oscillations everywhere – uniform intensity
Two Sources: Interference
The Wave Nature of Light 13
no oscillation in these points – intensity minima!
sources must be coherent
Effect of Distance
The Wave Nature of Light 14
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
The Wave Nature of Light 15
Eventually, the interference picture disappears
Double Slit Interference T. Young (1800)
The Wave Nature of Light 16
fringes
Position of Fringes
The Wave Nature of Light 17
R
d
mdrr sin12
2S
1S
1r
2r
y
mm Ry tanangle is small, so sinθ~tanθ~θ
Position of Fringes
The Wave Nature of Light 18
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?
The Wave Nature of Light 19
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
The Wave Nature of Light 20
,...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
The Wave Nature of Light 21
Effect of Many Slits
The Wave Nature of Light 22
Effect of Many Slits
The Wave Nature of Light 23
location is the same maxima get narrower
Effect of Many Slits
The Wave Nature of Light 24
two slits four slits eight slits
md sinposition of maxima:
Diffraction Grating
The Wave Nature of Light 25
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
The Wave Nature of Light 26
Grating and Color
The Wave Nature of Light 27
md sin
m=0: the same for all colors m=±1, ±2, …: depends on color
grating works like a prism!
Diffraction Grating Spectrometer
The Wave Nature of Light 28
Interference by Thin Films
The Wave Nature of Light 29
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
The Wave Nature of Light 30
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
The Wave Nature of Light 32
Newton’s Rings
The Wave Nature of Light 33
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
The Wave Nature of Light 35
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
The Wave Nature of Light 37
Linear and Circular Polarization
The Wave Nature of Light 38
)sin(2
)sin(2
max
max
kxtE
E
kxtE
E
z
y
Linear and Circular Polarization
The Wave Nature of Light 39
)2
sin(2
)sin(2
max
max
kxtE
E
kxtE
E
z
y
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