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5.
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5.
Geometric optics versus physical optics
Diffraction (Physical Optics)
Single slit calculation
Double slit calculation
Snells law (Geometric optics)
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5.
Light is treated as traveling as rays
What are consequences of this?
Shadows are 1:1 mapping of the obstruction
Beams of light can propagate withoutdiverging
When is this a valid assumption?
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5.
Field at any point is considered the sum of thecontributions from fields at all other points inspace (i.e. light does not travel as rays)
What are the consequences of this?
Diffraction
Shadows do not have sharp edges
Beams of light diverge
When must we consider this formalism?
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5.
Consider a slit of width d illuminated with aplane wave at normal incidence. What does itsshadow look like at a distance L where L>>d?
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d L
?
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5.
Diffraction as considered by Huygens principle
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Source: wikipedia
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E(x) =
d/2d/2
E(x)L2 + (x x)2
K(x, x)dx
E(x) =E0
LeikL
eikx2/2L
d/2d/2
eikxx/L
dx
I(x) = I0
d
L sinc2kxd
2L
E(x) = E0d
LeikL
eikx2/2Lsinc
kxd
2L
5. 7
d
L
Ax
B
x
Since small changes to the value of thedenominator hardly affect the value of
the function
L2 + (x x)2 L
K(x, x) = eik
L2+(xx)2
is called a Kernel and is a commonmathematical tool for expressing how
a quantity at one point in space andtime affect other points
L2 + (x x)2 L
1 +
(x x)
2L
L +
x
2L+xx
L
Since L>>x we can approximate thisfunction by the first order expansion
This is such a common function in
optics it has been given its own name!(pronounced sink)
sinc(u) s nu
u
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5.
Consider a slit of width d illuminated with aplane wave at normal incidence. What does itsshadow look like at a distance L where L>>d?
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d L
?
This is not predicted by geometric optics!
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5.
Based on the diffraction from a slit found usingHuygens principle, how would you set up acalculation of the diffraction pattern for a
double slit as shown?
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A
B
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5.10
A
Bx
Ld
dD
x
L
E(x) =EA
L2 + x
2eik
L2+x2
Later well learn some tricks that will allow us to evaluate E(x),
For now consider the slits to be infinitely narrow
E(x) =
D/2+d/2
D/2d/2
E(x)L2 + (x + D/2)2
eikL2+(x+D/2)2dx +
D/2+d/2D/2d/2
E(x)L2 + (xD/2)2
eikL2+(xD/2)2dx
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5.11
A
Bx
Ld
dD
x
L
E(x) =E(D/2)
L2 + (x + D/2)2
eikL2+(x+D/2)2 +
E(D/2)L2 + (x
D/2)2
eikL2+(xD/2)2
Consideringinfintesimal slits
with uniformillumination E(x)=E0
E(x)
2E0
L2
+x2eik(L+(x2+D2/4)/2L) cos
kxD
2L
E(x) E0
L2 + x2
eik(L+(x+D/2)2/2L) + eik(L+(xD/2)
2/2L)
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5.12
A
Bx
Ld
dD
x
L
Consideringinfintesimal slits
with uniformillumination E(x)=E0
E(x)
2E0
L2 + x2eik(L+(x2+D2/4)/2L) cos
kxD
2L
I(x) I0L2 + x2
cos2kxD
2L
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5.
Why does the spoon appearbent in this image?
Determine a relationship
between the angle of thespoon and its apparentangle in a glass of water
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5.14
a
it
nwater=1.33
nair=1
d
nair sin t = nwater sin i
dy
y = d tan i = dtan t
d
d=
tan i
tan t
sin i
sin t=
nair
nwaterh
x
w
tan a =x
h
tan w =x
h
nair
nwater
tan w = tan anair
nwater
apparentdistances get
compressed in thedirection normal to
the interface
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5.
Using the law of reflection, determine the anglefor a ray of light exiting a corner cubereflector as a function of the incident angle
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Using the law of reflection, determine the anglefor a ray of light exiting a corner cubereflector as a function of the incident angle
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Some phenomena can only be understood byconsidering physical optics
diffraction
Many phenomena are well modeled byconsidering geometric optics
refraction
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