Chapter 2 Plane Surfaces and Prisms
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Transcript of Chapter 2 Plane Surfaces and Prisms
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7/30/2019 Chapter 2 Plane Surfaces and Prisms
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What we learned in chapter 1
Speed of light is finite. Fixed in vac and slower
in media Laws of reflection and refraction (Snells law)
problem backwards). Similar to therelationship between Newtonian mechanicsand Lagrangian mechanics
Chromatic dispersion and the separation ofcolors
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Plane Surfaces and Prisms1. Parallel beam
External reflection
Reflected beam has the same cross section as the incident beam
Internal reflection Total Internal Reflection
Refracted cross section given by the ratio cos '/ cos
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Critical anglesin '
sin '
n
n
=
For n
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Total internal reflection
Apply the principle of reversibility
The critical angle is the smallest angle in incidence
in the higher indexed medium for which light is
totally reflected.
When TIR occurs, no energy goes into the lower
indexed medium
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Prism Applications
Read the moon reflector
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Prism materials
Most prisms are used at 45
degree angle so we need
'
sin 45
n
n
Materials can be used would
need n>1.414
Most materials can be used.
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Measuring the index of refraction
the Pulfrich refractometer
n>n
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Plane-parallel Plate only shifts a rays in ( ')d l =
(sin cos ' sin 'cos )cos '
td
=
sin ' sinn
=
'n
The displacement is given by
cos(sin sin )
' cos '
nd t
n
=
cossin (1 )
' cos '
nd t
n
=
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Approximationcos
sin (1 )' cos '
nd t
n
=
d
Off by about 3% for 30 degrees
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Refraction by a prismIn a parallel plate, the deviations of
the two surfaces are annulled
In a prism, they are made to
enhance each other
O
1 2
1 2
sin sin'
sin ' sin '
n
n
= =
1 1 ' =
2 2 ' =
1 1 2 2 1 2' ' = + = + = +
comes in by considering the ANBO quadragon
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Minimum deviationMinimum happens at
1 2
1 2' '
=
=
=
Principle of reversibility argues for this equality
Rotation around A
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Minimum deviation -II
1 2 1
1 1
2
' ' 2 '
'
Solve these to ether
m
= + =
= + =
= +
1
1
' (1/ 2)
(1/ 2)( )
Apply Snell's law
sin[(1/ 2)( )]'sin(1/ 2)
m
mn
n
=
= +
+=
Another way of measuring n.
Most prisms are used near this angle to cause less astigmatism from the
divergence or convergence of incident beam
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Thin prismsIf is small
sin[(1/ 2)( )]'
sin(1/ 2)( ' 1)
m mn
n
n
+ += =
=
m label is dropped since they are almost always used at min dev. in air
The prism Diopter, 1cm deviation at 1 m away, or =0.01 rad=0.0573
1-D dense flint prism, n=1.067050
/ ( ' 1) 0.85459n = =
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Combination of 2 thin prismsRisley or Herschel prism
Two of equal power
Power addition by vector addition
2 2
If is the angle between the two prisms
1 2 1 2
2
1 2
1 2
2 2 2
cos
Compared to only one prism
sintan
cos
If
2 (1 cos ) 4 cos ( / 2) 2 cos ( / 2)
tan tan( / 2)
/ 2
i i i
=
=+
=
= + = =
=
=
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Graphical method of ray tracing
ROQ=
RPQ=
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Direct vision prism n and n chosen for
the D line to have =0
Ray tracing done for all
colors
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Back to back
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Reflection of divergent rays
's s=Object distance = image distance
Virtual image
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Refraction of divergent rays
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Paraxial ray image
Angles are small
cosine=1 and sine equals angle
tan ' tan 'tan sin cos ' 'cos '
'tan ' cos sin ' cos
h s s
ns s s s
n
= =
= = =
since
' '
'
We have
' '
s n
s n
s n
s n
= =
=
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Fiber Optics
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Nobel Prize in Physics for 2009 one half to Charles Kuen Kao
Standard Telecommunication Laboratories, Harlow, UK, and ChineseUniversity of Hong Kong
Godfather of Broadband, "Father of Fiber Optics or"Father of Fiber Optic Communications
"for groundbreaking achievements concerning thetransmission of light in fibers for optical communication
other half jointly to
Willard S. Boyle and George E. SmithBell Laboratories, Murray Hill, NJ, USA
"for the invention of an imaging
semiconductor circuit the CCD
sensor"