chapter 2 plane surfaces and prisms

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"

chapter 2 plane surfaces and prisms

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