Cardinal planes and matrix methods

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Cardinal planes and matrix methods

• Monday September 23, 2002

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Principal planes for thick lens (n21.5) in air
Equi-convex or equi-concave and moderately thick
? P1 P2 P/2
H
H
H
H
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Principal planes for thick lens (n21.5) in air
Plano-convex or plano-concave lens with R2 ? ?
P2 0
H
H
H
H
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Principal planes for thick lens (n1.5) in air
For meniscus lenses, the principal planes move
outside the lens R2 3R1 (H reaches the first
surface)
H
H
H
H
H
H
H
H
Same for all lenses
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Examples Two thin lenses in air
H
H
ƒ1
ƒ2
n n2 n 1
Want to replace Hi, Hi with H, H
d
h
h
H1
H1
H2
H2
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Examples Two thin lenses in air
H
H
ƒ1
ƒ2
n n2 n 1
F
F
d
ƒ
ƒ
s
s
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Huygens eyepiece
In order for a combination of two lenses to be
independent of the index of refraction (i.e. free
of chromatic aberration)
Example, Huygens Eyepiece
ƒ12ƒ2 and d1.5ƒ2
Determine ƒ, h and h
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Huygens eyepiece
H1
H2
H
H
h -ƒ2
h2ƒ2
d1.5ƒ2
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Two separated lenses in air
f12f2
H
H
H
H
F
F
F
F
f
f
d f2
d 0.5 f2
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Two separated lenses in air
f12f2
Principal points at ?
H
H
F
F
f
d 3f2
d 2f2
e.g. Astronomical telescope
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Two separated lenses in air
f12f2
e.g. Compound microscope
H
H
F
F
f
d 5f2
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Two separated lenses in air
f1-2f2
e.g. Galilean telescope
d -f2
Principal points at ?
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Two separated lenses in air
f1-2f2
H
H
F
F
f
e.g. Telephoto lens
d -1.5f2
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Matrices in paraxial Optics
Translation (in homogeneous medium)
?
?0
y
yo
L
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Matrix methods in paraxial optics
Refraction at a spherical interface
?
y
?
?
?
f
n
n
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Matrix methods in paraxial optics
Refraction at a spherical interface
?
y
?
?
?
f
n
n
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Matrix methods in paraxial optics
Lens matrix
n
nL
n
For the complete system
Note order matrices do not, in general, commute.
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Matrix methods in paraxial optics
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Matrix properties
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Matrices General Properties
For system in air, nn1
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System matrix
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System matrix Special Cases
(a) D 0 ? ?f Cyo (independent of ?o)
?f
yo
Input plane is the first focal plane
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System matrix Special Cases
(b) A 0 ? yf B?o (independent of yo)
Output plane is the second focal plane
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System matrix Special Cases
(c) B 0 ? yf Ayo
yo
Input and output plane are conjugate A
magnification
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System matrix Special Cases
(d) C 0 ? ?f D?o (independent of yo)
Telescopic system parallel rays in parallel
rays out
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Examples Thin lens
Recall that for a thick lens
For a thin lens, d0
?
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Examples Thin lens
Recall that for a thick lens
For a thin lens, d0
?
In air, nn1
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Imaging with thin lens in air
?
?o
yo
y
Input plane
Output plane
s
s