Paraxial raytracing: Refraction and Translation

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Paraxial raytracing Refraction and Translation
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Sign Conventions angles radii
distances
r
u
y
CC
t
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Sign Conventions Angles
CCW from axis ()
CW from axis (-)
u ()
u (-)
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Sign Conventions Radii
CC to right of surface r ()
CC to left of surface r (-)
r (-)
r ()
CC
CC
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Sign Conventions Distance
Above axis y ()
Above axis y ()
Below axis y (-)
y ()
y (-)
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Sign Conventions Distance
Left to right t ()
t ()
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1. Refraction at an interface
?
?
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1. Refraction at an interface
n sin(?) n sin(?)
n sin(u - a) n sin(u - a)
For small angles sin(?) ?
n (u - a) n (u - a)
nu - na nu na
nu na - na nu
nu nu a (n n)
? (u a)
? (u a)
(note a is neg as drawn)
?
?
u
a
a
u
u
a
u
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1. Refraction at an interface
nu nu a (n n)
r
y
a
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1. Refraction at an interface
nu nu a (n n)
sin(a) -y/r
a sin-1(-y/r)
y r
For small a a -
r
y
a
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(n n) r
optical power
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(n n) r
optical power
n lt n
r (-)
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(n n) r
optical power
n lt n
r (-)
n lt n
r ()
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(n n) r
optical power
n lt n
r (-)
n gt n
n lt n
r ()
r (-)
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(n n) r
optical power
n lt n
n gt n
r ()
r (-)
(n- n) gt 0 r gt 0
(n- n) lt 0 r lt 0
? ()
? ()
(n- n) lt 0 r gt 0
(n- n) gt 0 r lt 0
? (-)
? (-)
n gt n
n lt n
r ()
r (-)
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1. Refraction at an interface
(n n) r
nu
nu
u
u
y
u
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2. Translation between two surfaces
n'
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2. Translation between two surfaces
angle u is constant height y ? y
n'
u
u
y
y
t
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2. Translation between two surfaces
y y t u
Since were carrying around index-angle product
nu
n'
u
y
y
t
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1. Refraction
2. Translation
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Find back focal length (BFL) distance from last
surface to F
n 1.5
n 1
n 1
n 1.4
r 10
r -6
r -20
u 0
y 4
t 7
t 2