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26
Physics Formulary by ir. J.C.A. Wevers
6.3
Matrix methods
A light ray can be described by a vector
(
n
α
,y
)
with
α
the angle with the optical axis and
y
the distance to
the optical axis. The change of a light ray interacting with an optical system can be obtained using a matrix
multiplication:
±
n
2
α
2
y
2
²
=
M
±
n
1
α
1
y
1
²
where
Tr(
M
)=1
.
M
is a product of elementary matrices. These are:
1. Transfer along length
l
:
M
R
=
±
10
l/n
1
²
2. Refraction at a surface with dioptric power
D
:
M
T
=
±
1

D
01
²
6.4
Aberrations
Lenses usually do not give a perfect image. Some causes are:
1.
Chromatic aberration
is caused by the fact that
n
=
n
(
λ
)
. This can be partially corrected with a lens
which is composed of more lenses with different functions
n
i
(
λ
)
. Using
N
lenses makes it possible to
obtain the same
f
for
N
wavelengths.
2.
Spherical aberration
is caused by secondorder effects which are usually ignored; a spherical surface
does not make a perfect lens. Incomming rays far from the optical axis will more bent.
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 Spring '10
 elder

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