
64 OPTICS FOR ENGINEERS
Thus the nal output is
V
2
= R
2
T
12
R
1
V
1
.
We can say
V
2
= LV
1
,
where we have dened the matrix of a simple lens, as
L = R
2
T
12
R
1
. (3.22)
We need to remember that, because each matrix operates on the output of the preceding one,
we cascade the matrices from right to left, as discussed in Equation C.8 in Appendix C.
Writing the component matrices explicitly according to Equations 3.10 and 3.18,
L =
⎛
⎝
10
−
P
2
n
2
n
1
n
2
⎞
⎠
1 z
12
01
10
−
P
1
n
1
n
1
n
1
, (3.23)
where we have used the fact that n
2
= n
1
. The product of these matrices is complicated, but
we choose to group the terms in the following way:
L =
10
−
P
t
n
2
n
1
n
2
+
z
12
n
1
−P
1
n
1
P
1
P
2
n
2
−P
2
n
1
n
2