
APPENDIX G 483
3.1d Use matrices and nd the focal length of this pair of lenses and the location of the prin-
cipal planes. Be sure to specify distances and directions from lens vertices.
Solution:
The matrix for the rst lens, from front principal plane to back principal plane is
10
−
1
f
1
1
. (G.35)
Note that we could have worked from vertex to vertex assuming an index of refraction
and computing the surface curvatures, but there is no real need to do this, and in the
case of complicated lenses, which are often proprietary designs, you will not know these
parameters.
The complete matrix is
10
−
1
f
2
1
1 z
12
01
10
−
1
f
1
1
(G.36)
Note that we use z
12
rather than ...