
78 5. Fermat's Principle and Abberrations
Instead of setting
AQ
= 0, which defines the exact path of the chief ray, we follow
the standard procedure of finding the angular difference in direction afl;er
refi*action between the actual and paraxial chief rays for plane object and
image surfaces. In the steps that follow, note that the usual statement for the
paraxial approximation
n'6^
=
nO
is not sufficient. In order to preserve the exact
direction fi-om which the chief ray approaches the center of the stop, and the
object and image surfaces as planes, it is necessary to express sines and tangents
of angles through third order.
From Eqs. (5.1.4 ...