
116 OPTICS FOR ENGINEERS
In the triangle shown by solid lines in Figure 5.3A, the height is the half-length of the minor
axis, b, the base is half the distance between S and S
, and the hypotenuse is half the total
optical path, so
b
2
=
s +s
2
2
−
s −s
2
2
= ss
. (5.17)
This mirror is the perfect choice to image the point S to the point S
. For these two conjugate
points, there are no aberrations. We note for later use that we can dene the focal length from
the lens equation (Equation 2.51 in air) by
1
f
=
1
s
+
1
s
=
s
+s
s
s
=
2a
b
2
f =
b
2
2a
. (5.18)
Summarizing the equations for the ellipsoidal mirror,
z −a
a
2
+
x
b
2
+
y
b
2
= 1 a =
s +s
2
b =
√
ss
. (5.19)
For s = s
, the ...