Page 72 - Modern Optical Engineering The Design of Optical Systems

Optical System Considerations 55

Note that these equations are equally applicable to systems composed
of either thick or “thin” lenses. Obviously, when applied to thin lenses,
d becomes the spacing between elements, since the element and its
principal planes are coincident.

Focal lengths of two-component systems
The preceding equations may be used to derive compact expressions
for the effective focal length and back focal length of a system
comprised of two separated components. Let us assume that we have
two components of powers a and b separated by a distance d (if the
lenses are “thin”; if they are thick, d is the separation of their princi-
pal points). The system is sketched in Fig. 4.2.
Beginning with a ray parallel to the axis which strikes lens a at y a ,
we have
u 0
a
u′ 0 y by Eq. 4.1
a a a
y y dy y (1 d ) by Eq. 4.2
b a a a a a
u′ y y (1 d ) by Eq. 4.1
b a a a a b
y ( d )
a a b a b
The power (reciprocal focal length) of the system is given by

2 ur 1
b 5 5 d
ab y a f ab a b a b
1 1 d
(4.4)
f f f f
a b a b

Figure 4.2 Raytrace through two separated components to determine
the focal length and back focus distance of the combination.