Page 48 - Modern Optical Engineering The Design of Optical Systems

Gaussian Optics: The Cardinal Points 31

m h′/h transverse magnification
u and u′ are the ray slopes at the object, and image
NA and NA′ are the numerical apertures at object and image
( u and u′)

2.5 Optical Systems Not Immersed in Air
If the object and image are not in air, as assumed in the preceding
paragraphs, the following equations should be used instead of the
standard expressions of Eqs. 2.2 through 2.9.
Assume an optical system with an object-side medium of index n,
and an image-side medium of index n′. The first and second effective
focal lengths, f and f′, respectively, may differ; they are related by

f f 9
5 (2.10)
n n9
nu n9u9
Note that 5 5 (2.10a)
y9 y
The focal lengths can be determined by a ray-tracing calculation, just as
with an air-immersed system. For example, f′ y 1 /u′ k (see Eq. 3.19).

Object and image distances
n′ n n n n′
(2.11)
s′ s f s f ′
ff ′
x′ (2.12)
x

Magnifications
h′ ns′ f x′
m (2.13)
h n′s x f ′

for an object at infinity,
h′ fu f ′u pn/n′ (2.14)
p

s′ ff ′
2

m
(note that m m ) (2.15)

s x 2
Focal point to nodal point distance equals the other focal length.