Page 319 - Modern Optical Engineering The Design of Optical Systems

298 Chapter Thirteen

We can now determine the new eye relief by tracing a principal ray
from the center of the objective through the field and eye lenses.
yf
u′ 0.0625 u
o f
f o
u′ u y 0.0625 0.5 (0.25) 0.0625
f f f f
y y u′ f 0.5 0.0625 (2) 0.375
e f f e
u′ u′ y 0.0625 0.375 (0.5) 0.25
e f e e
y 0.375
l′ eye relief e 1.5 in
e u′ 0.25
e
Note that u′ e and u o are still related by the magnification, as in Eq. 13.4,
where
0.25
u′ e
MP 4
u o 0.0625
since the power of the system has not been changed by the introduction
of the field lens located exactly at the focal plane. If we desire to locate
the field lens slightly out of the focal plane, the general approach would
be the same; the distances, ray heights, etc., in the computations would,
of course, be modified accordingly. The power of the telescope would be
increased if the field lens were placed to the right of the focus, and vice
versa. In either case the scope is slightly shortened.
For the Galilean version of our telescope, we solve for the component
focal lengths by substituting 4 for the magnification in the equa-
tions in the second paragraph of Example 13.1 and get

(MP) D ( 4) 10
f 13.33 in
o
(MP) 1 4 1
D 10
f 3.33 in
e
1 (MP) 1 ( 4)
If we assume the aperture stop to be at the objective lens of a
Galilean telescope, the exit pupil will be found to be inside the tele-
scope, and we obviously cannot put the viewer’s eye there. Thus in a
Galilean scope the aperture stop is not the objective lens but is the
pupil of the user’s eye, and the exit pupil is wherever the eye is located.
This is usually about 5 mm behind the eyelens. To determine the field
of view, we must trace a principal ray through the center of the pupil
and passing through the edge of the objective, as indicated in Fig. 13.7.
This can be done by assuming some arbitrary value for u e and tracing