Page 68 - Modern Optical Engineering The Design of Optical Systems

Paraxial Optics and Calculations 51

Figure 3.10 Raytrace through a two mirror system.

Following our sign convention, the radii are both negative and the dis-
tance from primary to secondary mirror is also considered negative, since
the light traverses this distance right to left. The index of the air is taken
as 1.0 before the primary and after the secondary; between the two, the
index is 1.0. Thus the optical data of the problem and the computation
are set up and carried through as shown in Fig. 3.10. Careful attention
to signs is necessary in this calculation to avoid mistakes.
The focal length of the system is given by y 1 /u′ 2 1.0/ 0.002
500 mm. The final intercept distance (from R 2 to the focus) is equal to
y 2 /u′ 2 0.2/ 0.002 100 mm, and the focal point lies 20 mm to the
right of the primary mirror. Notice that the (second) principal plane is
completely outside the system, 400 mm to the left of the secondary
mirror, and that this type of system provides a long focal length and a
large image in a small, compact system.

Bibliography

Bass, M., Handbook of Optics, Vol. 1, New York, McGraw-Hill, 1995.
Fischer, R. E., and B. Tadic-Galeb, Optical System Design, New York, McGraw-Hill, 2000.
Greivenkamp, J., Field Guide to Geometrical Optics, Bellingham, WA, SPIE, 2004.
Kingslake, R., Optical System Design, Orlando, Academic, 1983.
Smith, W. J., Modern Lens Design, New York, McGraw-Hill, 2002.
Smith, W. J., Practical Optical System Layout, New York, McGraw-Hill, 1997.

Exercises
1 A detector, 1 mm on a side, is “immersed” on the plano surface of a plano
convex lens with an index of 1.50 and a radius of 10.0 mm. When viewed
through the convex surface, where is the image, and what is the image size if
the immersion lens is:
(a) 7.0-mm thick
(b) 10.0-mm thick
(c) 16.666 . . . mm thick
ANSWER: (a) Using Eq. 3.16, trace a ray from the axial intercept of the plane
surface through the curved surface, at a height of 1 mm on that surface. The
ray slope in the glass is 1/7 0.142857 and the slope-index product nu is
thus 0.214286. The slope after refraction (in air n 1.0) will be given by