After learning how to trace the principal rays [Fig. 1(i)] through a thin lens in order to form the image in the conventional way, students sometimes ask whether it is possible to use other rays emanating from the object to form exactly the same image—for example, the two arbitrary rays shown in Fig. 1(ii). The answer is a definite yes, and this paper presents a method of doing so.

1.
F. M.
Goldberg
and
L. C.
McDermott
, “
An investigation of student understanding of the real image formed by a converging lens or concave mirror
,”
Am. J. Phys.
55
,
108
119
(Feb.
1987
).
2.
S.
Leinoff
, “
Ray tracing with virtual objects
,”
Phys. Teach.
29
,
275
277
(May
1991
).
3.
F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw‐Hill, New York, 1957), pp. 44–53.
4.
E. C.
Valadares
and
L. A.
Cury
, “
An image is worth a thousand rays
,”
Phys. Teach.
34
,
432
433
(Oct.
1996
).
This content is only available via PDF.
AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.