Page 414 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 32] LENSES 399

F′
F
(No image)

Fig. 32-4
LENS EQUATION

The object distance p, image distance q, and focal length f of a lens (Fig. 33-5) are related by the lens equation:
1 1 1
+ =
p q f
1 1 1
+ =
Object distance image distance focal length
This equation holds for both converging and diverging lenses. The lens equation is readily solved for p, q,or f :
q f pf pq
p = q = f =
q − f p − f p + q
As in the case of mirrors, a positive value of p or q denotes a real object or image, and a negative value
denotes a virtual object or image. A real image of a real object is always on the opposite side of the lens from
the object, and a virtual image is on the same side. Thus if a real object is on the left of a lens, a positive image
distance q signifies a real image to the right of the lens, whereas a negative image distance q denotes a virtual
image to the left of the lens.

h h
h′
q
h′
f f = focal length
p f p= object distance
p
q= image distance
q
(a) (b)

Fig. 32-5

MAGNIFICATION
The linear magnification m produced by a lens is given by the same formula that applies for mirrors:

h q
m = =−
h p
image height image distance
Linear magnification = =−
object height object distance
Again, a positive magnification signifies an erect image, a negative one signifies an inverted image. Table 32.1
is a summary of the sign conventions used in connection with lenses.