Page 411 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 32

Lenses

FOCALLENGTH

Figure 32-1 shows how a converging lens brings a parallel beam of light to a real focal point F, and Fig. 32-2
shows how a diverging lens spreads out a parallel beam of light so that the refracted rays appear to come from
a virtual focal point F. In this chapter we consider only thin lenses, whose thickness can be neglected as far as
optical effects are concerned. The focal length f of a thin lens is given by the lensmaker’s equation:
1 1 1
= (n − 1) +
f R 1 R 2
In this equation n is the index of refraction of the lens material relative to the medium it is in, and R 1 and R 2 are
the radii of curvature of the two surfaces of the lens. Both R 1 and R 2 are considered as plus for a convex (curved
outward) surface and as minus for a concave (curved inward) surface; obviously it does not matter which surface
is labeled as 1 and which as 2.
A positive focal length corresponds to a converging lens and a negative focal length to a diverging lens.
F = real focal point F = virtual focal point

F F

f f

Fig. 32-1 Fig. 32-2

SOLVED PROBLEM 32.1

A planoconvex lens has one plane surface and one convex surface. If a planoconvex lens of focal length
12 cm is to be ground from glass of index of refraction 1.60, find the radius of curvature of the convex
surface.
The radius of curvature of the plane surface is infinity, so if we call this surface 1, then 1/R 1 = 0. From the
lensmaker’s equation
1 1 1 1
= (n − 1) + = (n − 1)
f R 1 R 2 R 2
and so R 2 = (n − 1) f = (1.60 − 1.00)(12 cm) = 7.2cm
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