Simple Nature - Light and Matter

p/The radii of curvature ap-
pearing in the lensmaker’s
equation.

D Classify the examples shown in figure o according to the types of

images delineated in discussion question C.

E In figures n/1 and n/2, the only rays drawn were those that happened

to enter the lenses. Discuss this in relation to figure o.

F In the right-hand side of figure o, the image viewed through the lens

is in focus, but the side of the rose that sticks out from behind the lens is

not. Why?

o/Two images of a rose created by the same lens and recorded with the same camera.

12.4.3 ?The lensmaker’s equation

The focal length of a spherical mirror is simplyr/2, but we can-

not expect the focal length of a lens to be given by pure geometry,

since it also depends on the index of refraction of the lens. Suppose

we have a lens whose front and back surfaces are both spherical.

(This is no great loss of generality, since any surface with a suffi-

ciently shallow curvature can be approximated with a sphere.) Then

if the lens is immersed in a medium with an index of refraction of

1, its focal length is given approximately by

f=

[

(n−1)

∣

∣∣

∣

1

r 1

±

1

r 2

∣

∣∣

∣

]− 1

,

wherenis the index of refraction andr 1 andr 2 are the radii of

curvature of the two surfaces of the lens. This is known as the

lensmaker’s equation. In my opinion it is not particularly worthy

808 Chapter 12 Optics