Chapter 47
Lenses
Alensis a disk of transparent material (such as glass or plastic), of which one or both surfaces is curved. The
curved surfaces allow the lens to form an optical image of a real object, similar to the way an image is formed
by a curved mirror.
Each side of the lens may be be either concave or convex (Fig. 47.1). If both sides of the lens are convex,
the lens is calleddouble convex; if both sides are concave, the lens is calleddouble concave. If one side is
convex and the other concave, the lens is called ameniscuslens. If one side of the lens is flat, the lens is
calledplano-convexorplano-concave. In general, if the lens is thicker in the middle than at the edges, the
lens will beconverging, and light will be bent toward the axis; if it is thinner in the middle than at the edges,
it will bediverging, and light will be bent away from the axis.
Ideally, to form a perfect image, the lens surfaces should be in the shape ofhyperboloids(of two sheets).
However, spherical surfaces are often easier to manufacture, and can be almost as good, although the deviation
from the ideal hyperboloidal shape does give rise to an optical defect called aspherical aberration,tobe
described later.
Light coming from an object infinitely far away will come together at a single point in a converging (e.g.
double-convex) lens; this point is called thefocusof the lens, and the distance between the lens and the focus
is called thefocal lengthof the lens.
The typical problem in lens optics is the same as in mirror optics: we are given
- The distance between the object and the lens, called theobject distance,do.
- The “height” (size) of the object, called theobject height,ho.
- The focal length of the lens,f. (Iff is not known, it can be determined using thelens maker’s
equation, Eq. (47.1).)
We typically wish to find:
- The distance between the image and the lens, called theimage distance,di
- The “height” (size) of the image, called theimage height,hi
- Themagnificationof the image,m. This is a dimensionless number that indicates how much bigger
the image is than the original object. - Whether the image isrealorvirtual. (In a real image, light is present at the image location, and the
image can be projected onto a screen. In a virtual image, there is no light present; a virtual image
cannot be projected onto a screen.)