Figure 47.1: Types of lenses. (a) Converging lenses, left to right: biconvex, meniscus, plano-convex. (b)
Diverging lenses, left to right: biconcave, meniscus, plano-concave.
- Whether the image isupright(rightside-up) orinverted(upside-down).
Just as with mirrors, there are two methods that can be used to solve this type of problem: - Theray diagram methodis a graphical method. It gives a good intuitive picture of what’s going on, but
it can be a bit time-consuming, and is not particularly accurate. - Thealgebraic methoduses only algebra. It doesn’t give a good picture of what’s happening, but it’s
faster and more accurate. However, the algebraic method requires that you are very careful with the
equations, particularly with regard to getting the signs correct.
We’ll cover both methods here.
47.1 Ray Diagrams
Ray diagrams for lenses are very similar to ray diagrams for mirrors. To create such a diagram we draw the
lens, its axis, the object, and three light rays, as shown in Fig. 47.2. We also need to locate the focusFalong
the mirror’s axis. The three rays we draw are:
- In parallel to the axis, out through the focus.
- In through the focus, out parallel to the axis.
- In through the centerof the lens, out through the center of lens.
Notice one difference between these rays and the rays used for mirror diagrams: for mirrors, the third ray
is through the centerof curvature; for lenses, the third ray is through the centerof the lens.
A complication arises with lenses that did not occur with mirrors: while mirrors have a single focus,
lenses havetwofoci. So which focus should you use for rays 1 and 2? It depends on whether you have a
converging lens or a diverging lens, as shown in the following table. (Here “near” refers to the focus closer
to the object, and “far” is the focus farther from the object.)
Ray Converging Diverging
1 far near
2 near far