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# Lenses for AP Physics B

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By McGraw-Hill Professional
Updated on Feb 12, 2011

Practice problems for these concepts can be found at:

Optics Practice Problems for AP Physics B

We have two types of lenses to play with: convex and concave. A convex lens, also known as a "converging lens," is shown in Figure 24.9a.

And a concave lens, or "diverging lens," is shown in Figure 24.9b.

We'll start by working with a convex lens. The rules to follow with convex lenses are these:

• An incident ray that is parallel to the principal axis refracts through the far focal point.
• An incident ray that goes through near focal point refracts parallel to the principal axis.
• The lensmaker's equation and the equation to find magnification are the same as for mirrors. In the lensmaker's equation, f is positive.

Want to try these rules out? Sure you do. We'll start, in Figure 24.10, by placing our arrow farther from the lens than the focal point.

We could also demonstrate what would happen if we placed our object in between the near focal point and the lens. But so could you, as long as you follow our rules. And we don't want to stifle your artistic expression. So go for it.4

We are given do and f. So we have enough information to solve for di using the lensmaker's equation.

Solving, we have di = 20 cm. Now we can use the magnification equation.

Our answer tells us that the image is exactly the same size as the object, but the negative sign tells us that the image is upside-down. So our answer is that the image is 3 cm tall, and that it is real.

When working with diverging lenses, follow these rules:

• An incident ray parallel to the principal axis will refract as if it came from the near focal point.
• An incident ray toward the far focal point refracts parallel to the principal axis.
• The lensmaker's equation and the magnification equation still hold true. With diverging lenses, though, f is negative.

We'll illustrate these rules by showing what happens when an object is placed farther from a concave lens than the focal point. This is shown in Figure 24.11.

The image in Figure 24.11 is upright, so we know that it is virtual.

Now go off and play with lenses. And spoons. And take out that box of crayons that has been collecting dust in your cupboard and draw a picture. Let your inner artist go wild. (Oh, and do the practice problems, too!)

Practice problems for these concepts can be found at:

Optics Practice Problems for AP Physics B

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