Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

# Science in Focus: Shedding Light: Highlights

Workshop 2

## Curved Mirrors

Have you ever noticed that when you look in the right sideview mirror of your car, you see the words, "Objects may be closer than they appear"? Why is that?

Let's review briefly what happens when you look in a flat-surfaced (plane) mirror. Photons of light scatter from different parts of your face, some reaching the mirror and reflecting back into your eyes. When photons reflect from a flat surface, they behave in a certain way. Look at the diagram to the right. Note the dashed line drawn perpendicular to the mirror's surface. This line, called the normal, is a reference for photon paths. The diagram shows the path of a photon that reached the mirror and was reflected. The angle of the photon's incoming path measured from the normal is the same as the angle of the photon's outgoing path measured from the normal. Scientists often state this behavior very simply as the rule, "the angle of incidence (incoming angle) equals the angle of reflection (outgoing angle)."

When you look at yourself in a plane mirror, you see what looks like your identical twin appearing as far behind the mirror as you are in front of it. That image is called a virtual image because it does not really exist where it appears to — no photons are actually coming through the mirror from your twin! But why does the image seem to come from behind the mirror?

The right sideview mirror of your car is not flat-surfaced, but curved. Curved mirrors can be either concave (curved inward) or convex (curved outward). We can think of any curved mirror as a collection of very small flat mirrors, each set at a slightly different angle from the others (shown in orange). Thus you can apply the rule for plane mirror reflection to curved mirrors by thinking of how photons would reflect from a great many small flat mirrors. The one thing to keep in mind is that the normal lines will point in a different direction for each tiny mirror along a curved surface. The diagram at left shows some normal lines for different sections on a concave mirror; note how they meet at a point, something that normal lines on a flat mirror would not do. This pattern indicates a concave mirror will not act exactly like a flat mirror. Imagine what the pattern of normal lines for a convex mirror would look like.