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?

Look at the diagram above. The solid arrows show the real paths of two photons. These photons reflect from the plane mirror according to the rule stated earlier. Both photons enter your eye and are "read" by your brain. But there's a catch with "reading" photons; your brain is only aware of the photon's path when it entered your eye. Your brain always thinks that photons come straight in. Look again at the diagram. The dashed lines show what your brain "thinks" were the paths of the photons; these paths lead back behind the mirror. If the paths of all photons that came from your face, reflected off the mirror and into your eye were drawn, they would appear to have come from your virtual twin 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.

Now let's return to that right sideview mirror, which is a convex mirror. If you look directly into the mirror, you see an interesting effect. The image of your face, while still virtual as in a flat mirror, is quite small; your twin appears to be farther behind the mirror than you are in front of it. If you looked in your left sideview mirror, which is a plane mirror, and compared the two views, you would notice that you see more of the background in the convex mirror. What's going on? Look at the diagram to the right. The real paths of two photons are shown by the solid arrows; the dashed lines indicate the directions your brain thinks these photons followed to your eye. If the paths of all photons from your face that reflected into your eye were shown, your twin would appear smaller than "life-size," which also gives the impression of being farther away. The same phenomenon is true for anything you see in a convex mirror: the images of cars and other objects look farther away than the objects actually are from the mirror. Thus the cautionary message on your mirror.

Concave mirrors have properties similar to convex mirrors. However, there is a situation when your twin can appear larger than "life size," or give the impression of being closer to the mirror than you are. If you need to closely examine your face, you can do so most easily by using a concave mirror to bring your virtual twin "up close." Cosmetic and shaving mirrors often make use of this.

Concave mirrors can also turn images upside down. Look at yourself in the inside of the bowl of a shiny spoon. The photon paths result in a collective message that your brain thinks of as light coming from an upside twin behind the mirror. That twin can seem larger than life if you can put yourself closer to the mirror than where all of its normal lines meet; see the diagram below. Try tracing out the photon paths shown to figure out how the photons appear to be from a giant, inverted twin.

Some trucks have a different sort of mirror — really a mirror within a mirror. The larger mirror is a flat mirror and the smaller, inset mirror is convex. Think about how this helps a truck driver negotiate in traffic. Also think about the notice posted on the back of many large trucks: "If you can't see my mirrors, I can't see you." What is the trucker actually telling you?

Resources

For more information and indepth explanations of concave mirrors, reflections, and refraction in Spanish and English.

http://www.carsoncity.k12.mi.us/~cpeirce/b23a.html

The Physics Classroom

http://www.glenbrook.k12.il.us/gbssci/phys/class/BBoard.html

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