Ever since Narcissus peered into the pond, mirrors have fascinated
us. They show us what we want to see (and what we don't), but they
also surprise us. The main rule for mirrors is that the angle of incidence equals
the angle of reflection. What does that mean exactly? This diagram
will help make the rule clear:
Ever since Narcissus peered into the pond, mirrors have fascinated us. They show us what we want to see (and what we don't), but they also surprise us.
The main rule for mirrors is that the angle of incidence equals the angle of reflection. What does that mean exactly? This diagram will help make the rule clear:
To make this rule work reliably in unusual situations, you have to get this straight: the angles in question are "from the normal," that is, they're the angle between the beam and the normal to the mirror. (What's normal? In geometry and optics, normal means "perpendicular." So the normal, or normal line, to the mirror is the line perpendicular to it.)
When the mirror is curved, the rule still holds. But how do you use the rule to tell what the image looks like? It can be confusing to figure out just which beams of light are relevant. The key to solving the problem is to realize that while light goes off in all directions from every part of your body, the only beams that you see in the mirror are the ones that hit your eyes.
Furthermore, the easiest beams to figure out are the ones that come from your eyes, bounce off the mirror, and go right backbecause they are normal to the mirror. The angle of incidence is zero, so the angle of reflection is too. From this you can see that concave mirrors make you tall (you have to look up to get a perpendicular line: your eyes appear above you) while convex make you short (you have to look down).
Curved mirrors are interesting at any age. It's good to give students mirrors to hold and play with. Reflective plastic sheets (e.g., Mylar) are safe and work fine. You can also get Mylar from those shiny party balloons. These days, you can also find highly reflective wrapping paper. Just be sure you can see yourself well enough before you buy.
Even young children can experiment and figure out which kind of curve stretches and which one squishes (even if they can't articulate why this happens).
Where do curved mirrors lead? As students get older, they can take their knowledge in different directions.
The National Science Education Standards (1996) state that "as a result of the activities in grades K-4, all students should...[understand that] "light travels in a straight line until it strikes an object. Light can be reflected by a mirror, refracted by a lens, or absorbed by the object" (p. 127). Furthermore, students in grades 5-8 should understand that "light interacts with matter by transmission (including refraction), absorption, or scattering (including reflection). To see an object, light from that object emitted by or scattered from itmust enter the eye" (p. 155).
Distributed by Key Curriculum Press, Kaleidomania is computer software that simulates reflections (and other transformations). It will let you make any kind of kaleidoscope you wantand even let you import your own pictures.
The Exploratorium has lots of small activities (they call them "snacks") about mirrors, both flat and curved. You can build and explore corner reflectors, cylindrical mirrors (like the ones in this lab), spherical mirrors (like the Escher print, above) and even, parabolic mirrors as well as many others.
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