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GCSEC'S IMAGES IN A MIRROR

Version 1.0 Written 10 April 1999

(This exhibit was inspired by the Spherical Reflections exhibit.)

This exhibit consists of two large reflecting surfaces, side by side. One surface is a flat 18"square mirror. The second surface is a convex mirror 18" in diameter. This exhibit was created to allow visitors to work with a basic concept of mirrors, that the angle of incidence is equal to the angle of reflectance; and to compare and contrast flat and convex reflecting surfaces.

A review of some basic concepts follows.

  1. Angle of incidence is the angle an incoming ray of light makes with a surface.
  2. Angle of reflectance is the angle a reflected ray of light makes with a surface.
  3. The angle of incidence always equals the angle of reflectance.
  4. A burning match is essentially a point source of light. It emits light in all directions. Each ray of light from the match travels in a unique direction, but the match is emitting an infinite number of such rays of light.
  5. If a burning match is near a mirror, different rays of light from the match will strike every point on the surface of the mirror. Each such ray will have its own (identical) angles of incidence and reflection.
  6. A reflection in the mirror of this match will be seen at a number of different viewing positions, but each of these reflections is the result of a unique ray of light being emitted from the match.
  7. A larger object, such as a matchbook, does not emit light. However, it is reflecting light that strikes it from the sun, a light bulb, a flashlight, and so on.
  8. Each point on the surface of the matchbook is reflecting light in all directions.
  9. When we see a larger object such as a matchbook in a mirror, our retina and brain are interpreting and making sense of individual rays of light from all of the different points on the surface of the matchbook.
  10. Field of view refers to the extent of the surrounding area that can be seen in the mirror.
  11. The field of view depends upon the relative position of the individual in relation to the mirror surface
  12. A convex surface is higher in the middle than at the edges. The outside of a tennis ball is a convex surface.
  13. A concave surface is lower in the middle than at the edges. The inside of a tennis ball is a concave surface.
  14. A tangent only touches a curved surface at one point. Think of a ping pong ball resting on a table. The table is only touching the ball at one point and is therefore a tangent to the ping pong ball at that point. A two dimensional curved surface, such as a circle, has tangent lines to points on the circumference of the circle. A three dimensional curved surface, such as a ping pong ball, has a tangent plane at each point on its surface.
  15. Angles of incidence and reflectance are in relation to the tangent at the point where the incoming ray of light strikes the surface.
  16. A convex mirror has a much greater field of view than a flat mirror.
  17. It is expected (but not confirmed) that a concave mirror would have a smaller field of view than a flat mirror.
  18. The reflection in a convex mirror is smaller than the same reflection in a flat mirror. Our brain is most used to interpreting reflections from flat mirrors. Thus it will interpret the smaller reflection in a convex mirror as indicating that the object being observed is further away from the reflecting surface.
  19. Convex mirrors are being used for passenger side door mirrors, probably because they offer a greater field of view. These side door mirrors usually are labeled "Objects are closer than they seem" or something similar.

To help people use this exhibit, suggest some of the basic concepts such as angles of incidence and reflectance. Ask them to identify some of the similarities and differences between the two mirror surfaces. Then suggest they stand a few feet away and between the two mirrors, so that they can see their reflection in both at the same time. Ask them to compare and comment on their two reflections. Then review the concept of field of view, and ask them to compare and comment on the field of view of the two mirrors.

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