10.7 Summary & Keep the Curiosity Alive

Key Points

  • Spherical mirrors are curved: concave (curves inward) and convex (curves outward).
  • A concave mirror forms images that can be enlarged, diminished, or same-size, and erect or inverted, depending on the object’s distance. A convex mirror’s image is always erect and diminished. A plane mirror gives an erect, same-size image.
  • The two laws of reflection (valid for all mirrors): (1) angle of incidence = angle of reflection (i = r), measured from the normal; (2) the incident ray, normal and reflected ray lie in one plane.
  • A concave mirror converges parallel light (it can focus sunlight to burn paper); a convex mirror diverges it.
  • A lens is curved transparent material: convex (thick middle) and concave (thick edges). A convex lens behaves like a concave mirror (near = erect/enlarged, far = inverted); a concave lens gives an always erect, diminished image.
  • A convex lens converges light (a converging lens); a concave lens diverges it (a diverging lens).
  • Uses: concave mirrors (headlights, dentist’s mirror, telescopes); convex mirrors (side-view, safety); lenses (spectacles, cameras, microscopes, the eye).

A Closing Challenge: Keep the Curiosity Alive

Think It Through

  1. The angle puzzle. A ray hits a mirror at 40° from the normal. What angle does the reflected ray make with the mirror surface?
  2. Along the normal. When light falls straight along the normal, what are the angles of incidence and reflection?
  3. Walking toward a mirror. A woman walks toward a large concave mirror. How does her image change — and at what point does it flip?
  4. Match the image. A sketch-pen cap is placed in front of plane, concave and convex mirrors; match each image (same size / enlarged-or-inverted / small-erect) to its mirror.
  5. The bent pencil. Stand a pencil behind an empty glass, then half-fill the glass with water. Why does the pencil look broken or bent? (This is light bending through a curved water surface — a lens effect!)

We’ve followed light as it bounces and bends. Next, we look up: the same Sun and Moon whose light fills our days have, for thousands of years, told humans how to keep time — the subject of Chapter 11.