A First Course in Physics · Ch. XX, §§ 528–537 · Chapter 20: Formation of Images
62. Images in plane and convex mirrors
Goal: Your student can locate the image in a plane mirror, explain why it is reversed, and explain why a convex mirror always gives a small, upright image behind it.
You'll need
- The book, open to these pages
- A flat mirror, a ruler and paper
- A sheet of clear glass or plastic (a picture frame glass with taped edges) and two identical candles or small toys
- A shiny spoon (back side for a convex mirror) or a car's side mirror
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
The image of a point in a plane mirror lies as far behind it as the point is in front; why the angle of reflection equals the angle of incidence; constructing an image; reversed images; the candle-in-water trick and the stage ghost; multiple images in an ordinary mirror; convex mirrors, their focal length (half the radius) and their small, erect images. Four questions follow.
The lesson, step by step
Hook question
SayWhen you raise your right hand in a mirror, your image raises its left. Why doesn't the mirror also flip you upside down?
Read together
Read §§ 528–537. The rule:
the image of a point in a plane mirror lies on the perpendicular drawn from the point to the mirror, and is as far back of the mirror as the point is in front of it.
Try it: the ghost in the glass
Stand the clear glass upright on a table. Put one toy (or unlit candle) in front of it and move an identical one behind it until it seems to sit exactly where the reflection is (§ 531). Measure both distances from the glass: they are equal. A lit candle in front makes a candle that seems to burn behind the glass (with an adult).
Explain the idea
Light from each point reflects so that it seems to come from a point just as far behind the mirror. Front and back are swapped, which is why writing looks reversed (§ 530). Draw Fig. 439 with an arrow and its image.
Try it: convex mirrors
Look into the back of a shiny spoon: you look small and upright, and the image stays close behind the spoon however far away you go (§ 533). A car's side mirror and a store's security mirror are convex for the same reason: they show a wide view. Point out the warning printed on many car mirrors: objects are closer than they appear.
Say it back
Your student explains why a convex mirror's image can never be farther back than its focal point.
Questions
Work questions 1–4 on book page 419. For question 4, draw the man, the mirror and the rays from his head and feet to his eye.
Afterwards
Find convex mirrors in the world: store corners, driveways, car side mirrors, the bell of a shiny teapot.
Answers to the book's problems
1. His image lies horizontally, as though he were lying stretched out (above or in front of him), since a 45° mirror turns vertical into horizontal. 2. 60° (each ray makes 30° with the normal). 3. 24 ft. a second. 4. The mirror must reach from halfway between his eyes and the top of his head to halfway between his eyes and his feet, which is half his height; his distance from the mirror does not matter.
Worked out for this site from the scan. If a number in your copy differs, trust the book.