Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

# A Searchlight

Suppose we need to create a parallel beam of light, as in a searchlight. Where should we place the lightbulb? A parallel beam has zero angle between its rays, so θi=0. To place the lightbulb correctly, however, we need to know a distance, not an angle: the distance do between the bulb and the mirror. The problem involves a mixture of distances and angles, so we need to get everything in terms of one or the other in order to solve it. Since the goal is to find a distance, let's figure out the image distance corresponding to the given angle θi=0. These are related by di=1/θi, so we have d i=∞. (Yes, dividing by zero gives infinity. Don't be afraid of infinity. Infinity is a useful problemsolving device.) Solving the distance equation for do, we have

The bulb has to be placed at a distance from the mirror equal to its focal point.

Last Update: 2010-11-11