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.... 
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A SearchlightSuppose 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 θ_{i}=0. To place the lightbulb correctly, however, we need to know a distance, not an angle: the distance d_{o} 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 θ_{i}=0. These are related by d_{i}=1/θ_{i}, 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.


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