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Mission RM7 Concave Mirror Mathematics

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Hold down the T key for 3 seconds to activate the audio accessibility mode, at which point you can click the K key to pause and resume audio. Useful for the Check Your Understanding and See Answers.

 The Question

In a classroom demonstration, a physics teacher places a candle a distance of 68.1 cm from a concave mirror and measures an image distance of 94.8 cm. What is the focal length of the mirror?

 Formula Fix

The mirror equation relates the object distance (do), the image distance (di) and the focal length (f):
 
1 / do + 1 / di = 1 / f

 Math Magic

The mirror equation, with its three reciprocal terms, is a little awkward to work with. The focal length (the unknown) is already by itself on the right side of the equation; so an algebra step is not needed here. Simply substitute the two numerical values into the equation and use your calculator to evaluate the left side. Once done, the reciprocal of the focal length is equal to the number on your calculator. Take the reciprocal of this number to determine the focal length.

 A Very Fine Detail

The Minds On Physics program calculates answers accurate to the fourth decimal place. Your answer does not need to be that accurate. The program will allow you to have a 1 percent deviation from the right answer without being wrong. This means two things: 1) Enter your answer with at least three significant digits. 2) Do not round any numbers until your final calculation.

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