How is the power of a combination of lenses described? The powers of the lenses are $P_{1}, P_{2}, P_{3}$ and $P_{4}$ .

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Solution

Step 1: Given data,
The powers of the lenses are $P_{1}, P_{2}, P_{3}$ , and $P_{4}$ .
Step 2: Describe the power of a combination of lenses,
Power of lens is defined as the inverse of its focal length, that is, $P o w e r o f a l e n s = \frac{1}{f o c a l l e n g t h o f t h e l e n s}$
The net power of the combination of lenses is equal to the algebraic sum of powers of all lenses in the combination, that is, $P = P_{1} + P_{2} + P_{3} + P_{4}$ .
As the power of the lens and the focal length are inversely related to each other, the relation $P = P_{1} + P_{2} + P_{3} + P_{4}$ can be expressed as $\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}} + \frac{1}{f_{4}}$ , where, $f$ is the focal length of the combination of lenses and $f_{1}, f_{2}, f_{3}$ and $f_{4}$ are the focal lengths of the four lenses in combination.
Thus, the power of a combination of lenses is described as $P = P_{1} + P_{2} + P_{3} + P_{4}$ or $\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}} + \frac{1}{f_{4}}$ .

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