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Determine the optical power of a system where the combined focal length is given by the formula \( \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} \).

1. \( P = \frac{f_1 + f_2}{f_1 f_2} \)
2. \( P = \frac{f_1 f_2}{f_1 + f_2} \)
3. \( P = \frac{1}{f_1 + f_2} \)
4. \( P = \frac{1}{f_1 f_2} \)

Correct answer: \( P = \frac{f_1 f_2}{f_1 + f_2} \)

Solution

The power of a lens is given by the reciprocal of its focal length, i.e., P = 1/f. For a combination of lenses, the combined power is the sum of the individual powers: P = P1 + P2 = 1/f1 + 1/f2. Substituting this into the formula for combined focal length, we get P = 1/f = (f1 + f2) / (f1 * f2).

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