Question

Powers of two lenses kept in contact are \( P_1 \) and \( P_2 \). The power of the equivalent lens will be:

• A. \( P_1 + P_2 \)
• B. \( P_1 - P_2 \)
• C. \( P_1 \times P_2 \)
• D. \( \frac{P_1}{P_2} \)

Hint:

Power of lenses in contact adds algebraically.

Answer 1

The Correct Option is A

When two lenses are placed in contact (i.e., their separation is negligible), the combined power \( P \) of the lens system is the algebraic sum of the powers of the individual lenses. Mathematically, this is expressed as: \[ P = P_1 + P_2, \] where \( P_1 \) and \( P_2 \) are the powers of the first and second lenses respectively. This result assumes the lenses are thin and placed close together, so their focal lengths combine according to the formula: \[ \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}, \] and since power \( P = \frac{100}{f} \) (in diopters if \( f \) is in centimeters), the powers add directly.