Two lenses of focal lengths, \( 20\,\mathrm{cm} \) and \( -25\,\mathrm{cm} \), respectively are placed in contact with each other. The power of the combination of lenses is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 1\,\mathrm{D} \)
For thin lenses in contact the powers add, and the power of a lens is \( P = 1/f \) with \( f \) in metres.
\( \displaystyle f_1 = 20\,\mathrm{cm} = 0.20\,\mathrm{m}, \qquad f_2 = -25\,\mathrm{cm} = -0.25\,\mathrm{m} \)
\( \displaystyle P_1 = \frac{1}{0.20} = +5\,\mathrm{D}, \qquad P_2 = \frac{1}{-0.25} = -4\,\mathrm{D} \)
\( \displaystyle P = P_1 + P_2 = 5 - 4 = +1\,\mathrm{D} \)