Question

Two convex lenses of focal lengths \( 60 \, \text{cm} \) and \( 20 \, \text{cm} \) are held coaxially in contact with each other. The power of the combination is:

Hint:

The combined power of coaxial lenses in contact is the algebraic sum of their individual powers. Always use focal lengths in the same unit and ensure consistency in calculations.

Answer 1

The power of a lens, denoted by \(P\), is calculated as \(P = \frac{1}{f}\), where \(f\) is the focal length in meters. When two lenses are in contact, their total power is the sum of their individual powers: \(P_{\text{total}} = P_1 + P_2\). For the first lens with a focal length of \(60 \, \text{cm}\) (\(0.6 \, \text{m}\)), its power is \(P_1 = \frac{1}{0.6} = 1.67 \, \text{D}\). For the second lens with a focal length of \(20 \, \text{cm}\) (\(0.2 \, \text{m}\)), its power is \(P_2 = \frac{1}{0.2} = 5 \, \text{D}\). The total power of the combined lenses is \(P_{\text{total}} = 1.67 \, \text{D} + 5 \, \text{D} = 6.67 \, \text{D}\). Therefore, the total power is approximately \(6.6 \, \text{D}\). \[\boxed{6.6 \, \text{D}}\]