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 \(P\) of a lens is given by the equation: \[ P = \frac{1}{f} \] Where \(f\) is the focal length of the lens in meters. The power of two lenses in contact is the sum of their individual powers: \[ P_{\text{total}} = P_1 + P_2 \] For the first lens with a focal length of \(60 \, \text{cm}\) (or \(0.6 \, \text{m}\)): \[ P_1 = \frac{1}{0.6} = 1.67 \, \text{D} \] For the second lens with a focal length of \(20 \, \text{cm}\) (or \(0.2 \, \text{m}\)): \[ P_2 = \frac{1}{0.2} = 5 \, \text{D} \] The total power of the combination is: \[ P_{\text{total}} = 1.67 \, \text{D} + 5 \, \text{D} = 6.67 \, \text{D} \] Thus, the correct answer is approximately \(6.6 \, \text{D}\). \[ \boxed{6.6 \, \text{D}} \]