Question

A lens of power \( +1 \, \text{D} \) is made in contact with another lens of power \( -2 \, \text{D} \). The combination will then act as:

• A. Diverging lens of focal length 100 cm
• B. Diverging lens of focal length 33.3 cm
• C. Converging lens of focal length 33.3 cm
• D. Converging lens of focal length 100 cm

Hint:

When two lenses are combined in contact, their powers add algebraically. A negative total power indicates a diverging lens, while a positive total power indicates a converging lens.

Answer 1

The Correct Option is A

The power of a lens is related to its focal length (\(f\)) by the equation: \[ P = \frac{1}{f} \] where \(P\) is the power of the lens in diopters (D) and \(f\) is the focal length in meters. For a lens combination, the total power \(P_{\text{total}}\) is the sum of the individual powers: \[ P_{\text{total}} = P_1 + P_2 \] Given that the power of the first lens \(P_1 = +1 \, \text{D}\) and the power of the second lens \(P_2 = -2 \, \text{D}\), the total power is: \[ P_{\text{total}} = 1 + (-2) = -1 \, \text{D} \] Now, the total focal length \(f_{\text{total}}\) can be calculated using the formula: \[ f_{\text{total}} = \frac{1}{P_{\text{total}}} = \frac{1}{-1} = -1 \, \text{m} \] The negative sign indicates that the lens combination behaves as a diverging lens. The focal length of the diverging lens is \(100 \, \text{cm}\) (since \(f = -1 \, \text{m}\)).
Thus, the combination of the two lenses behaves as a diverging lens with a focal length of \(100 \, \text{cm}\).