Question

A thin converging lens of focal length 20 cm and a thin diverging lens of focal length 15 cm are placed coaxially in contact. The power of the combination is:

• A. \( -\frac{5}{6} \) D
• B. \( -\frac{5}{3} \) D
• C. \( \frac{4}{3} \) D
• D. \( \frac{3}{2} \) D

Hint:

The total power of lenses in contact is the algebraic sum of their individual powers: \( P_{\text{total}} = P_1 + P_2 \).

Answer 1

The Correct Option is B

Power of a Combination of Lenses

Step 1: Understanding Lens Power
- Lens power \( P \) is calculated as: \[ P = \frac{100}{f} \quad \text{(in diopters, D)} \] where: - \( f \) is the focal length in cm.

Step 2: Calculating Individual Lens Powers
- Converging lens (convex): \[ P_1 = \frac{100}{20} = 5D \] - Diverging lens (concave): \[ P_2 = \frac{100}{-15} = -\frac{100}{15} = -\frac{20}{3}D \] 

Step 3: Total Power of the Combined Lenses
For lenses in contact, the net power is the sum of individual powers: \[ P_{\text{net}} = P_1 + P_2 \] \[ P_{\text{net}} = 5 - \frac{20}{3} \] \[ P_{\text{net}} = \frac{15}{3} - \frac{20}{3} = -\frac{5}{3} D \] 

Step 4: Result
The power of the combination is: \[ \boxed{-\frac{5}{3} D} \), corresponding to option (B).