Question

If a thin lens of focal length 20 cm is in contact with another lens of power 4 D, then the effective power of the combination is

• A. 9 D
• B. 6 D
• C. 5 D
• D. 10 D
• E. 11 D

Hint:

Always check the focal length unit! If given in cm, use \( P = 100/f \).
\( 100/20 = 5 \text{ D} \).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
When two or more thin lenses are in contact, the total power of the combination is the algebraic sum of the powers of individual lenses.

Step 2: Key Formula or Approach:
Power \( P = 1/f \) (where \( f \) is in meters).
\( P_{\text{eff}} = P_1 + P_2 \).

Step 3: Detailed Explanation:
Given:
Focal length of lens 1, \( f_1 = 20 \text{ cm} = 0.2 \text{ m} \).
Power of lens 1, \( P_1 = 1 / 0.2 = 5 \text{ D} \).
Power of lens 2, \( P_2 = 4 \text{ D} \).
Total effective power:
\[ P_{\text{eff}} = 5 \text{ D} + 4 \text{ D} = 9 \text{ D} \]

Step 4: Final Answer:
The effective power of the combination is 9 D.