Question

A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 40 cm. The power of the combination is

• A. +2.5 D
• B. -2.5 D
• C. +5.0 D
• D. -5.0 D
• E. +1.25 D

Hint:

Since the resulting power is positive, the entire combination acts as a \textbf{converging} (convex) lens. Always remember: Convex is positive (+), Concave is negative (-).

Answer 1

The Correct Option is A

Concept:
Physics - Combination of Lenses.
Step 1: Identify focal lengths with sign convention.

• Convex lens ($f_1$): +20 cm
• Concave lens ($f_2$): -40 cm

Step 2: Calculate individual powers.
Power $P = \frac{1}{f \text{ (in meters)}}$ or $P = \frac{100}{f \text{ (in cm)}}$.

• $P_1 = \frac{100}{20} = +5.0$ D
• $P_2 = \frac{100}{-40} = -2.5$ D

Step 3: Find the total power of the combination.
The total power $P$ of lenses in contact is the algebraic sum of their individual powers: $$ P = P_1 + P_2 $$ $$ P = (+5.0) + (-2.5) $$ $$ P = +2.5 \text{ D} $$