Question

Two thin convex lenses of focal length $f_1$ and $f_2$ are placed in contact with each other. The equivalent power of the lens combination is ______.

• A. $f_1 \times f_2$
• B. $\frac{f_1 + f_2}{f_1 \times f_2}$
• C. $f_1 + f_2$
• D. $\frac{f_1 \times f_2}{f_1 + f_2}$

Hint:

If the question asked for the equivalent \textbf{focal length}, the answer would be the reciprocal: $\frac{f_1 f_2}{f_1 + f_2}$ (Option d). Always check if they are asking for Power or Focal Length!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
When lenses are in contact, their powers are additive: $P_{eq} = P_1 + P_2$. Power is defined as the reciprocal of the focal length ($P = 1/f$).
Step 2: Detailed Explanation:
$$P_{eq} = \frac{1}{f_1} + \frac{1}{f_2}$$ Taking the Least Common Multiple (LCM) of the denominators: $$P_{eq} = \frac{f_2 + f_1}{f_1 \times f_2} = \frac{f_1 + f_2}{f_1 \times f_2}$$
Step 3: Final Answer:
The equivalent power is $\frac{f_1 + f_2}{f_1 \times f_2}$.