Question

Find the focal length of a lens in a compound lens system.

• A. \( \frac{1}{f_{total}} = \frac{1}{f_1} + \frac{1}{f_2} \)
• B. \( \frac{1}{f_{total}} = \frac{1}{f_1} - \frac{1}{f_2} \)
• C. \( f_{total} = f_1 + f_2 \)
• D. \( f_{total} = f_1 - f_2 \)

Hint:

When two lenses are in contact, use the reciprocal rule: \( \frac{1}{f_{total}} = \frac{1}{f_1} + \frac{1}{f_2} \). This is essential for calculating the total focal length.

Answer 1

The Correct Option is A

To solve the problem, we need to find the focal length of a lens in a compound lens system.

1. Understanding the Concept:

- Focal Length (f): The distance between the center of the lens and the point where parallel rays of light converge or diverge.
- In a compound lens system, the total focal length \( f_{\text{total}} \) of the system is related to the focal lengths of the individual lenses \( f_1 \) and \( f_2 \) by the formula:

\( \frac{1}{f_{\text{total}}} = \frac{1}{f_1} + \frac{1}{f_2} \)

2. Given Values:

- The focal lengths of the individual lenses, \( f_1 \) and \( f_2 \).

3. Calculating the Total Focal Length:

The formula for the total focal length of a compound lens system is:

\[ \frac{1}{f_{\text{total}}} = \frac{1}{f_1} + \frac{1}{f_2} \]

4. Final Answer:

The correct formula for the focal length in a compound lens system is \( \frac{1}{f_{\text{total}}} = \frac{1}{f_1} + \frac{1}{f_2} \), which corresponds to Option A.