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 resolve the problem, it is necessary to determine the focal length of a lens within a compound lens system.

1. Conceptual Definition:

- Focal Length (f): This denotes the distance from the lens's center to the point where parallel light rays converge or diverge.
- For a compound lens system, the aggregate focal length \( f_{\text{total}} \) is derived from the individual focal lengths \( f_1 \) and \( f_2 \) using the subsequent formula:

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

2. Provided Data:

- The focal lengths of the constituent lenses, denoted as \( f_1 \) and \( f_2 \).

3. Computation of Total Focal Length:

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

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

4. Concluding Result:

The definitive formula for focal length in a compound lens system is \( \frac{1}{f_{\text{total}}} = \frac{1}{f_1} + \frac{1}{f_2} \), aligning with Option A.