Question

If two converging lenses of equal focal length \(f\) are kept in contact, then the focal length of the combination will be

• A. \(f\)
• B. \(2f\)
• C. \(\frac{f}{2}\)
• D. \(3f\)

Hint:

For two lenses in contact, the focal length of the combination is given by \(f = \frac{f}{2}\) if both lenses have equal focal lengths.

Answer 1

The Correct Option is C

Step 1: Formula for focal length of two lenses in contact.
When two lenses of focal lengths \(f_1\) and \(f_2\) are in contact, the focal length \(f\) of the combination is given by: \[ \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} \] For two lenses with equal focal lengths \(f_1 = f_2 = f\), this becomes: \[ \frac{1}{f} = \frac{1}{f} + \frac{1}{f} \] Solving for \(f\): \[ \frac{1}{f} = \frac{2}{f} \quad \Rightarrow \quad f_{\text{combination}} = \frac{f}{2} \]
Step 2: Analyze options.
- (A) \(f\): Incorrect. This would be the case for two lenses in parallel, not in contact.
- (B) \(2f\): Incorrect. The focal length of the combination is not twice the focal length of one lens.
- (C) \(\frac{f}{2}\): Correct. The focal length of two lenses in contact is half the focal length of one lens.
- (D) \(3f\): Incorrect. This is not the correct relationship for two lenses in contact.
Step 3: Conclusion.
The focal length of the combination of two converging lenses in contact is \(\frac{f}{2}\).