Question

Find the focal length of the combination of two thin lenses in contact.

Hint:

When two lenses are in contact, the focal length of the combination is determined by the sum of their individual powers.

Answer 1

Step 1: Formula for focal length of lens combination.
When two thin lenses are in contact, the focal length \( f_{\text{comb}} \) of the combination is given by the formula: \[ \frac{1}{f_{\text{comb}}} = \frac{1}{f_1} + \frac{1}{f_2} \] where \( f_1 \) and \( f_2 \) are the focal lengths of the individual lenses. Step 2: Determining the focal length.
For two lenses in contact, the total power \( P_{\text{comb}} \) is the sum of the individual powers: \[ P_{\text{comb}} = P_1 + P_2 \] where \( P_1 = \frac{1}{f_1} \) and \( P_2 = \frac{1}{f_2} \).
Step 3: Conclusion.
Thus, the focal length of the combination can be determined from the above formulas. If you know the powers or individual focal lengths of the lenses, you can calculate the total focal length of the combination.