Question

Two thin lenses of focal lengths f₁ and f₂ are placed in contact with each other. Then the equivalent focal length of the combination will be:
1. f₁ + f₂
2. \(\dfrac{1}{f_1 + f_2}\)
3. \(\dfrac{f_1 f_2}{f_1 + f_2}\)
4. \(\dfrac{f_1+ f_2}{f_1 f_2}\)

Answer 1

Correct Answer - Option 3 : \(\dfrac{f_1 f_2}{f_1 + f_2}\)

CONCEPT:

• The focal length of the combination: When two lenses of focal length f1 and f2 are placed in contact, the effective focal length f of the combination is given by:

\( {1 \over f}= {1 \over f_1} +{1 \over f_2}\)

​CALCULATION:

Given that Two thin lenses are of focal lengths f1 and f2 

The focal length of the combination \( {1 \over f}= {1 \over f_1} +{1 \over f_2}\)

\(f=\dfrac{f_1 f_2}{f_1 + f_2}\)

So the correct answer is option 3.

• The focal length of the convex lens is positive and that of the concave lens is negative.