Question

Two thin convex lenses are kept in contact coaxially. If the focal length of the combination is $4~\text{cm$ and the sum of the focal lengths of the two lenses is $18~\text{cm}$, then the focal length of the lens of low power is}

• A. $8~\text{cm}$
• B. $10~\text{cm}$
• C. $6~\text{cm}$
• D. $12~\text{cm}$

Hint:

Use lens combination formula $\dfrac{1}{f} = \dfrac{1}{f_1} + \dfrac{1}{f_2}$ and total sum to solve.

Answer 1

The Correct Option is D

Let $f_1$ and $f_2$ be the focal lengths.
Given: $\dfrac{1}{f} = \dfrac{1}{f_1} + \dfrac{1}{f_2}$ and $f = 4~\text{cm}$, $f_1 + f_2 = 18$
Assume $f_1 = 6~\text{cm}, f_2 = 12~\text{cm}$
Check: $\dfrac{1}{6} + \dfrac{1}{12} = \dfrac{2+1}{12} = \dfrac{3}{12} = \dfrac{1}{4} \Rightarrow f = 4$
Thus, lens of low power has longer focal length = $12~\text{cm}$