Question

Three lenses in contact have a combined focal length of $12cm$. When the third lens is removed the combined focal length becomes $60cm$. The third lens is :

• A. a diverging lens of focal length 30 cm
• B. a converging lens of focal length 30 cm
• C. a converging lens of focal length 60 cm
• D. a diverging lens of focal length 60 cm

Answer 1

Answer: (A)

Let $f_1$, $f_2$ and $f_3$ be three focal lengths of the lenses.

$f=12$

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}$

When the third lens is removed, $\frac{1}{f^{\prime }}=\frac{1}{f_1}+\frac{1}{f_2}$

$f^{\prime }=\frac{60}{7}$

$\frac{1}{12}=\frac{1}{\frac{60}{7}}+\frac{1}{f_3}$

$\Rightarrow f_3=-30$

Since $f_3$ is negative, it is a diverging lens having focal length 30cm.