Question

Three lenses in contact have a combined focal length of $12\text{cm}$. When the third lens is removed, the combined focal length is $\frac{60}{7}\text{cm}$. The third lens is a

• A. converging lens of focal length $30\text{cm}$
• B. converging lens of focal length $60\text{cm}$
• C. diverging lens of focal length $30\text{cm}$
• D. diverging lens of focal length $60\text{cm}$

Answer 1

The correct option is C diverging lens of focal length $30\text{cm}$

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

Then we have, initially

$\frac{1}{F_1}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}.....\left(1\right)$

where $F_1=12\text{cm}$

When the third lens is removed, we have

$\frac{1}{F_2}=\frac{1}{f_1}+\frac{1}{f_2}.....\left(2\right)$

where $F_2=\frac{60}{7}\text{cm}$

On subtracting $\left(2\right)$ from $\left(1\right)$ we get,

$\frac{1}{F}-\frac{1}{F_2}=\frac{1}{f_3}$

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

$\frac{5-7}{60}=\frac{1}{f_3}$

$f_3=-30\text{cm}$.

Since $f_3$ is negative, it is a diverging lens.