Question

A convex lens of focal length $f_1$ is combined with a concave lens of focal length $f_2$ and their combined focal length is observed to be $f$. The combination of these lenses will behave like a concave lens if

• A. $f_1>f_2$
• B. $f_1<f_2$
• C. $f_1=f_2$
• D. cannot be determined

Answer 1

The correct option is A $f_1>f_2$

We know that, if lenses are placed in contact, the focal length of the equivalent lens can be given as,
$$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$$

Focal length of converging lens is positive and that of diverging lens is negative.

$\therefore \frac{1}{f}=\frac{1}{f_1}-\frac{1}{f_2}$

or we can say that, $P=P_1+P_2$

where $P_1$ is the power of convex lens and $P_2$ is the power of concave lens.

If the power of concave is greater than the power of convex lens, then the power of the combination of lenses is negative i.e it behaves like a concave lens.

Thus we can say that,

$\frac{1}{f_2}>\frac{1}{f_1}\Rightarrow f_1>f_2$

Hence, option (a) is the correct answer.

Why this question ? Note:- Power of a lens is reciprocal of its focal length.