Question

Two similar plano-convex lenses are combined together in three different ways as shown in the figure below. The ratio of the focal lengths in the three cases will be

• A. $2:2:1$
• B. $1:1:1$
• C. $1:2:2$
• D. $2:1:1$

Answer 1

The correct option is B $1:1:1$

We know that, focal length of a plano-convex lens is given by
$$f=\frac{R}{\mu -1}.......\left(1\right)$$
where $\mu$ is refractive index of medium of lens.

For two lenses in contact with each other, the focal length of combination is given by,

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

This is same for all the three given cases.

Substituting $\left(1\right)$ in $\left(2\right)$, we get

$\frac{1}{f}=\frac{\mu -1}{R}+\frac{\mu -1}{R}$

$\Rightarrow \frac{1}{f}=\frac{2(\mu -1)}{R}$

$\Rightarrow f=\frac{R}{2(\mu -1)}$

Thus the ratio of focal length in three cases will be $1:1:1$

Hence, option (b) is the correct answer.

Why this question ? Note:-The focal length of all possible combinations of any two plano-convex lenses is same.