Question

Two convex lenses of focal length $20\text{cm}$ each are placed coaxially with a separation of $60\text{cm}$ between them. Find the equivalent focal length of the combination and also comment on the nature of lens.

• A. $-20\text{cm}$, diverging
• B. $-20\text{cm}$, converging
• C. $+20\text{cm}$, converging
• D. $-30\text{cm}$, diverging

Answer 1

The correct option is A $-20\text{cm}$, diverging


Given,
focal length of lens $1$, $f_1=20\text{cm}$
focal length of lens $2$, $f_2=20\text{cm}$
distance between the lens, $d=60\text{cm}$

We can replace the lenses by an equivalent lens having focal length $f$ given by
$$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1{f}_2}$$
Substituting the given data we get,

$\frac{1}{f}=\frac{1}{20}+\frac{1}{20}-\frac{60}{400}$

$\therefore f=-20\text{cm}$

Since, focal length is negative, we can say that equivalent lens behaves as a diverging lens.

Hence, option (a) is the correct answer.