Question

A convex lens A of focal length 4 m and a concave lens B of focal length 1 m are kept along the same axis with a distance d between them. If a parallel beam of light falling on A leaves B as a parallel beam, then d in m is equal to:

Answer 1

The focal length of combination is given by the formula
$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1{f}_2}$
Here $f_1$, $f_2$ are the focal lengths, d is the distance between lenses and f is the combined focal length.
Since the resultant ray is parallel to the axis, the real image is going to be formed at infinity and hence the combined focal
length $f=\infty$
We will now substitute,
$f=\infty ,f_1=4m,f_2=-1m$
To find the value of d
$\frac{1}{\infty }=\frac{1}{4}+\frac{1}{(-1)}-\frac{d}{\left(4\right)(-1)}$
$\therefore d=3m$