A convex lens ‘A’ of focal length 20 cm and a concave lens ‘B’ of focal length 5 cm 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 the distance ‘d’ in cm will be :

The correct option is 15.

Let us analyze the behavior of the light beam passing through the combination of lenses step-by-step:

1. Action of Convex Lens A:
A parallel beam of light falling on the convex lens A (of focal length $f_A=20\text{cm}$) converges towards its principal focus. Therefore, in the absence of lens B, the light rays would converge at a point $F_A$ situated at a distance of $20\text{cm}$ to the right of lens A.

2. Action of Concave Lens B:
A concave lens B of focal length $f_B=-5\text{cm}$ is placed coaxially at a distance $d$ from lens A. The converging rays from lens A serve as a virtual object for lens B.

For the rays to leave lens B as a parallel beam (i.e., focus at infinity), the virtual object must lie at the focus of lens B ($F_B$). This means that the virtual object distance $u$ for lens B must be equal to its focal length:
$u=+5\text{cm}$

3. Calculating the Distance $d$:
Since the focal points of both lenses must coincide for the final beam to emerge parallel:
$d=f_A-\left|f_B\right|$

Substituting the given values:
$d=20-5=15\text{cm}$

Thus, the distance $d$ between the two lenses is $15\text{cm}$.