Question

A convex lens $A$ of focal length $20cm$ and a concave lens $B$ of focal length $5cm$ are kept along the same axis with a distance ${}^{\prime }{d}^{\prime }$ between them as shown in a figure. If a parallel beam falling on $A$ emerges parallel from $B$, then ${}^{\prime }{d}^{\prime }$ is equal to

• A. $15$
• B. $20$
• C. $22.5$
• D. $25$

Answer 1

The correct option is A $15$

$\frac{1}{V}=\frac{1}{U}=\frac{1}{f}$

As the incident beam is parallel; (Let the there be no second lens), the image will form at $V$ such that

$\frac{1}{V}-\frac{1}{-\infty }=\frac{1}{20}$

$V=+20cm$

(i) if d is the distance between two lenses, then distance between the image and the concave lens is $(20-d)$

(ii) Image will act as object for 2nd refraction and image will be at infinity.

$\frac{1}{\infty }-\frac{1}{(20-d)}=\frac{1}{-5}$

$(20-d)=-5$

$d=15cm$