Question

Figures shows a convex lens cut symmetrically into two equal halves and separated laterally by a distance h. A point object placed at a distance 30 cm, from the lens halves, forms two real images separated by a distance d. A plot of d versus h is shown in figure. The focal length of the lens is

• A. 35 cm
• B. 40 cm
• C. 45 cm
• D. 60 cm

Answer 1

Answer: (D)

60 cm

Image distance from each part of the lens=$v=\frac{uf}{u+f}$

$⟹M=\frac{v}{u}=\frac{f}{u+f}=\frac{f}{f-30}$

Thus the distance of each image from corresponding principle axis=$M\frac{h}{2}$

Thus distance of image from dotted line=$\frac{h}{20}+M\frac{h}{2}=(M+1)\frac{h}{2}$.

Thus the distance between the objects=$d=(M+1)h=\frac{2f-30}{f-30}h$

$⟹\frac{d}{h}=\frac{2f-30}{f-30}=3$

$⟹f=60cm$