question_answer

A point object is placed at a distance of 30 cm along the principal axis of a convex lens of focal length 20 cm and aperture 4 cm. The lens is cut by a plane parallel to its principal axis and both the identical pieces are inverted and placed in contact at their vertex. The distance between the images formed is

A) 4 cm

B) 8 cm

C) 12 cm

D) 16 cm

Correct Answer: C

Solution :

[c] Here, magnification \[m=\frac{f}{m+f}=\frac{20}{-30+20}=-2\frac{{{h}_{i}}}{{{h}_{0}}}\] \[\Rightarrow \]   \[{{h}_{i}}=-2{{h}_{0}}\] So, the image is real and inverted. Thus, due to upper lens, image will be formed \[{{h}_{i}}=-2(-2cm)=\] above upper principal axis and similarly for lower lens, 4 cm below lower principal axis. So, the separation between the images is \[4+4+(d)\,cm=12\,cm.\]