A lens is formed by placing the plane faces of two identical plano-convex lenses (each of focal length 40 cm) touching each other. It is used to obtain a real, inverted image of the same size as the object. The distance of the object from the lens is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 40 cm
When two lenses are kept in contact, the effective focal length $(F_{eff})$ is -
$(F_{eff})=\frac{1}{F_1}+\frac{1}{F_2}$
$(F_{eff})=\frac{1}{40}+\frac{1}{40}=\frac{2}{40}=\frac{1}{20}$
$(F_{eff})=20cm$ [Both lens had $f = 40 cm$ and identically]
Now,
Since, $v=-u$ a image should be inverted and be of the same size.
$(F_{eff})=\frac{1}{u}-\frac{-1}{u}$
$\frac{1}{20}=\frac{2}{u}$
$=u=40cm$