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
Two thin lenses in contact act as one lens whose power is the sum of the two powers.
\( \displaystyle \frac{1}{F} = \frac{1}{40} + \frac{1}{40} = \frac{1}{20}\,\mathrm{cm^{-1}} \Rightarrow F = 20\,\mathrm{cm} \)
A real, inverted image of the same size has magnification \( m = v/u = -1 \), so \( v = -u \). Taking \( u = -x \) and \( v = +x \) in the lens formula (distances measured from the lens, positive along the incident light):
\( \displaystyle \frac{1}{v} - \frac{1}{u} = \frac{1}{F} \Rightarrow \frac{1}{x} + \frac{1}{x} = \frac{1}{20} \)
\( x = 40\,\mathrm{cm} \)