Question

A lens forms a real image of an object at a distance of $20cm$ . It is observed that on placing another identical lens in contact with it, the image gets shifted by $10cm$ towards the combination. The power of the lens is

• A. $5D$
• B. $2.5D$
• C. $10D$
• D. $2D$

Answer 1

Answer: (A)

As image formed is real therefore lens must be convex, $v=20cm$ . Let $f_1$ , be focal length for this lens.
$\therefore \frac{1}{f_1}=\frac{1}{v}-\frac{1}{u}=\frac{1}{20}-\frac{1}{u}$
After placing it in contact with another lens, the image is shifted $10cm$ towards the combination.
$i.e,.v=\left(20-10\right)cm=10cm$
$\therefore \frac{1}{10}-\frac{1}{u}=\frac{1}{f_1}+\frac{1}{f_2}=\left(\frac{1}{20}-\frac{1}{u}\right)+\frac{1}{f_2}\Rightarrow f_2=20cm$
$\therefore P=\frac{100}{20}{m}^{-1}=5D$