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 $10 \, cm$ towards the combination. The power of the lens is

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

Answer 1

Answer: (A)

As image formed is real therefore lens must be convex, $v=20 \, cm$ . 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 $10 \, cm$ towards the combination.
$i.e,. \, v=\left(20 - 10\right)cm=10 \, cm$
$\therefore \frac{1}{10}-\frac{1}{u}=\frac{1}{f_{1}}+\frac{1}{f_{2}}=\left(\frac{1}{20} - \frac{1}{u}\right)+\frac{1}{f_{2}}\Rightarrow f_{2}=20 \, cm$
$\therefore \, P=\frac{100}{20}m^{- 1}=5D$