Question

A 10 cm long pin lies along the principal axis of a convex lens of focal length 10 cm such that the nearer end of the pin is at a distance of 15 cm from the lens. Find the length of the image of the pin formed by the lens.

Answer 1

Treat two ends of the pin as two different objects.

For $O_1$

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\frac{1}{v}=\frac{1}{f}+\frac{1}{u}=\frac{1}{+10}+\frac{1}{-15}\therefore v=\frac{10\times -15}{-5}=30cm$

For $O_2$

$\frac{1}{v}=\frac{1}{f}+\frac{1}{u}=\frac{1}{+10}+\frac{1}{-25}\therefore v=\frac{10\times -25}{-15}=\frac{50}{3}cm$

Hence length of image formed$=(30-\frac{50}{3})=\frac{40}{3}=13.4cm$