Question

An object placed at $15cm$ from the lens is moving towards the lens at a speed of $4cm/s$. The focal length of the lens is given as $f=10cm$. Find the velocity of the image.

Answer 1

u = -15cm f = 10cm

from lens formula

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{v}+\frac{1}{15}=\frac{1}{10}$

$v=30cm$

hence magnification, $m=\frac{v}{u}=\frac{30}{-15}=2$

So speed of image = -m speed of object

$speedofimage=+8cm/s$