Question

An extended object of size $2mm$ is placed on the principal axis of a converging lens of focal length $10cm$. It is found that when the object is placed perpendicular to the principal axis the image formed is $4mm$ in size. The size of image when it is placed along the principal axis is ____________ mm.

Answer 1

When the object is placed perpendicular to the principle axis,

$M=\frac{4}{2}=2=\frac{v}{u}$

From lens equation, $\frac{v}{u}=\frac{f}{u+f}=2$

Hence, $u=-15cm$,$v=30cm$

Now when the object is placed along the principle axis, one of the end point lies $15cm$ from the lens, and the other end point lies $14.8cm$ from the lens.

Image of first end point is again obtained at $30cm$ from the lens.

Using lens equation,

$\frac{1}{v_2}-\frac{1}{-14.8}=\frac{1}{10}$

$⟹v_2\approx 30.8cm$

Hence the size of the image is the distance between two end point of the image=$0.8cm=8mm$