Question

A lens of focal length $f$ produces an image of an object located $15cm$ on one side of it at a distance of $30cm$ on the other side. If the lens is replaced by another lens of focal length $\frac{f}{2}$, where would the image form? If the image has to form at the earlier position by what distance should the object be shifted?

Answer 1

Here object distance $u=-15cm$

$v=30cm$

So, using the lens' formula

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\frac{1}{f}=\frac{1}{30}-\frac{1}{-15}$

$f=10cm$

When the focal become half $f_1=f/2=5cm$

Let say image forms at $v_1$

So $\frac{1}{f_1}=\frac{1}{v_1}-\frac{1}{u}$

$\frac{1}{5}=\frac{1}{v_1}-\frac{1}{-15}$

$v_1=7.5cm$

If the image has to form at the earlier position,

Let say object is placed at $u_1$

$v=30cm$

$\frac{1}{f_1}=\frac{1}{v}-\frac{1}{u_1}$

$\frac{1}{5}=\frac{1}{30}-\frac{1}{u_1}$

$u_1=-6cm$

So initially it was at $15cm$ and now it should be placed at $6cm$ from lens.

So it need to move $15-6=9cm$ towards lens.