The focal length of a convex lens is $30cm$ and the size of the image is half of the object. The object distance is

The correct option is A

$90cm$

Step 1: Given and find,

The focal length of a convex lens $f=30cm$

$sizeofimage=\frac{1}{2}\times sizeofobject$

To find: Distance of object

Step 2: Explanation:

Magnification $m=\frac{f}{u-f}$

$m=\frac{sizeofimage}{sizeofobject}$

$m=\frac{1}{2}$

$\frac{1}{2}=\frac{30}{u-30}$

$u-30=30\times 2$

$u-30=60$

$u=90cm$

Thus. the distance of the object is $90cm$.

Hence, the correct option is (A) $90cm$.