The image formed by a convex mirror of focal length 30cm is a quarter of the size of the object. The distance of the object from the mirror is

The correct option is B. 90 cm.

Given,

Focal length = f = 30 cm

Magnification = m = $\frac{1}{4}$

From mirror formula,

We know,

1f=1v+1u\frac{1}{f}=\frac{1}{v}+\frac{1}{u}f1​=v1​+u1​ and magnification formula m=−vum=-\frac{v}{u}m=−uv​

$\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{(u-f)}{uf}$ $\Rightarrow v=\frac{uf}{(u-f)}$

put in magnification we get: $m=-\frac{uf}{u(u-f)}=\frac{f}{(f-u)}$

After combining above both equations we have, m=ff−um=\frac{f}{f-u}m=f−uf​.

Put values in above formula :

$\frac{1}{4}=\frac{30}{(30-u)}\Rightarrow 30-u=120\Rightarrow u=-90$

Hence the object distance is 90 cm