Question

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

• A. 30cm
• B. 90cm
• C. 120cm
• D. 60cm

Answer 1

The correct option is B 90cm

The focal length of the convex mirror is $f=30cm$ and the magnification of the image is $m=1/4$

We have to calculate the object distance $u$.

According to sign convention, the measurements along the direction of light are taken as positive and opposite to the light taken as negative. The transverse measurement above the principal axis is taken as positive and below the principal axis is taken as negative.

Thus, $f=+30cm$ and $m=+1/4=+0.25$

Using formula, $m=\frac{f}{f-u}$

or $mf-mu=f$

or $u=\frac{mf-f}{m}=\frac{m-1}{m}f=\frac{0.25-1}{0.25}\left(30\right)=-90cm$