Physics - Geometrical Optics Question with Solution | TestHub

The image formation by a convex lens is as follows

The image formed is diminished, when objects lie between$2f$and infinity.

Magnification

$\left(M\right)=\frac{image size}{object size}$

$=\frac{1}{2}=\frac{v}{u} \dots .\left(i\right)$

From lens formula

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u} \dots .\left(ii\right)$

Where,$f$is focal length,$v$the image distance and$u$the object distance.

From eqs. (i) and (ii), we get

$\frac{1}{f}=\frac{1}{u}+\frac{2}{u}$

As$f=30\mathrm{ }\mathrm{cm}$

$\frac{1}{30}=\frac{3}{u}$

$⟹u=90\mathrm{ }\mathrm{cm}$