Question:
A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object ? (Figure drawn as schematic and not to scale)
Correct Option: 1
Solution:
$\mathrm{f}=\frac{-8}{2}=-4 \mathrm{~cm}$
$\mathrm{u}=-10 \mathrm{~cm}$
$\mathrm{v}=?$
as $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\left(\frac{1}{-10}\right)=\frac{1}{-4}$
$\frac{1}{v}=\frac{1}{10}-\frac{1}{4}$
$\frac{1}{v}=\frac{4-10}{40}$
$v=\frac{40}{-6}$
$v=\frac{-20}{3}$
$\mathrm{m}=\frac{-\mathrm{v}}{\mathrm{u}}$
$\mathrm{m}=\frac{-\left(-\frac{20}{3}\right)}{-10} \Rightarrow \mathrm{m}=\frac{-2}{3}$
or image will be real, inverted and unmagnified.