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)

• A. Inverted, real and magnified
• B. Erect, virtual and magnified
• C. Erect, virtual and unmagnified
• D. Inverted, real and unmagnified

Answer 1

Answer: (D)

$f=\frac{-8}{2}=-4cm$
$u=-10cm$
$v=?$
as $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\left(\frac{1}{-10}\right)=\frac{1}{-4}$
$\frac{1}{v}=\frac{1}{10}-\frac{1}{4}$
$\frac{1}{v}=\frac{4-10}{40}$
$v=\frac{40}{-6}$
$v=\frac{-20}{3}$
$m=\frac{-v}{u}$
$m=\frac{-\left(-\frac{20}{3}\right)}{-10}$
$\Rightarrow m=\frac{-2}{3}$
or image will be real, inverted and unmagnified.