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)

$f =\frac{-8}{2}=-4 cm$
$u =-10 cm$
$v =?$
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.