A concave mirror produces three times enlarged virtual image of an object placed at 10cm in front of it. Calculate the radius of curvature of the mirror.
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m = 3 (virtual image) u = -10cm R = ? We know that$\text{m}=-\frac{\text{v}}{\text{u}}$
$3=-\frac{\text{-v}}{(-10)}$
$\text{v}=30\text{cm}$
and$\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\frac{1}{30}+\frac{1}{(-10)}=\frac{1}{\text{f}}$
$\frac{-20}{300}=\frac{1}{\text{f}}$
$\frac{1}{\text{f}}=-15\text{cm}$
Radius of ourvature=R=2f$=2\times(-15)=-30\text{cm}$
$3=-\frac{\text{-v}}{(-10)}$
$\text{v}=30\text{cm}$
and$\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\frac{1}{30}+\frac{1}{(-10)}=\frac{1}{\text{f}}$
$\frac{-20}{300}=\frac{1}{\text{f}}$
$\frac{1}{\text{f}}=-15\text{cm}$
Radius of ourvature=R=2f$=2\times(-15)=-30\text{cm}$
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