Question

A concave mirror produces a real image twice the size of the object when placed at a distance of 22.5 cm from it. Where should be object be placed so that the size of the image becomes three times that of the object?

• A. 20 cm
• B. 22.5 cm
• C. 30.4 cm
• D. 24 cm

Answer 1

The correct option is A 20 cm

Case 1 :

Magnification $m=-2$ (image is real)

Object distance $u=-22.5cm$

From $m=\frac{-v}{u}$

$\therefore$ $-2=\frac{-v}{u}$
We get $v=2u=-45cm$

Using $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\frac{1}{f}=-\frac{1}{45}-\frac{1}{22.5}=\frac{-1-2}{45}$

$\frac{1}{f}=\frac{-3}{45}$

$⟹$ $f=-15cm$

Case 2 :

Let the new object distance be $x$ i.e. $u=-x$ now.

Magnification $m=-3$ (image is real)

From $m=\frac{-v}{u}$

$\therefore$ $-3=\frac{-v}{-x}$ $⟹v=-3x$

Using $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
$-\frac{1}{15}=\frac{1}{-3x}+\frac{1}{-x}$

$-\frac{1}{15}=-\frac{1+3}{3x}$

$-3x=-60$

$x=+20cm.$

Hence, object must be placed at 20 cm.