Question

A convex mirror has a radius of curvature of $20cm$. An object is placed at such a distance from the mirror that the size of the image is exactly half that of the object. The object distance must be :

• A. $20cm$
• B. $30cm$
• C. $10cm$
• D. $40cm$

Answer 1

The correct option is C $10cm$

Given, $R=2f=+20cm$ (since convex mirror)

$\Rightarrow f=10cm$

Also, magnification, $m=\frac{-v}{u}=\frac{1}{2}$

$\Rightarrow v=-\frac{u}{2}$

Now, by mirror formula:

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

$\Rightarrow \frac{-2}{u}+\frac{1}{u}=\frac{1}{10cm}$

$\Rightarrow \frac{-2+1}{u}=\frac{1}{10cm}$

$\Rightarrow \frac{-1}{u}=\frac{1}{10cm}$

$\therefore u=-10cm$

Thus, the object is placed at a distance of $10cm$ in front of the mirror.