Question

A convex mirror has a radius of curvature of $20\text{cm}$. 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. $40\text{cm}$
• B. $30\text{cm}$
• C. $20\text{cm}$
• D. $10\text{cm}$

Answer 1

The correct option is D $10\text{cm}$

Given that
$R=20\text{cm}f=\frac{R}{2}=\frac{20}{2}=10\text{cm}m=\frac{1}{2}$
$m=\frac{f}{f-u}\Rightarrow \frac{1}{2}=\frac{10}{10-u}$
$10-u=20$
$u=10-20=-10\text{cm}$
$u=-10\text{cm}$
i e the object distance is $10\text{cm}$.