Question

A convex mirror has a focal length $f$. A real object is placed at a distance $f$ in front of it from the pole, produces an image at: ($\text{R}$ is the radius of curvature of the convex mirror).

• A. Infinity
• B. $\frac{R}{4}$
• C. $\text{R}$
• D. $\frac{R}{2}$

Answer 1

The correct option is B $\frac{R}{4}$

Sign convention: The direction along the ray is taken as positive.

Given that,
Focal length of the convex mirror, $f=\frac{R}{2}$
The object distance, $u=-f$
Let the image if formed at $v$
By using mirror formula:
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$
Substitute values
$\Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{(-f)}$
$\Rightarrow \frac{1}{v}=\frac{2}{f}$
$\Rightarrow v=\frac{f}{2}$
Substitute $f=\frac{R}{2}$
$\therefore v=\frac{R}{4}$
Hence, option (b) is correct.