Question

The correct relation between the radius of curvature ($\text{R}$), distance of object from the mirror ($\text{u}$), and distance of image formed ($\text{v}$) from the mirror is

• A. $\frac{1}{\text{R}}=\frac{1}{\text{v}}+\frac{1}{\text{u}}$
• B. $\text{R}=\frac{2}{\text{u + v}}$
• C. $\text{R}=\frac{2\left(\text{u + v}\right)}{\text{uv}}$
• D. $\text{R}=\frac{2\text{uv}}{\text{u + v}}$

Answer 1

The correct option is D $\text{R}=\frac{2\text{uv}}{\text{u + v}}$

We know that,
$\frac{1}{f}=\frac{1}{\text{v}}+\frac{1}{\text{u}}$

That gives,
$f=\frac{\text{uv}}{\text{u + v}}$

Also, $f=\frac{\text{R}}{2}$
Putting this in previous equation,
$\frac{\text{R}}{2}=\frac{\text{uv}}{\text{u + v}}$

This gives,
$\text{R}=\frac{2\text{uv}}{\text{u + v}}$