Question

Which of the following correctly represents the relation between $u$ (object distance from pole), $v$ (image distance from pole) and $R$ (radius of curvature of spherical mirror)?

• A. $R=\frac{2uv}{u+v}$
• B. $R=\frac{2}{u+v}$
• C. $R=\frac{2(u+v)}{uv}$
• D. None of the above

Answer 1

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

As per mirror formula,

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

$\Rightarrow f=\frac{uv}{u+v}$

also $f=\frac{R}{2}$ [For spherical mirrors ]

$\therefore \frac{R}{2}=\frac{uv}{u+v}\Rightarrow R=\frac{2uv}{u+v}$