Question

What is the relation between the focal length and the radius of curvature ? prove?

Answer 1

Answer:

radius of currvature is twice of focal length

Answer 2

$\large\underline{\sf Relation \: between \: f \: and \: R \: for \: the \: spherical \: mirror}$

If B is near to line P then from ${\sf triangle BCP}$

${\sf tan \theta≈\theta=\dfrac{BP}{R}}$

and from ${\sf \triangle BFP}$

${\sf tan2\theta≈2\theta=\dfrac{BP}{f}}$

So ,

$\implies{\sf \dfrac{2BP}{R}=\dfrac{BP}{f}}$

$\large\implies\color{violet}\underline{\boxed{\sf f=\dfrac{R}{2} }}$