An object is placed at $A\;(OA > f)$ Here, f is the focal length of the lens. The image is formed at B, A perpendicular is erected at 0 and C is chooses such that $\angle BCA =90^{\circ}$. Let $OA=a,OB=b$ and $OC=c$ then f is :

Question

 

$(a)\;\frac{c^2}{a^2+b^2+c^2} \\ (b)\;\frac{c}{a+b} \\ (c)\;\frac{c^2}{a+b} \\ (d)\;None$