Derivation of Lens Formula for concave lens:

Let AB represent an object placed at right angles to the principal axis at a distance greater than the focal length f of the convex lens. The image A¹B¹ is formed between O and F₁ on the same side as the object is kept and the image is erect and virtual.

 

 

OF₁ = Focal length = f

OA = Object distance = u

OA¹ = Image distance = v

But from the ray diagram we see that OC = AB

From equation (1) and equation (2), we get

Dividing throughout by uvf