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Derivation of Lens Formula (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.

lens formula

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

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