derive lens formula for convex lens when virtual image is formed.

derive lens formula for concave lens.

Please post different questions as separate queries.

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

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