Lens Formula

Consider about a convex lens. O is the optical centre. AB is an object placed on the principle axis. The image A'B' is formed on the principle axis due to refraction of light. 

Mathematical Calculation 

Consider about the ∆ABO and ∆A'B'O.

Both triangles are similar.

AB/A'B' = OB/OB'   ....... (I)

Again, consider about the ∆MOF₂ and A'B'F₂

Both triangles are similar.

MO/A'B' = OF₂/B'F₂ ....... (ii)

From figure it is clear that

AB = MO

OB = -u

OB' = v

OF₂ = f

Form of equation no (ii) will be

AB/A'B' = OF₂/B'F₂ ...... (iii)

Now, from equation no (i) and (iii)

OB/OB' = OF₂/B'F₂

Now, putting the values of        OB = -u OB' = v OF₂ = f B'F₂ = v - f

-u/v = f/v - f

or, -uv + uf = vf

or, uf - vf = uv

Now, dividing both sides by uvf.

1/v - 1/u = 1/f

This is the lens formula.