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.
