# Linear magnification produced by a lens (m):

m = size of image formed by lens/size of object = I/O

For Real & inverted image, m → negative

For virtual & erect image, m → positive

(i) Magnification in terms of u and v:

Triangle’s ABO & A’B’O are similar

∴ (A’B’/AB) = OB’/OB

-I / +O = +v / -u      

Or      I / O = v / u

m = I/O = v/u

(ii) Magnification in terms of u & f:

(1/v – 1/u = 1/f)

Multiplying both sides by u

u/v – 1 = u/f

Or      u/v = u/f + 1 = u + f/f

Or      v/u = f/u + f

Or      m = f/u + f

(iii) Magnification in terms of v and f:

(1/v – 1/u = 1/f)

Multiplying both sides by v;      1 – v/u = v/f

v/u = 1 – v/f = f – v/f

Or      m = f – v/f