An object AB is placed in front of a concave mirror. The mirror produces an image A′B′.
AX and AY are two rays from the point A on the object AB, M is the concave mirror while XA′ and YA′ are the reflected rays.
Using sign conventions,
Consider ∆ABF and ∆FOY. These are similar triangles.
AB/OY = FB/OF
Similarly, from similar triangles ∆XOF and ∆B′A′F,
XO/A'B' = OF/FB'
But AB = XO, as AX is parallel to the principal axis. Also A′B′= OY.
Since left hand sides of the two equations are equal, you can equate their right hand sides.
FB/OF = OF/FB'
(OF)2 = FB x FB'
(-f)2 = (- u - (-f)) x (- v - (-f))
f2 = uv - uf - vf + f2
uv = uf + vf
Dividing throughout by uvf,
1/f = 1/v + 1/u
Magnification indicates the ratio of the size of image to that of the object.
m = size of the image / size of the object
m = v/u