Mirror Formula

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,

  • Object distance, OB = –u
  • Focal length, OF = –f
  • Image distance, OB′ = –v
  • Radius of curvature OC = – 2f

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

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