CBSE Class 12-science Answered

Mirror Formula (Concave Mirror)

Mirror formula is the relationship between object distance (u), image distance (v) and focal length.

Derivation

The figure shows an object AB at a distance 'u' from the pole of a concave mirror. The image A₁B₁ is formed at a distance 'v' from the mirror. The position of the image is obtained by drawing a ray diagram.

Consider the D A₁CB₁ and D ACB

[when two angles of D A₁CB₁ and D ACB are equal then the third angle

But ED = AB

From equations (1) and (2)

If D is very close to P then EF = PF

But PC = R, PB = u, PB ₁ = v, PF = f

By sign convention

PC = -R, PB = -u, PF = -f and PB ₁ = -v

Equation (3) can be written as

Dividing equation (4) throughout by uvf we get

Hence, equation (5) gives the mirror formula.