derive the mirror formula with a ray diagram.

dear student

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, PB₁ = v, PF = f

By sign convention

PC = -R, PB = -u, PF = -f and PB₁ = -v

Equation (3) can be written as

Dividing equation (4) throughout by uvf we get

Equation (5) gives the mirror formula

 

We hope that clarifies your doubt

 

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