how to derive mirror equation?

Asked by Akshatha Chandrashekar | 2nd Oct, 2013, 05:33: PM

Expert Answer:

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.

Answered by Faiza Lambe | 2nd Oct, 2013, 07:07: PM

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