please derive the mirror formula for concave and convex mirrors. explain it broadly pleas.
The following sign convention is used for measuring various distances in the ray diagrams of spherical mirrors:
- All distances are measured from the pole of the mirror.
- Distances measured in the direction of the incident ray are positive and the distances measured in the direction opposite to that of the incident rays are negative.
- Distances measured above the principal axis are positive and that measured below the principal axis are negative. ?
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 conventionPC = -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