Linear magnification or simply magnification of a spherical mirror is the ratio of the size of the image formed by the mirror to the size of the object.
It is represented by m.
Thus
m = \(\frac{\text {size of image }(h_2)}{\text {size of object }(h_1)} = \frac{A_1B_1}{AB}\)
Fig. ∆s ABP and A1B1P are similar.
\(\frac{A_1B_1}{AB} = \frac{PB_1}{PB}\)
In case of concave mirror. Using new cartesian sign conventions,
A1B1 = -h2, AB = +h1
PB1 = -v, PB = -u
∴ \(\frac{-h_2}{h_1} = \frac{-v}{-u} = \frac{v}{u}\)
∴ m = \(\frac{h_2}{h_1} = -\frac{v}{u}\)
In case of a convex mirror, using new cartesian sign conventions,
A1B1 = +h2, AB = +h1
PB1 = +v, PB = -u
∴ \(\frac{h_2}{h_1} = \frac{v}{-u} \)
∴ m = \(\frac{h_2}{h_1} = -\frac{v}{u}\)
When m > 1, image formed in enlarged.
When m < 1, image formed in diminished.
Again, when m is +ve, image must be erect (i.e. virtual).
When m is -ve, image must be inverted (i.e. real)
Other formulae for magnification.
From mirror formula,
\(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\)
Multiplying both sides by v,
Again, multiplying both sides of mirror formula by u,
