Question

using the mirror formula obtain relation between m and f

Answer 1

Magnification, m = – v/u


Mirror formula is 1/f = 1/v + 1/u


or, 1/v = 1/f – 1/u


or, v = uf / (u -f)


Therefore, m = v/u = f / u -f  

Answer 2

Explanation:

The ratio of image distance to the object distance is called the magnification of the mirror.

or

The ratio of size of the image to the size of the object is called the magnification

Mathematically, $m=\dfrac{-v}{u}=\dfrac{h'}{h}$..............(1)

v is image distance

u is object distance

Mirror's formula is :

$\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$

Multiplying above equation by (-v)

$-1-\dfrac{v}{u}=\dfrac{-v}{f}$

$-1+m=\dfrac{-v}{f}$

$m=\dfrac{-v}{f}+1$

$m=\dfrac{f-v}{f}$

Hence, the above equation shows the relationship between m and f