The relation between the linear magnification m, the object distance u and the focal length f is

Question

The relation between the linear magnification m, the object distance u and the focal length f is (A) m=(f-u/f) (B) m=(f/f-u) (C) m=(f+u/f) (D) m=(f/f+u)

Tardigrade Admin · Accepted Answer

∵ m=-(v/u) also (1/f)=(1/v)+(1/u) ⇒ (u/f)=(u/v)+1 ⇒ -(u/v)=1-(u/f) ⇒ (-v/u)=(f/f-u) so m=(f/f-u)

Q. The relation between the linear magnification $m$ , the object distance $u$ and the focal length $f$ is

$m = \frac{f - u}{f}$

$m = \frac{f}{f - u}$

$m = \frac{f + u}{f}$

$m = \frac{f}{f + u}$

$∵ m = - \frac{v}{u}$ also $\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \Rightarrow \frac{u}{f} = \frac{u}{v} + 1$
$\Rightarrow - \frac{u}{v} = 1 - \frac{u}{f} \Rightarrow \frac{- v}{u} = \frac{f}{f - u}$ so $m = \frac{f}{f - u}$

Q. The relation between the linear magnification m, the object distance u and the focal length f is

m=ff−u​

m=f−uf​

m=ff+u​

m=f+uf​