The correct relation between the linear magnification m, the object distance u and the focal length f, for a mirror is given by

Question

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

Tardigrade Admin · Accepted Answer

Magnification, m=(-v/u) But (1/f)=(1/v)-(1/u) (Mirror formula) ⇒ (u/f)=(u/v)+1 ⇒ -(u/v)=1-(u/f) ⇒ (-v/u)=(f/f-u) So, m=(f/f-u)

Q. The correct relation between the linear magnification m, the object distance u and the focal length $f,$ for a mirror is given by

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

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

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

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

Magnification, $m = \frac{- v}{u}$ But $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ (Mirror formula) $\Rightarrow$ $\frac{u}{f} = \frac{u}{v} + 1$ $\Rightarrow$ $- \frac{u}{v} = 1 - \frac{u}{f}$ $\Rightarrow$ $\frac{- v}{u} = \frac{f}{f - u}$ So, $m = \frac{f}{f - u}$

Q. The correct relation between the linear magnification m, the object distance u and the focal length f, for a mirror is given by

m=f−uf​

m=ff−u​

m=f+uf​

m=ff+u​