Question

The linear magnification for a mirror is the ratio of the size of the image to the size of the object, and is denoted by $m$. Then we may write: (symbols have their usual meanings)

• A. $f=\frac{1+m}{mu}$
• B. $f=mu$
• C. $f=\frac{mu}{1+m}$
• D. None of these

Answer 1

Answer: (C)

$f=\frac{mu}{1+m}$

Mirror equation: $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Multiplying both sides by $u$, we get:

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

or, $\frac{u}{v}=\frac{u}{f}-1=\frac{u-f}{f}$

or, $\frac{v}{u}=\frac{f}{u-f}$

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

or, $mu=f+mf$

or, $f=\frac{mu}{1+m}$