Question

If linear magnification for a spherical mirror is $\frac{3}{2}$, then we may write: (symbols have their usual meanings)

• A. $f=\frac{u}{2}$
• B. $f=\frac{3u}{2}$
• C. $f=\frac{3u}{5}$
• D. None of these

Answer 1

The correct option is C $f=\frac{3u}{5}$

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

Multiplying both sides by $u$, we get:

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

Or $\frac{u}{v}=\frac{u}{f}-1=\frac{u-f}{f}$

Or $\frac{v}{u}=\frac{f}{u-f}$

Now, magnification, $m=\frac{v}{u}=\frac{3}{2}$

$\therefore$ $\frac{f}{u-f}=\frac{3}{2}$

Solving the above equation we get $\frac{5}{2}f=\frac{3}{2}u$

$⟹f=\frac{3u}{5}$