Question

If for a spherical mirror object distance, $u=(50.1\pm 0.5)cm$ and image distance $v=(20.1\pm 0.2)cm$, then focal length of the spherical mirror will be

• A. $(14.3\pm 0.1)cm$
• B. $(14.3\pm 0.5)cm$
• C. $(30.1\pm \pm 0.1)cm$
• D. $25.3\pm 0.5)cm$

Answer 1

The correct option is A $(14.3\pm 0.1)cm$

We have $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}=\frac{v+u}{uv}$;
$\therefore f=\frac{uv}{v+u}=\frac{\left(50.\right)\left(20.1\right)}{(50.1+20.1)}$
$=14.3cm$
From $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$
$\frac{-△f}{f^2}=\frac{-△u}{u^2}+\frac{△v}{v^2}$
$\Rightarrow △f=△u{\left(\frac{f}{u}\right)}^2+△v{\left(\frac{f}{v}\right)}^2$
$=0.5{\left(\frac{14.3}{50.1}\right)}^2+0.2{\left(\frac{14.3}{20.1}\right)}^2$
$=0.04+0.10=0.14cm$
$\therefore f=(14.3\pm 0.1)cm$.