Question

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

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

Answer 1

Answer: (A)

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