Question

An object is placed at a distance of 40 cm from the pole of a converging mirror. The image is formed at a distance of 120 cm from the mirror on the same side. If the focal length is measured with a scale where each 1 cm has 20 equal divisions. If the fractional error in the measurement of focal length is $\frac{1}{10\ k}$.Find k.

Answer 1

The correct answer is 60.
u = – 40 cm
v = – 120 cm
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$⇒-\frac{1}{120}-\frac{1}{40}=\frac{1}{f}$
$\frac{1}{f}=(\frac{-1-3}{120})=-\frac{4}{120}$
f = – 30 cm
Least count of scale $=(\frac{1}{20})\ cm$
Fractional error $=\frac{\frac{1}{20}}{30}=(\frac{1}{600})$
as $\frac{1}{10\ k}=\frac{1}{600}$
k = 60