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In an experiment for estimating the value of focal length of converging mirror, image of an object placed at 40 cm from the pole of the mirror is formed at distance 120cm from the pole of the mirror. These distances are measured with a modified scale in which there are 20 small divisions in 1cm. The value of error in measurement of focal length of the mirror is $\frac{1}{K} cm$ . The value of K is _____

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answer is 32.

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Detailed Solution

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$\begin{array}{l} \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{f} = \frac{1}{- 120} + \frac{1}{- 40} \\ \Rightarrow f = - 30 cm \\ Δu = Δv = \frac{1}{20} cm \\ \frac{Δu}{v^{2}} + \frac{Δv}{u^{2}} = \frac{Δf}{f^{2}} \Rightarrow Δf = \frac{1}{32} c m \\ k = 32 \end{array}$

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