In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is 10±0.1cm and the distance of its real image from the lens is 20±0.2cm. The error in the determination of focal length of the lens is n%. The value of n is_____.

1v−1v=1f 120+110=1f f=203 Δff2=ΔUU2+ΔVV2 Δff=0.2400+0.1100×203Δff×100=0.6400×203×100 Δff×100=1%

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In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is $10 \pm 0.1 cm$ and the distance of its real image from the lens is $20 \pm 0.2 cm$ . The error in the determination of focal length of the lens is n%. The value of n is_____.

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Detailed Solution

$\frac{1}{v} - \frac{1}{v} = \frac{1}{f} \frac{1}{20} + \frac{1}{10} = \frac{1}{f} f = \frac{20}{3} \begin{array}{l} \frac{Δf}{f^{2}} = \frac{ΔU}{U^{2}} + \frac{ΔV}{V^{2}} \frac{Δf}{f} = (\frac{0.2}{400} + \frac{0.1}{100}) \times \frac{20}{3} \\ \frac{Δf}{f} \times 100 = \frac{0.6}{400} \times \frac{20}{3} \times 100 \frac{Δf}{f} \times 100 = 1 % \end{array}$