In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is cm and the distance of its real image from the lens is cm. The error in the determination of focal length of the lens is n%. The va

Question

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 ____. [2023]

Smart Achievers · Accepted Answer

(1)

Given: Differentiating lens formula, $u = 10 \pm 0.1 cm, v = 20 \pm 0.2 cm$

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{v^{2}} d v + \frac{1}{u^{2}} d u = - \frac{1}{f^{2}} d f$

$\frac{1}{20} + \frac{1}{10} = \frac{1}{f} \Rightarrow \frac{1}{f} = \frac{3}{20} \Rightarrow f = \frac{20}{3} cm$

$\Rightarrow \frac{1}{{(20)}^{2}} (0.2) + \frac{1}{{(10)}^{2}} (0.1) = \frac{9}{400} d f$

$d f = \frac{1}{9} (\frac{400}{400} \times 0.2 + \frac{400}{100} \times 0.1)$

$\Rightarrow d f = \frac{1}{9} (0.2 + 0.4) \Rightarrow d f = \frac{0.6}{9}$

$\Rightarrow \frac{d f}{f} = \frac{0.6}{9} \times \frac{3}{20} = \frac{1}{100}$

$∴$ $% error = \frac{d f}{f} \times 100 = \frac{1}{100} \times 100 = 1 %$

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Solution

Q. In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is 10±0.1 cm and the distance of its real image from the lens is 20±0.2 cm. The error in the determination of focal length of the lens is n%. The value of n is ____. [2023]

Ans. (1) Given: Differentiating lens formula, u=10±0.1 cm, v=20±0.2 cm 1v+1u=1f⇒1v2dv+1u2du=-1f2df 120+110=1f⇒1f=320⇒f=203 cm ⇒1(20)2(0.2)+1(10)2(0.1)=9400df df=19(400400×0.2+400100×0.1) ⇒df=19(0.2+0.4)⇒df=0.69 ⇒dff=0.69×320=1100 ∴ % error=dff×100=1100×100=1%

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