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

Physics · Units, Dimensions & Error Analysis

JEE Advanced 2023 — Paper 1 — Question 26

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

Answer: 1

Numerical answer — enter this value.

Step-by-step solution

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ $\Rightarrow \frac{\Delta \mathrm{f}}{\mathrm{f}^{2}}= \pm\left(\frac{\Delta \mathrm{v}}{\mathrm{v}^{2}}+\frac{\Delta \mathrm{u}}{\mathrm{u}^{2}}\right)$ $\Rightarrow \frac{\Delta f}{\mathrm{f}}= \pm\left(\frac{\Delta \mathrm{v}}{\mathrm{v}^{2}}+\frac{\Delta \mathrm{u}}{\mathrm{u}^{2}}\right) \mathrm{f}$ $= \pm\left(\frac{0.2}{(20)^{2}}+\frac{0.1}{(10)^{2}}\right) \times \frac{20}{3}$ $\Rightarrow \frac{\Delta \mathrm{f}}{\mathrm{f}}= \pm 0.01$ $\Rightarrow \frac{\Delta f}{\mathrm{f}} \times 100 \%= \pm 1 \%$

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Exam: JEE Advanced 2023
Paper: Paper 1
Subject: Physics
Chapter: Units, Dimensions & Error Analysis
Topic: Significant Figures and Error Analysis