In an experiment for estimating the value of focal length of… | JEE Main 2023 (30 Jan, Shift 1)

Q27JEE Main 2023 · 30 JAN · SHIFT 1Medium

Reflection & Mirrors

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

Numerical answer type. Work it out, then open the answer.

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Answer: 32

Mirror formula (magnitudes, real image): $\frac{1}{f} = \frac{1}{u} + \frac{1}{v} = \frac{1}{40} + \frac{1}{120} = \frac{4}{120} \Rightarrow f = 30\text{ cm}$
Least count of the scale: $\Delta u = \Delta v = \frac{1}{20} = 0.05\text{ cm}$
Differentiating: $\frac{\Delta f}{f^2} = \frac{\Delta u}{u^2} + \frac{\Delta v}{v^2}$
$\Delta f = 900\left(\frac{0.05}{1600} + \frac{0.05}{14400}\right) = 900 \times \frac{0.5}{14400} = \frac{1}{32}\text{ cm}$
So $K = 32$ .

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