In an experiment to measure focal length ( f) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are Δ u and Δ v, respectively. The error in the measurement of the focal length of the convex lens will be: (a) 2f[(Δ u)/(u) + (Δ v)/(v)] (b) f[(Δ u)/(u) + (Δ v)/(v)] (c) f²[Δ uu² + Δ vv²] (d) (Δ u)/(u) + (Δ v)/(v)

Answer: (c). Lens formula: 1/f = 1/v - 1/u. Differentiate: (Δ f)/(f²) = (Δ v)/(v²) + (Δ u)/(u²) (maximum error, terms added). Δ f = f²[(Δ u)/(u²) + (Δ v)/(v²)] So the answer is (c).

In an experiment to measure focal length ( f) of convex lens, the… | JEE Main 2024 (4 Apr, Shift 1)

Q63JEE Main 2024 · 4 APR · SHIFT 1Medium

Errors in Measurement

In an experiment to measure focal length ( $f$ ) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are $\Delta u$ and $\Delta v$ , respectively. The error in the measurement of the focal length of the convex lens will be:

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Answer: (c)

Lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ .
Differentiate: $\frac{\Delta f}{f^2} = \frac{\Delta v}{v^2} + \frac{\Delta u}{u^2}$ (maximum error, terms added).
$\Delta f = f^2\left[\frac{\Delta u}{u^2} + \frac{\Delta v}{v^2}\right]$
So the answer is (c).

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