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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

Asked in JEE Main 4th April 1st Shift 2024 · Lens formula and magnification

• (1) f[(Δ u)/u+(Δ v)/v]
• (2) 2f[(Δ u)/u+(Δ v)/v]
• (3) (Δ u)/u+(Δ v)/v
• (4) f²[(Δ u)/(u²)+(Δ v)/(v²)]

Step-by-step solution

Why the other options are wrong

• (1) Treats f as a product u v and adds fractional errors, ignoring the sum in the denominator.
• (2) Doubles the product-rule result with no basis.
• (3) Gives a fractional error, not the absolute error in f.

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