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 _____.
A. A
Given: Object distance = 10 ± 0 . 1   cm Image distance = 20 ± 0 . 2   cm As per lens formula 1 v - 1 u = 1 f                 . . . i ⇒ 1 20 - 1 - 10 = 1 f ⇒   f = 20 3   cm Differentiate equation i on both sides, we get - 1 v 2 d v - - 1 u 2 d u = - 1 f 2 d f For calculating maximum error, we will add all values ⇒ 1 f 2 d f = + 1 v 2 d v + 1 u 2 d u ⇒ d f f × 100 = 0 . 2 20 2 + 0 . 1 10 2 20 3 × 100 = 0 . 2 4 + 0 . 1 1 20 3 = 1 Therefore, d f f × 100 = 1 % = n
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