The focal length of a mirror is given by 2 f = 1 v - 1 u . If in the measurement of u and v , the errors are equal to p each, then the relative error in f is

Question

The focal length of a mirror is given by 2 f = 1 v - 1 u . If in the measurement of u and v , the errors are equal to p each, then the relative error in f is, p 2 1 u + 1 v, p 1 u + 1 v, p 2 1 u - 1 v, p 1 u - 1 v

MARKS App · Accepted Answer

Given, equation is 2 f = 1 v - 1 u ....(i) Differentiating the given equation, we have - 2 f 2 df = - 1 v 2 dv - - 1 u 2 du = - p 1 v - 1 u 1 v + 1 u ∵ dv = du = p = - 2 p f 1 v + 1 u [using Eq. (i)] ∴ df f = p 1 v + 1 v

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