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NTA Abhyas JEE Main2020PhysicsUnits and DimensionsPractice

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

Options

  1. Ap 2   1 u + 1 v
  2. Bp   1 u + 1 v
  3. Cp 2 1 u - 1 v
  4. Dp   1 u - 1 v

Correct answer

B. p   1 u + 1 v

Step-by-step solution

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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