A 2 meter long scale with least count of 0 . 2 cm is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at 80 cm mark and 1 m mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at 180 cm mark. The % error in the estimation of focal length is:

Step-by-step solution

The formula for a lens is given by 1 f = 1 v - 1 u       . . . ( i ) u = 100 ± 0 . 2   cm - 80 ± 0 . 2   cm = 20 ± 0 . 4   cm v = 180 ± 0 . 2   cm - 100 ± 0 . 2   cm = 80 ± 0 . 4   cm Substituting the values in the equation of focal length, 1 f = 1 v - 1 u = 1 80 - - 1 20 = 5 80 ⇒ f = 16   cm Differentiating the equation (i) d f f 2 = d v v 2 + d u u 2 (Only positive sign is considered for error calculation) = 0 . 4 6400 + 0 . 4 4