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:
Text Solution
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The formula for a lens is given by 
... (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,
= 16 cm
Differentiating the equation (i)
(only positive sign is considered for error calculation)
The percentage error is
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