Question

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 ____ .

Answer 1

Object distance $= 10 ± 0.1$ cm Image distance $= 20 ± 0.2$ cm
Applying lens formula ….. (1)

$\frac {1}{20} - \frac{1}{-10} = \frac {1}{f}$

f = $\frac{20}{3} cm$

differentiate equation 1:

$\frac {1}{f^2}df = +\frac{1}{v^2}dv+\frac{1}{u^2}du$

$\frac{df}{f}\times 100 = \frac{0.2}{20^2}+\frac{0.1}{10^2}\times \frac{20}{3}\times 100$

= 1

$\frac{df}{f}\times 100 = 1$

So, the answer is $1$.