JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Units & Measurement

WhatsApp Email

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

Solution

Using lens formula:

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

With

u = - 10

cm and

v = 20

cm:

\frac{1}{20} + \frac{1}{10} = \frac{1}{f}

\frac{3}{20} = \frac{1}{f}

f = \frac{20}{3}

cm

Differentiating:

\frac{1}{v ^{2}} d v + \frac{1}{u ^{2}} d u = - \frac{1}{f ^{2}} df

\frac{df}{f ^{2}} = \frac{d v}{v ^{2}} + \frac{d u}{u ^{2}}

\frac{df}{f} = f (\frac{d v}{v ^{2}} + \frac{d u}{u ^{2}})

\frac{df}{f} = \frac{20}{3} (\frac{0.2}{400} + \frac{0.1}{100}) = \frac{20}{3} \times \frac{0.6}{400} = \frac{1}{100}

Percentage error = 1%.

JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Integer answer

Practise more: all JEE Advanced PYQs on Units & Measurement →

JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Units & Measurement

Solution

More JEE Advanced questions on Units & Measurement