A boy is trying to start a fire by focusing Sunlight on a piece of paper using an equiconvex lens of focal…

A boy is trying to start a fire by focusing Sunlight on a piece of paper using an equiconvex lens of focal length $10 \mathrm{~cm}$. The diameter of the Sun is $1.39 \times 10^9 \mathrm{~m}$ and its mean distance from the earth is $1.5 \times 10^{11} \mathrm{~m}$. What is the diameter of the Sun's image on the paper?
  1. $12.4 \times 10^{-4} \mathrm{~m}$
  2. $9.2 \times 10^{-4} \mathrm{~m}$
  3. $6.5 \times 10^{-4} \mathrm{~m}$
  4. $6.5 \times 10^{-5} \mathrm{~m}$

Solution

Here, $\frac{D / 2}{u}=\frac{d / 2}{f}$ $\begin{aligned} \Rightarrow \quad d & =\frac{D f}{u} \\ & =\frac{1.39 \times 10^8 \times 10 \times 10^{-2}}{1.5 \times 10^{11}}=9.2 \times 10^{-4} \mathrm{~m} \end{aligned}$

Asked in: NEET 2008 (Mains)

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