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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?
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2312 Upvotes
Verified Answer
The correct answer is:
$9.2 \times 10^{-4} \mathrm{~m}$
Here, $\frac{D / 2}{u}=\frac{d / 2}{f}$
$$
\begin{aligned}
\Rightarrow \quad d & =\frac{D f}{u} \\
& =\frac{1.39 \times 10^8 \times 10 \times 10^{-2}}{1.5 \times 10^{11}}=9.2 \times 10^{-4} \mathrm{~m}
\end{aligned}
$$
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