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(C) The angular diameter of the sun as seen from the earth is $\alpha = \frac{	ext{Diameter of Sun}}{	ext{Distance of Sun}} = \frac{1.39 	imes 10^9

Vedclass · Accepted Answer

$9.2 	imes 10^{-4}\, m$

Vedclass · Answer

(C) The angular diameter of the sun as seen from the earth is $\alpha = \frac{	ext{Diameter of Sun}}{	ext{Distance of Sun}} = \frac{1.39 	imes 10^9}{1.5 	imes 10^{11}} \approx 9.26 	imes 10^{-3}\, 	ext{radians}$.When the sunlight is focused by a lens of focal length $f = 10\, cm = 0.1\, m$,the image of the sun is formed at the focus.The diameter of the image $d$ is given by $d = f 	imes \alpha$.Substituting the values: $d = 0.1\, m 	imes (\frac{1.39 	imes 10^9}{1.5 	imes 10^{11}})$.$d = 0.1 	imes 0.926 	imes 10^{-2} = 0.0926 	imes 10^{-2} = 9.26 	imes 10^{-4}\, m$.Rounding to the nearest provided option,the diameter is $9.2 	imes 10^{-4}\, m$.

$A$ boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length $10\, cm$. The diameter of the sun is $1.39 \times 10^9\, m$ and its mean distance from the earth is $1.5 \times 10^{11}\, m$. What is the diameter of the sun's image on the paper?

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