A boy is trying to start a fire by focusing sunlight on a piece of paper using an equal convex lens of focal length 10 cm. The diameter of the sun is 1.39 x 10⁹ m and its mean distance from the earth is 1.5 x 10¹¹ m. What is the diameter of the sun's image on the paper?

9.2 x 10^-4 m

6.5 x 10^-4 m

6.5 x 10^-5 m

12.4 x 10^-4 m

Solution

9.2 x 10^-4 m

For the relation

$straight I over straight O space equals space straight v over straight u Here comma space straight O thin space equals space 1.39 space space straight x space 10 to the power of 9 comma space straight v equals space 0.1 space straight m comma straight u space equals space 1.5 space straight x space 10 to the power of 11 space straight m therefore comma therefore space straight I space equals space fraction numerator 0.1 over denominator 1.5 space straight x space 10 to the power of 11 space end fraction space straight x space 1.39 space straight x space 10 to the power of 9 space equals space 9.2 space straight x space 10 to the power of negative 4 end exponent space straight m space$

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