Ray Optics and Optical Instruments - Result Question 37
37. 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?
(a) $9.2 \times 10^{-4} m$
(b) $6.5 \times 10^{-4} m$
(c) $6.5 \times 10^{-5} m$
(d) $12.4 \times 10^{-4} m$
[2008]
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Answer:
Correct Answer: 37. (a)
Solution:
- (a) We have, $|\frac{v}{u}|=\frac{\text{ Size of image }}{\text{ Size of object }}$
or, Size of image $=|\frac{v}{u}|$, Size of object
$=(\frac{10^{-1}}{1.5 \times 10^{11}}) \times(1.39 \times 10^{9})$ $=0.92 \times 10^{-3} m=9.2 \times 10^{-4} m$
$\therefore$ Diameter of the sun’s image $=9.2 \times 10^{-4} m$.
