A point source is kept at a distance of 1000m has an illumination I. To change the illumination to 16I the new distance should become.

250 m

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500 m

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750 m

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800 m

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Solution

The correct option is A $250 m$
We know illumination intensity $α \frac{1}{(d i s t a n c e)^{2}}$
Initial illumination $= I$ , changed value $= 16 I$
Initial distance $= 1000 m$ , changed value $= x$
$\frac{1}{161} = \frac{\frac{1}{(1000)^{2}}}{\frac{1}{x^{2}}} \Rightarrow \frac{1}{16} = \frac{x^{2}}{(1000)^{2}}$
$\Rightarrow x^{2} = \frac{(1000)^{2}}{16} \Rightarrow x = \frac{1000}{4} = 250 m$

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A point source is kept at a distance of 1000m has an illumination I. To change the illumination to 16I the new distance should become.

The correct option is A 250mWe know illumination intensity α1(distance)2Initial illumination =I, changed value =16IInitial distance =1000m, changed value =x1161=1(1000)21x2⇒116=x2(1000)2⇒x2=(1000)216⇒x=10004=250m