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The intensity of light from a central source varies inversely as the square of the distance. If you lived on a planet only half as far from the Sun as our Earth, how would the intensity compare with that on Earth?

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usmanbiu

Answer:

the intensity will be 4 times that of the earth.

Explanation:

let us assume the following:

intensity of light on earth =J

distance of earth from sun = d

intensity of light on other planet = K

distance of other planet from sun = [tex]\frac{d}{2}[/tex] (from the question, the planet is half as far from the sun as earth)

from the question the intensity is inversely proportional to the square of the distance, hence

  • intensity on earth : J = [tex]\frac{1}{d^{2} }[/tex]

        J[tex]d^{2}[/tex] = 1 ... equation 1

  • intensity on other planet : K =  [tex]\frac{1}{(\frac{d}{2}) ^{2} }[/tex]  (the planet is half as far from the sun as earth)

        K[tex](\frac{d}{2}) ^{2}[/tex] = 1 ....equation 2

  • equating both equation 1 and 2 we have

       J[tex]d^{2}[/tex] = K[tex](\frac{d}{2}) ^{2}[/tex]

       J[tex]d^{2}[/tex] = K[tex]\frac{d^{2}}{4}[/tex]

       J = [tex]\frac{K}{4}[/tex]

        K = 4J

       intensity of light on other planet (K) = 4 times intensity of light on earth (J)

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