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skad [1K]
3 years ago
15

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?
Physics
1 answer:
sertanlavr [38]3 years ago
5 0

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 = \frac{d}{2} (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 = \frac{1}{d^{2} }

        Jd^{2} = 1 ... equation 1

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

        K(\frac{d}{2}) ^{2} = 1 ....equation 2

  • equating both equation 1 and 2 we have

       Jd^{2} = K(\frac{d}{2}) ^{2}

       Jd^{2} = K\frac{d^{2}}{4}

       J = \frac{K}{4}

        K = 4J

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

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