Question

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?

Answer 1

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

        J$d^{2}$ = 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

       J$d^{2}$ = K$(\frac{d}{2}) ^{2}$

       J$d^{2}$ = 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)