Question

If ‘I’ is the intensity of the solar radiation at a distance ‘x’ from the surface of the Sun, the intensity at a distance ‘2x’ from the sun is _________% of I

Answer 1

intensity is inversely proportional to square of distance between source and observation.
e.g., $\displaystyle I\propto\frac{1}{r^2}$
where I is intensity and r is distance between source and observation point.

we can use formula,
$\frac{I_1}{I_2}=\frac{r_2^2}{r_1^2}$
Here, $I_1=I,r_1=x,r_2=2x$
$\frac{I}{I_2}=\frac{4x^2}{x^2}$
$I_2=0.25I$

hence, the intensity at a distance 2x from the sun is 25% of I.