Solution

Let $I$ be the intensity of light from the Sun on the Earth. As the distance between the Moon and the Earth is much less than that between the Sun and the Earth, we may assume that the intensity of light from the Sun on the Moon is $I$ as well. Consequently, the power of light from the Sun intercepted by the cross section of the Moon is $I\cdot\pi r^2$, where $r$ is the radius of the moon. Since the light is reflected by a half of the Moon, the intensity of light from the Moon on Earth is

$$\frac{I\cdot\pi r^2}{2\pi d^2}=I\cdot\frac{1}{2}\left(\frac{r}{d}\right)^2,$$

where $d$ is the distance between the Moon and the Earth. Using $r=2000$ km and $d=400000$ km, we see that the intensity of the light on the Earth from the Moon is $1/80000$ of that from the Sun.