Amount of light blocked by a body at the Earth-Sun L1 point I came across this question on the World Building SE. It has an accepted answer but it seems to be under some debate (see comments). So I thought I'd put it to some physicists:
What formula would describe the amount of light blocked by a body of a given radius placed at the L1 Lagrangian point?
 A: The L1 Lagrange point is at a distance of approximately:
$$D_{\oplus\text{-}\rm L1}=D_{\odot\text{-}\oplus}\left(\frac{{\rm M}_\oplus}{3{\rm M}_\odot}\right)^{1/3}$$
from Earth. An object of linear size $L$ subtends an angular size, in radians, of $\Theta=L/D$ (assuming that the size is much smaller than the distance, which in this case it is). The angular size of the Sun is about $\Theta_\odot = 0.5^\circ=0.01\,{\rm rad}$. The fraction of light blocked $f_L$ is proportional to the square of the ratio of the angular sizes (assuming here a round object):
$$f_{L} = \left(\frac{L}{\Theta_\odot D_{\rm \oplus\text{-}L1}}\right)^2$$
This is valid if $\Theta < \Theta_\odot$; if you make the object any bigger than the light is completely blocked and $f_L=1$, obviously. I've neglected some geometric details here, most importantly that the light source has finite size/is not distant enough for the wavefront to be completely flat. A more realistic treatment would involve thinking along these lines.
