The physics of the lighting of a Halo ring

[ruiluth]

With the launch of Halo Infinite showing the nighttime on the ringworld being unusually bright, there has been some debate on why that might be. Just now, this video was posted and got me thinking about it again.

My thought is that if there is no atmosphere to scatter the light, the shadowed surface should be in total darkness, other than whatever planetshine comes from the daytime side of the ring, which I don't think should be that much.

A point was raised about the ring being broken and allowing more light through, but I'm still not sure if that would cause enough diffusion to light it up very well.

Since I'm not a real scientist and can't back any of this up with math, I thought I'd ask here where real scientists hang out and might be able to help. Thanks in advance!

EDIT: quick illustration I made for clarity

Edited December 23, 2021 by ruiluth

[Nuke]

i think you end up getting a lot of  light bouncing off of the day side. sort of like how a bright moon can provide some illumination for night vision. the moon has a lot of area but is far away, the halo dayside surface is a lot smaller but a lot closer. so id guess that it would provide comparable illumination, if not more. i think its an inverse square thing.

Edited December 26, 2021 by Nuke

[magnemoe]

On 12/26/2021 at 6:23 AM, Nuke said:

i think you end up getting a lot of  light bouncing off of the day side. sort of like how a bright moon can provide some illumination for night vision. the moon has a lot of area but is far away, the halo dayside surface is a lot smaller but a lot closer. so id guess that it would provide comparable illumination, if not more. i think its an inverse square thing.

Agree here the ring would take up much more of the sky than the moon unless the ring is very thin, also the surface will be more reflective than the moon who is dark. 
Make me wonder how much light is it on the moon during the night during the night on the side facing the earth. 

[Nuke]

basking in the earthlight.