Ok this is how things work. (A lot also depends on colour, we are talking about the lighter coloured objects of course….close to white).
(1) If you really want to ID something under all conditions, regardless if you are in the city or suburbs or super dark desert/great outdoors conditions, go for 1 lux @ target.
ie Sq rt of 50000 lux @ 1m calculated = 223m. This is 1 lux @ target and over here in a very bright city (red zone to white zone in astronomy speak) you still get to see the hotspot without serious dark adaptation.
To get double the throw, you times 2 = 446m. This is 0.25 lux @ target (double distance, divide by 4).
In a bright city you are not going to to be able to see the hotspot clearly if you are the person holding the light. But if you move like 20 deg to the left or right of the light, you can see the hotspot painted white.
Double the distance again, we’d have 892 metres (the said 1100 yards in OP’s example). This is 0.0625 lux. This is a very low light level and those with light meters can try it out by ceiling bouncing a 3 lumen light in a 100% dark room and you’d still get like 0.1 lux (eg a room at night with heavy curtains drawn). I suppose if you are out in the dark, extremely clear dry air (eg PSI reading/pollution index below 10), at least 1hr of dark adapation, with someone standing like 10m from the light, you might have a chance of detecting the hostspot on a white surface.
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In astronomy, just with direct vision dark adaptation (scotopic vision) you can easily boost your eyes sensitivity by at least 1 magnitude in astronomy, that is approx 2.5 times intensity. Being in an absolutely dark place in the desert does not guarantee dark adapted, you need to be there preferably at least 1hr from the last light source, ie having a headlight to setup the camera/tripod and bring the lights out from the car with the car headlamp helping out does not count even if you are in the middle of the desert/mountains. That is just the initial part of dark adaptiona - the dilation of the pupils,only part of the night-time dark adapted vision process. This increase in retina sensitivity is due to the chemical buildup in rhodopsin, also known as “visual purple”. I guess with pupil dilation + dark adapted scotopic vision you can easily boost 4X, or double the distance.
So I guess in the most perfect of conditions, even with the unaided eye, you can detect 0.0625 lux with direct vision.
However at these low light levels where our eyes are using the rod cells, everything is either grey or black. There is no colour.
(if it rained then it stays close to 90–100)
