Goes for any light source really, just using a fireplace/bonfire as an example. If you were to look at a bonfire from a distance in the dark, the light seems to stop rather suddenly. But the only way you’re seeing it in the first place is from the light hitting your eyes.
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The intensity of light, as one gets further away from the light source, dissipates according to something called the ‘inverse square law’. In general, if the distance from the light source is x, then the intensity of the light reaching you is proportional to 1/x^2 . In other words, if you move twice as far away from the light, you’re a *quarter* as illuminated as you were before. The geometric reasons why this must be so, are best explained with [diagrams like this one.](https://lh3.googleusercontent.com/proxy/2-oOBXjC-vGDwN3BkkNNyBi-LTwpha-UW6a48KOdbDi1iImSFtQ7UjHAcV2DMjsg3dRAS5ULTllaFZKuyQDX3CtcdEE66rEeFrpsrAg113nLmQfi6QoT2w)
This inverse square law, if graphed out as a function, has a [much steeper dropoff](http://www.math-mate.com/chapter48_1_files/image011.gif) than an inverse, or 1/x function. So that’s a reason why the transition from light to dark might seem so abrupt.
There’s probably also lots to talk about regarding human vision and the dynamic range that we perceive, because what subjectively feels ‘twice as bright’ to us, isn’t necessarily the same in all conditions. Our eyes do all kinds of stuff like pupil dilation/contraction and retinal cell exhaustion/satiation which can mess with our sense of brightness.
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