If the light source illuminating the shadows on one side of the subject is in the nature of a diffused "fill" light, it will also be contributing illumination to the other, highlight side. Thus a change to that fill light will not only change the ratio, it will also necessitate a change to the camera exposure settings.
So it is important to differentiate between lighting setups that have two sources that illuminate separate sides, from lighting setups where one source is more of an all-over "fill".
The dome, covering 180 degrees, takes that flare/spill into consideration. This is why I prefer it to the disc for measuring lighting ratios.
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