Originally Posted by Esoteric
As I was taught, distance effects brightness because it increases the coverage area. Also, most zooms decrease output because of the effects of the glass (I am not 100% clear on the technicalities of why zoom effects output, but I have been assured it does).
If you have a fixed lens then the throw distance and image brightness do directly correlate as the throw distance and image size also directly correlate. With a fixed lens a shorter throw distance (closer to the screen) results in a smaller image and thus a greater image brightness while a longer throw distance direct results in a larger image and thus lower image brightness. But when you throw in zoom lenses that all changes as you can vary the relationship of image size and throw distance, a throw distance no longer relates to a specific image size nor an same image size to a specific throw distance.
In both cases it is the image size that is determining the image brightness. With a zoom lens there is simply no longer a fixed relationship of image size and throw distance, and thus also no longer a fixed relationship between image brightness and throw distance. When zoom lenses are involved, one has to base the resulting image brightness on the image size rather than the throw distance.
What also happens is that lenses incur some losses in their optics, not 100% of the light from the projector's light engine comes out the other end of the lens or at least not all in the image area. These losses tend to vary over the zoom range of a zoom lens and also with the general lens characteristics, for example very long throw lenses tend to have greater losses versus comparable shorter throw lenses. The losses may also vary between lenses or manufacturers.