Short throw vs Longer throw light output

If you are filling the same image size by moving the projector closer, it will be brighter to use the wider lens.
If you are projecting the same distance and correcting the image size by reducing the raster area, it will be dimmer using a wider lens.
 
Generally speaking, no. A long throw lens can often have a decrease in brightness due to the amount of lensing required to keep a good image. On the other hand, the shorter the throw, the more you need your projector to be centered on the projection surface. It requires precision due to the focal plane.
 
Think of it in camera terms, every lense has an f-stop number. The lower the f-stop number, the more light passes through the lense. Zoom lenses increase their f-stop as the focal length is increased. To put it another way, increasing zoom for a longer distance increases the light loss of the lense. In the photography world, a really "fast" (efficient) lense might be F 1.2, and a crappy, slow one F 5.6.

The same is true with fixed focal length lenses. The longer the lense, the more light it loses, all other things being equal. The losses can be reduced with better quality glass and physically larger optical elements, along with greater cost.
 

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