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The distance calculation is the diagonal size of the screen times the throw ratio of the projector (x/12 for feet).
If the projector has a physical zoom this plays in as well, throw ratios are usually displayed at 1x or for the whole range (e.g. 82C; 1.2 zoom means 1.43-1.71 throw).
Light calculations are somewhat inside the scope of this question, but suffice it to say, they aren't fun to do IMHO which is why I like the online calcs for a quick reference. Rule of thumb, the brighter the room or bigger the picture, the brighter the need.
If you don't want to do the calculations yourself, there are hundreds of calculators out there. Projector Central has a good distance calculator that is preset for actual projector specs. I use it often so I don't have to mess with the calculations. Just go to their website and select "Calculator Pro" at the top. It even does estimated light readings (we aim for 80fL because of the bright room environment we have to deal with, but for controlled lighting 30-50 is a good range too.)
There are also apps available on Android and iOS like AV Tools or Alford Calc.
If you want to do precise calculations, you need to know the size of your screen, the throw ratio of the projector and the brightness of the projector (and the brightness of the room) and the reflectivity of the surface (gain).
The latter two of these deal with picture intensity, the fact as your image gets smaller, the image gets brighter; to a point that it can be uncomfortable to watch. The opposite is also true, that as the the image gets larger, it gets darker since the amount of light coming from the projector doesn't change.
And finally, the more ambient light in the room, the darker or more faded the image will appear as it competes with other light sources.
From your description, it sounds like an alignment problem. There are 3 LCD panels in the projector. Each one displays an exact duplicate image of the others except it's either red, green, or blue. Under normal conditions, the images precisely overlay one another so you get a sharp image. Due to age, heat, or vibration/shock(impact) it would appear that the red LCD panel has shifted a little, giving the "ghosting" effect. You'll have to have the unit repaired by a qualified tech. He'll have the special electronic equipment needed to align the panels properly. Before sending the unit in, try a reset in the menu. Sometimes, the projectors can shift the image electronically, using math algorithms which will try to auto-sharpen the display. Hope I was able to help!---Rick
Let me start by saying that my projector is an InFocus Screenplay 4805, but that I have had the shadow you're talking about on the left foot or so of my screen for about 18 months now. I've researched it and found out that it has something to do with the glue holding something called a "Light Tube" in place heating up and essentially becoming liquid enough to allow this light tube to shift positions...the further out of position it gets the more of that "eclipse" effect you see on the screen. It sound like yours has shifted far enough that no light can pass through it at all.
I dont know if this helps but I have of few of these at my company and when I had the repair people out they said it was a bad prism. If anyone can repair these and whats to buy them cheap let me know. [email protected]
I had the same problem with a few pj800's that I have worked on. It turns out that with old age and constant hot and cold temperature exposure the pixels in lcd panels will become shorted or actually die out. When current is applied there is no pixel activity therefore causing distorted images and lines that appear to drop out or down in the picture. Replacement of all 3 lcd assemblies is needed to correct problem. And being such an old projector the price of the parts would exceed the cost of a new bulb. I reccomend trying to find a used one for parts working or not 99% of the time the lcds are usually fine. Or check out ebay for some used projectors you can find up to date used ones with three times better picture quality than the pj800 for under $300.00 shipped. Good luck!