
You're up against a law of physics, here: the angle of reflection is 
equal to the angle of incidence.  The only solutions are:
A.  Make the surface less reflective.  I have never found a way to do 
this that wouldn't make the floor either too slippery or too sticky, 
and that wouldn't rub off during the course of the performance.
B. Change the angle of incidence.  You've discovered this already; 
when you use a different lighting angle, the problem disappears.  The 
problem with this is that backlight (which I prefer greatly to 
downlight) is very, very helpful in separating dancers from the 
background -- especially if the dancers are dark-haired and the 
background is black.  Note that backlight  will give you even more of 
a reflection than downlight.
C. Move the camera so that the angle of reflection passes over it 
rather than directly into it (remember that you can't change the 
angle of reflection except by changing the angle of incidence; they 
will alway be the same, as any billiards player will attest).  
Putting the camera at just above floor level wold virtually eliminate 
the problem, but this may not, of course, be practical with your 
system.
>  front light has no 
> reflection problems but creates shadows.
I'm not sure what you mean here, since front light is usually used to 
*eliminate* shadows. . .or perhaps you mean shadows on the backdrop 
rather than on the dancers?  If so, this can be eliminated by using a 
vertical angle steep enough (and keeping enough separation between 
dancers and backdrop) so that the light can be shuttered off the 
background.  Note that front light tends to "flatten" dancers out.
> the stage, the angle of the camera is such that the camera does not "see" 
> the effect of the near side lights
Side light, of course, is a staple of dance lighting (although I hate 
to generalize), as it reveals body shape so well.  Can the camera be 
farther away (which would change the angle so that it would pick up 
more of the "near" sidelights)?
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Jeffrey E. Salzberg, Lighting Designer
http://www.flash.net/~salzberg
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