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Here is a link someone else here on LJ's gave me, and it has been very useful:

http://www.woodbin.com/calcs/sagulator.htm

I just finished a little project similar to yours, using painted #2 pine for shelves for paperback books and VHS tapes or DVDs, with a 36" span, and I would not have even considered not supporting it along the entire back length of the shelves. In my case I used 1-1/2 inch strips, which I rabbeted 3/4×3/8 to accept the back of the shelf, since this was to be attached the wall. I am not among the experts on such things here, but it seems to me that if the back of each shelf is firmly attached to your 1/4 inch plywood, it should serve the same purpose.
 
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