I will demonstrate one way to "illuminate" something in a deep display case, while preserving it's integrity and keeping it as safe and preserved as possible..
Step 1: Planning, Calculating Resistor Values & Arrays
Although one can (and should, at least a few times) use Ohm's law (one of the pictures below) to calculate resister values for LED's it can get a bit "odd" if parallel lines are used...warning, ALWAYS use segments of parallels, each with it's own resistor. For my purposes here, because of some unknowns and the complexity of the number of LED's and types I was using, I decided to use THIS calculator.
With the calculator you will still need to know
#2: diode forward voltage
#3: diode forward current (mA)
and finally #4: the number of LEDs in your array.
The calculator will give you several choices to pick from many times.
Step 2: The Switches and the Wiring
I originally mounted the switches to a small board, but I was unable to find an esthetic way to attach it to the frame an make it look good. So I removed the board (desoldered the switches) and mounted them on a small box.
Step 3: The Box Frame Itself
I measured around the outside perimeter of the box, and divided by the number of holes I needed. This gave me an approximate spacing for the LEDs (since one set had nine, one had six, and the last had only three, I came up with 2.83 inches between each for exact even spacing. For this project, preciseness was not essential, but esthetically, it would be better if I got them close. I marked them with a small y with a soft lead pencil.
I set the frame in a vise (the one pictured is VERY heavy, otherwise I would have mounted it to a table before using it). All the holes were drilled straight in, except the one's nearest the corners, which I put a little "slant" on them so they'd point away from the corner. If you want to, you can mark the "inside" of the frame and drill outwards, but be aware that the bit, when it breaks through, will splinter the wood a little (of a LOT if you push too hard).....having it on the inside meant it would be hid by a strip of cardboard eventually.
Wearing safety goggles and clamping pieces down before drilling are recommended.
I found after finishing and testing the prototype that I didn't have enough UV and IR LEDs, so I ordered more, and this made me late for the contest, but as promised, I wanted to publish this in the event it might be useful to someone.
Step 4: For the Prototype, I Created the Harness First...
But this may not be the most efficient way to do that.
I probably should have mounted the LEDs and then soldered the wires to them and created the harness as I went, this way, I would have fewer bad measurements. Keeping the harness untangled was nearly impossible.
Oh, before placing ANY LEDs etc. PLEASE remember to put the glass front in (or you'll never GET it in :-)
Step 5: Spacing and Placing the LEDs
I tried to give each "stretch" of LEDs enough wire to allow them to not be too tight nor have too much extra to have to deal with.
Once the LED is pushed all the way through the hole, I bent the leads and taped them to the display box so they wouldn't move.
Then, I pushed a dab of hot glue into the hole and allowed it to harden.
I figured that at least 1/3 (and probably more like more then 1/2) of the light of the LED would be wasted shining towards the sides of the frame and towards the glass, where it would only distract from the view.
SO, I went looking for a simple way to reflect the light back towards the displayed item.
FAILING to find a simple way, with what I had at home, I browsed a hardware store and came up with the little copper crimps, much like thin copper tubes really, and brought them home. Carefully cutting them in half (one side at a time), I ended up with two half tubes of shiny copper (well, the inside wasn't overly shiny, it had a dull coating of something on it, so I used a needle nosed pliers to hold it and brushed it with a wire brush until they GLOWED :-)
Each LED got one hot glued between it and the glass.
Step 6: Next I Had to Deal With Hiding/the Nest, Er Harness
I ran a bit of black tubing (the kind used to organize cables) behind the frame and ran them all through that.
Step 7: Before Finishing...I Added My Extra LEDs
And although it still didn't illuminate the t-shirt as well as I wanted it to, it did a fairly decent job of it, behind glass. In each case below, the pictures were taken in complete darkness; with only the IR, UV, or White LED's lit.