By etching any design into mirrored acrylic and then edge lighting it, you will find the image pops out at you quite magnificently. I will show you two methods here, one without the need of any special tools, powered by a small battery. The other one can be made more elaborately with a laser engraving machine and remote controlled color-cycling LEDs you plug into a regular outlet.
Read on to see how I crafted these...
Step 1: The Materials - What to buy & where to find it
1. Mirrored acrylic sheet, about 8inches square, Quantity = 2
--8 inches square, 1/8th inch thickness is what I found ($2.50 each)
--TAP plastics (they will even cut it into any shape to save you time): http://www.tapplastics.com/
--other online sources for acrylic exist, may be a little more $$ though.
2. LED flexible strip (any color you like!)
--best to get the thinest possible, or close to the thickness of your acrylic
--I found a sample that was about 18inches in length, 3/16ths inch wide, 12volt DC, $2.00
--online at: http://www.hobbypartz.com/79p-10198.html
3. small camera sized battery
--this needs to match your LED strip's voltage
--found a pack of 2 for $5 at RadioShack (model# 27A): http://www.radioshack.com/
4. a battery holder
--will need to fit the battery you buy
--also found at RadioShack, model "N", part# 270-405A, $1.20
5. plastic glue
--best to find one for acrylic specifically, some types silicone should also work
--$3 at a local hardware store
TOTAL cost = $16.20