Materials for one mirror:
Bottle cap (pick a good one!)
Acrylic mirror (TAP plastics has scraps for real cheap)
Bicycle spoke (free from local bike shop, ask when they cut up a wheel)
Spoke nipple (should come with the spoke)
Glue (I like "E 6000" from TAP plastics)
1 1/8" Hole saw (sans arbor)
Access to a Drill press
Dremel tool (not needed, but nice)
Step 1: Cutting the mirror
Take the arbor out of the hole saw. (That's the drill bit in the middle of it, that helps center your hole. Since that would put a hole in the middle of the mirror, we don't want it there.)
Mount the hole saw and mirror on your drill press. Have a punch-out tool (I use a blunt stick) ready. If your mirror piece has the protective film on it, leave it on! It will help keep the mirror surface good throughout the process.
Cut the mirror out, and then swiftly punch it out of the hole saw before the acrylic gets too solidified. If you're doing lots, do one at a time! Filling up the hole saw with stuck-together mirror bits is bad.
Step 2: Drilling out the bottle caps
Clamp the cap down securely.
Use a sharp nail or the like to punch a small hole to start the hole.
Drill out the hole with a drill bit.
Match the size to your spoke diameter! It's nice if the spoke's threads engage with the hole, it makes it more secure with the nipple. This could be over-engineering, but whatever.
Step 3: Cutting the spoke nipple
Clamp the spoke nipple in a vice or something.
Use a dremel with a cutoff wheel to cut the nipple just where the square part of the shaft ends. (Wear safety glasses!)
Save the cut-off ends, they will go inside the bottle cap uder the mirror, and act as a backing for the nipple on the outside to tighten against.
Step 4: Assemble the bottle cap and spoke
If the bottle cap isn't rotationally symmetrical and you care what side is up. make sure you go through the right way. The nipple will be on the outside of the cap when it's mounted, so if you're looking at the cap from the front, the spoke should go in the left side and out the right. Clear as mud, right? Look at the pictures for help, I guess.
Once it's in one side, thread the cut-off part of the spoke nipple onto the spoke.
Then thread the spoke though the other side of the cap, and thread the nipple on.
Step 5: Glue in the mirror
Not so much glue that it gooshes all over the place, but enough to securely stick the mirror in there. It also adds some resistance to the spoke rotating inside the cap, so the mirror stays where you aim it.
Step 6: Wait 24 hours for the glue to dry
Step 7: Bend up the spoke for attachment
First, bend the cap and mirror about *that* much. It's a little past 90 degrees.
Then measure about 7cm from the initial bend for the first little loop. You want the mirror to not interfere with your helmet visor, if you have one.
Bend the spoke 90 degrees, in the opposite direction from your initial bend.
Then grab it with a needle-nose pliers and bend it backthrough 180 degrees, making a tight little loop. Pinch that loop together with your pliers. Bend the rest of the spoke back out, following its original line.
Move down the spoke about 1cm, and repeat the bending process to make another loop. Do it one more time.
Finally, cut off the remaining piece of spoke (if you started with a long one). I usually use a dremel to make it smooth there, but that's not necessary.
Step 8: Attach the mirror!
First figure out about where it should go on the helmet. You can put the helmet on and hold the mirror in about the right place as a guide, then push it against the styrofoam to make an impression.
Use a sharp object to poke into the styrofoam and make some holes where the impressions from the loops are.
Then, shove the mirror's loops into the holes. Secure!
I like to glue it in place also, using some more E-6000.
How to aim it? You should see just the tip of your ear in it, and have to turn your head just a little to the lft to be able to see behind you.