The heart of this Instructable is a simple tool for carving spherical lenses out of ice. Essentially, you place the tool squarely on the ice's surface, and then you scrape off ice until no more ice can be removed. At this point a more or less spherical surface has been created.

Carving lenses from ice and using them to burn things isn't a new idea, but this method makes it easier to achieve a spherical lens surface without a lot of careful measurement or a practiced eye. It's also scalable -- a fact which prompted me to try to make a really, really big one. I think the result may be a world record. If you've seen a bigger ice lens, let me know, and I will change my video title. For now I'm claiming a world record.

I teach high school physics, and I thought this could be a fun demonstration or even a class project. Unfortunately, I let my last reasonable size lens melt, and I don't think I can get the big one to school.

Supplies

Parts/Materials:

Chisel (woodworking variety, the sharper the better)
Metal strapping
Wood Screws (or drywall) (approx. 2")
Plywood or solid plank for side panels (around 3/4" thick) -- 1-2 square feet of area
A short block of wood for the spacer (2"x4" or other scrap wood)
A block of ice -- the bigger the better. It doesn't have to be round! More surface area = more light gathering ability, so it can be good to keep it square.

Necessary Tools:

Drill with 3/32" bit (or any bit that is a little narrower than your screws.
Screwdriver (or impact driver)
Saw for cutting curves (coping saw, scrollsaw, or bandsaw)
Small bolt cutters (or other tool for cutting metal strapping -- a hacksaw, dremel, or cutoff tool will work)
Sharpie (for marking)

Optional Tools:

Sandpaper (coarse grit)
Palm sander (optional)
Heat source (torch, hairdryer, or heat gun)

Step 1: Familiarize Yourself With the Carving Tool

The diagrams really show it all...

The basic tool touches the ice at three points of contact: the chisel point and two feet. The figures show two side panels connected by a spacer block and a brace. The chisel is clamped tightly to the spacer block using screws and a piece of metal strapping. The angle of the chisel can be adusted by removing the adjustment screws and pivoting the spacer block (or the panels, depending on your perspective) around the axis of the pivot screws.

Step 2: Working Principle of the Carving Tool

The chisel blade carves away the ice in front of it and above its back, while the carving tool feet ride along the surface of the ice. In theory, this creates a spherical surface that contacts both feet and the chisel tip, and which is also tangent to the back of the chisel blade. The first video explains this more clearly. The second video explains very briefly how this tool developed from its predecessor.

Step 3: Measure Your Ice (or Estimate Its Dimensions)

You should size your carving tool for your ice, so it would be a good idea to first think about the size of your ice and how you're going to get it. Make a plan.

Here are some options for obtaining clear ice. There are plenty of resources relating to this on the web.

Cut some ice from a body of water. A chainsaw would work great, but I didn't use one, because I didn't want to get bar and chain oil in the water. Plus, I happen to have a nice old ice saw. If you know someone who ice fishes, drilling a series of holes with a power auger would probably be the easiest way to get some ice. I'll leave it to you to figure out how to get the ice out of the water.
Freeze water in a large cooler, outside. This works well. Fill the cooler to near the top. Remove the ice when it has frozen down to the thickness you want. If you let it freeze to the bottom, the bottom will be bubbly and cloudy (in my experience, anyway). I have had good luck with ice frozen in 40+ quart coolers. I tried an 8 quart cooler, and the ice was too small to work with easily.
Freeze water in a cooler, in your freezer. The problem here is that you'll need a big freezer in order to freeze a sufficiently large block of ice.
Buy some ice. I suppose you could even buy a block of ice, but if you're going to do this, buying blocks of ice probably isn't your thing.

Step 4: Size Your Carving Tool and Sketch Your Design

The carving tool needs to be small enough so that it has room to move around on your ice block without falling off the edge. At the same time, it needs a broad stance for stability. You need to be able to keep both of its feet in contact with the ice at all times.

To avoid trouble, the maximum distance between the carver's contact points (particularly the feet and chisel, circled in red) should be less than 1/2 the shorter dimension (length or width) of your ice block.

For my cooler sized ice block, the distance from chisel to feet was about 5 inches. For my giant ice lens (47" diameter), the distance from chisel tip to feet was about 9".

Step 5: Cut a Spacer Block and Attach the Chisel

Cut a solid block of wood that will fit against your chisel as shown in the diagram.
Place the chisel on the block, flat side out, with about 1/2" of the chisel extending beyond the block.
Lay some strapping across the chisel, and mark off a length of the strapping so that one or two holes extend on each side of the chisel.
Cut the strapping.
Screws will go in the two holes closest to the chisel, on either side. Mark these positions and drill a small pilot hole in each location. The hole will prevent the block from splitting, but it should be small enough so that the screws grab.
Screw the strapping in place, securing the chisel.
If the chisel doesn't look straight, loosen the screws and readjust the chisel. Then retighten.

Step 6: Trace and Cut the Side Panels

Find a 3/4" thick board (I used plywood), and sketch out one side panel. Do this by holding the chisel on a table, as shown, and tilting it at a 10-20 degree angle. Hold the side panel wood next to it and trace the edges of the spacer block. Then add some handles and some feet (points where the side panel will touch the table), as shown.

Cut out the side panel that you traced. Then duplicate that panel by tracing it and cutting another side panel.

Step 7: Adding the Pivot Screws and Adjustment Screws

Match up the side panels and the spacer block as shown. Then, on one panel, mark locations for the pivot screw and the adjustment screw, so that they will secure the side panel to the spacer block. These screws should be at least 1/2" from either end of the spacer block. Make sure that the holes of each side panel line up with their counterparts on the other panel. This is especially important for the pivot screw holes.

Now assemble the side panels and spacer block, by inserting screws. To prevent splitting of the spacer block, it would be a good idea to use the side panel holes as guides to drill small pilot holes into the spacer block.

**The last two diagrams show how the chisel angle can be adjusted by removing the adjustment screws, pivoting the chisel around the pivot screws, and then re-inserting the adjustment screws to keep the new angle.

Step 8: Add a Brace (optional) to Stabilize the Legs

This should be straightforward. Just make sure that the brace doesn't interfere with the chisel handle, and that it stays off of the ice. The brace isn't completely necessary. I have included pictures of tools with and without braces.

Step 9: Set Your Chisel Angle

The most important thing to know is that a steeper angle (larger angle, as shown int these pictures) produces more curve (a smaller radius).

After having tried a variety of strategies for setting the angle, I recommend "guess-and-check." I usually begin with a chisel angle of about 15 degrees (first figure). I then start carving and pay attention to the curve that's forming. If don't like it, I adjust the angle before I go too far. If you have a piece of "test ice," you can try out your chisel angle on that, first.

The physics teacher in me really wanted to be able to calculate the exact chisel angle necessary for achieving a given spherical radius. Alas, guess-and-check seems to work best for me. When I made my giant lens, I carved the first side with a 15 degree chisel angle (first figure), and then I carved the second with a 10 degree chisel angle (2nd figure). Most of the other lenses that I have made needed about a 15 degree chisel angle.

In case you're interested, the third figure illustrates the difference between my theoretical model of how this carving tool works -- and the actual results of using the tool. The smaller, complete circles show the radii that I predicted (based on my carving tool's footprint, chisel angle, and assumptions laid out in step 2), while the actual radii which fit the lenses' true curvature don't fit on the page. My calculations undershot the actual radii by about a factor of 3. But the fact that they were both wrong by about a factor of 3 makes me feel better.

Step 10: Level Your Chisel Edge

Notice how the edge of the chisel sits flat against a table top. If your chisel blade doesn't sit flat like that, it won't carve smoothly. There are a couple of fixes to try. First, you can loosen up the metal strapping and reposition the chisel. It may be tilted in some dimension. Second, you can sand off a tiny bit of one of the legs until the chisel edge sits flat on the table surface.

Step 11: Carve!

Rules:

Rule number 1: Aways keep both of the tool's feet in contact with the ice! [because, if you don't, your chisel will plunge too deeply into the ice]

Rule number 2: Keep your stroke length at or below the length of the carver (except in the final stages). [because, if you're carving into flat ice, the feet can't follow the new curve that's being created by the plunging chisel. They don't ride along the same part of the ice as the chisel, so the feet will stay high, and the chisel will just go deeper and deeper.]

Steps:

Begin!
I suggest chiseling the edges off first, working away from the center. Theoretically, it might make more sense to start near the center and work out, but in my experience it's safer to start about a tool length from the edge and work inward (but with the chisel blade pointing out!). Remember to keep both tool feet touching the ice!
By the way, if your spherical surfaces don't end up being centered on the ice block or on one another, they will still be functionally aligned, so don't sweat it. [They will still represent the surfaces of an intersection of two spheres. I will add an explanation for this if I have time.]
Soon after you begin, assess how the tool is working. If you think the tool is digging in too much or too little, remove the adjustment screws, change the chisel angle, and reinsert the adjustment screws to keep the chisel at the new angle. The last picture here shows how the two feet and the blade will ultimately define the curve of the lens.
Use short strokes in the beginning (shorter than the tool length).
When you feel the blade biting less and less into the ice, that means the surface is getting closer to its ultimate spherical profile.
When very little ice is coming off, you can lengthen your strokes and carve in various directions. Just make sure that you keep the feet touching the ice, and that you don't use a lot of pressure.
When you're done with the first side of the lens, flip it over. The curvature of the other side can be different, so change it if you want by changing the chisel angle. You can also make the other side totally flat, and your lens can still work. It will just have a longer focal length.

Step 12: Polishing

The first step is to continue with the carving tool, but with less pressure and longer, faster strokes (but make sure you don't lift a leg off of the carving surface!). After that, I sand and then do a final polish with heat.

Sanding. My most exciting discovery during this project may be that I could sand ice, and that the sandpaper lasts virtually forever. Use coarse grit sandpaper. If you're working in below freezing temperatures, the sandpaper will stay dry, and you can clean off the "dust" with a brush.
Heat, in moderation, smooths the surface and turns it from hazy to crystal clear. Too much heat can fracture your ice, so be careful. I have found that it is often a good idea to rub the newly heated surface with my hand, to prevent the meltwater from freezing into big drips. Here are some possible heat sources that can work.
A propane torch. The one I used is actually MAPP gas, but propane is fine.
Hairdryer
Heat gun
Warm water (in a soaked cloth)
Warm hands

Step 13: Find a "use" for Your Lens

An ice lens really isn't practical at all. But that's not the point. Here are some things I've tried...

Burning stuff (black, dry paper is easiest) Notice that this lens is rectangular; the important thing is that it has spherical survaces.
Cooking
Lawn ornament