"Structural color" - where colors come from the size and shape of the material - is beautiful, and often seems magical. Those from oil on water or from a soap bubble are especially beautiful, but don't last. To make something that you can preserve forever, you can use clear nail polish.

Nail polish dripped on water spreads over the surface and floats there, forming a very thin layer - from nanometers to microns thick. This thin film produces rainbows of color thanks to the interference of the light waves.

Supplies

I used the following:

Clear nail polish. It helps if it's fast-drying.
A well-ventilated room. Nail polish has a strong odor; so it helps to have the windows open, especially if you plan to make a lot of films, or if you have a room full of people doing this.
A straw, a disposable dropper, small syringe, or shake drops directly from the nail polish brush.
Black paper. Many people use black construction paper or card stock, but I prefer black presentation covers (polypropylene or vinyl, rough not glossy).
A waterproof container. I used a plastic shoebox.
Water. It's very handy to have something to pour from, rather than using water directly from the faucet.
A place to dry the sheet. I used the lid of the plastic shoebox, lined with a paper towel.
Optional: Wax paper or aluminum foil, to rest the nail polish brush/lid and dropper when you're not using them.
Optional: A partner, to help hold things as you work.

Step 1: Prepare the Sheet

Use matte black construction paper, card stock, or presentation cover.
If you're using a plastic shoebox, then half of an 8.5"x11" sheet (i.e. trimmed to 8.5"x5.5") works very well. If you have a larger container, you can use a full sheet (but construction paper can become hard to work with or tear when wet). If you want more people to make their own (without buying more paper) and/or want smaller results, you can quarter the sheets (i.e. trimmed to 4.25"x5.5"). If you do, some nice parts of the nail polish may fall beyond the edge.
Cut slots along the short edges of the sheet to fold up as "handles". Cut roughly a half inch in from those edges, and leave a roughly one inch portion that is not cut.
Fold the "handles" together, and secure them. I used binder clips.

Step 2: Prepare the Water

Place the sheet in the shoebox, with the handles facing up.
Pour enough water into the shoebox to cover the sheet with around an inch of water.
IMPORTANT: if you're using construction paper or card stock, the handles will "flop over" as soon as the paper gets wet. It's very helpful to have someone holding the handles as you're pouring, or they may break off as you fish them out of the water.
Plastic presentation covers don't absorb moisture so they avoid that problem, but, most types of plastic are less dense than water, and will float to the top. The binder clips may be enough to weigh down your sheet, but it is again helpful to have a partner hold the handles to make sure it doesn't float.

The depth of water is not critical - it just needs to be deep enough that you're sure the drop of nail polish will spread over the surface of the water without touching the sheet until you're ready.

Step 3: Make the Nail Polish Film

Get a drop of nail polish to fall over the center of the sheet.
If you try to drip or shake a drop out directly from the nail polish brush, you want the brush to hold as much nail polish as possible - otherwise, the drops tend to be too small. It's tricky to get the drop to fall where you want it, but you can do it, with practice.
If you use a narrow drinking straw, dip the straw in to a depth slightly less than the diameter of the straw, then cap the top of the straw with your finger so that the polish is trapped in the straw. Then, lead the straw over the center of the sheet before removing your finger from the straw. If you're not careful, it's easy to transfer far too much nail polish, making a film that's too thick to see the colorful patterns.
I like the control you get when using plastic droppers. (They're a very common item, available from many sources.) If you use them, single drops gently dripped are almost always too small to see many colors. So, either drip 2-3 drops very rapidly, or "sqirt" out the equivalent of 2-3 drops. Or, trim the plastic back to a slightly thicker section so that you get a larger drop.
For even greater control, use just over 0.1 mL from a small plastic syringe, such as these from American Science and Surplus.
Watch as the drop spreads on the surface of the water, forming a rainbow-like series of rings. (Some types of nail polish take a few seconds.)
If you want to use the dropper later, drop the remaining nail polish back into the bottle.
IMPORTANT: Wait for the film to completely dry, before lifting your sheet out of the water. This usually takes a few minutes. If you lift it out too soon, the pattern will fade or become nearly invisible as it dries. Some types of nail polish wrinkle slightly as they dry, helping you identify sections as they dry.
After you're sure the film is totally dry, use the handles to gently lift the sheet through the film.
Transfer the sheet with your rainbow film to dry on the paper towels placed on the shoebox lid.
If you plan to make more films in the same container of water, it may be helpful to skim off any remaining nail polish using paper or a paper towel. You may also want to change out for fresh water, since card stock and construction paper leave some color in the water.

Step 4: Let the Sheet Dry

Card stock and construction paper absorb water, so expect this to take a while. You can speed things along by changing out the paper towels as they get wet. And since the paper is black, they dry more rapidly when placed on a sunny window sill.
Card stock and construction paper also wrinkle as they dry, so keep them as flat as possible.
Plastic presentation covers avoid both of these problems (they stay flat and themselves dry quickly), but introduce a new one: since water doesn't flow through them, a layer of water can get trapped between the cover and the nail polish film, which can bulge and take a long time to dry. One way to speed things up: tilt it on its side, and gently touch a paper towel to the edges where the water pools. Since you don't have to worry about the plastic getting wrinkled, it dries more quickly standing vertically in the sun.

Now, enjoy your beautiful creation! You can also trim portions of the rainbow, and use them in other crafts.

Step 5: How Does This Work?

For many observations, light behaves as a wave. ["What light is" gets stickier once you consider quantum mechanics. But for this, we'll be OK thinking "light is a wave."] Different colors correspond to different wavelengths.

As with any wave (sound waves, water waves, waves in strings), when they interact, they "add" by superposition. If they're both "up", then the result is higher than either one alone; if both "down", then lower then either. But if one is "up" and the other "down", they tend to cancel each other out.

And as with any wave, any time they hit the boundary between two materials, some will reflect back, and some may be transmitted. With thin films, you get reflections from both the front and the back. This creates the two waves that interfere to produce the colors you see. That is: for a given thickness, some wavelengths (colors) will cancel; the reflected color you see is a proportional blend of what's left.

Some very good images and interactives are available on the web, but there are also plenty that are confusing or incorrect.

My animations in this step show the waves as they're transmitted and reflected from each boundary. The first keeps the wavelength (color) of the light constant while changing the thickness of the film - for each wavelength, the reflection will be strong for some thicknesses, while at other thicknesses there is no reflection at all. The second animation keeps the film thickness constant while changing the wavelength. Note that the colors in the animation are to help you identify which wave is which - they all represent the same color of light. [TALL notes: these aren't perfect: the amplidute of each wave is reduced at each boundary - which I indicate roughly by the thickness of the line. Also, the behavior very close to each boundary is more complex.

If you want to see the same effects interactively, please check out

https://www.geogebra.org/m/ZzUQnmjB and

https://loganms.github.io/ThinFilmInterferenceSimulation/

The resulting intensity vs. film thickness for assorted colors can be seen at

https://www.geogebra.org/m/mSv7zFxu

Our brains blend the resulting reflected colors together into what we perceive as a single color. That is approximated at

http://markkness.net/colorpy/ColorPy.html (which I used to generate the image above) and

https://demonstrations.wolfram.com/ThinFilmInterferenceSpectrum/

For all of the above, use for the index of refraction n₁=1 (air), n₂=1.4 (approximate for nail polish), and n₃=1 (air); or if that's not an option, use "Num phase flips"=1

Some other good discussions/tutorials of thin film interference and structural color include:

Step 6: Avoiding Problems

Most of the light actually passes through the film; to make sure you notice the reflected light, you need a dark background to absorb the light that goes through both layers. That's why you need a black background.

It is very important to let the nail polish cure completely before removing it from the water, and to use a sheet that has a rough texture. If you do, the thin film will have mostly air behind it (since the rough surface means only a small area of the film touches the sheet). If nail polish hasn't cured, it conforms to the shape of the sheet, leaving little air gap. The index of refraction n of nail polish and paper fibers are different enough to see some pattern most of the time - but it is far less vivid. The index of refraction of my plastic report cover is close enough to that of the nail polish that I saw almost no color when I removed the film too early.

Using too thin a film may make it only silvery, or have very few colors. This can happen if you try to shake a drop from the nail polish's bottle, since the polish wants to stick to the brush rather than drop down. Too thick a film gives faded colors, and really thick looks a lot like plastic wrap. This may happen if you try to use a straw to transfer nail polish drops - it's easy for the drop to be quite big.

Step 7: What Can You Learn From This?

As shown in the first figure, you can quickly glance at your film and for some colors, you can immediately identify how thick the film is. Using nothing but your eye and your sense of color, you can say, "The film is 210 nanometers thick there."

For some of the colors, it's hard to tell exactly how thick the film is just by looking at the color. But you can easily use light to find differences in film thickness.

You may have noticed in the animations above that there was a fairly broad range of thicknesses that gave a significant reflection, but only a narrow range where the reflection cancelled, for any one wavelength. So, if we shine light that's just one wavelength onto a film that varies in thickness, we see broad bright stripes separated by thin black lines.

Fortunately, lasers are common light sources emitting just one wavelength. We want to shine the light over the entire film rather than just one spot, so we need to spread it out. Here's a method that works well:

Trim small squares from several layers from a white plastic grocery bag. (Trimming about 2 in. x 2 in. from a corner usually works, since you can then use anywhere from one to four layers.)
In a dark room, press pieces of the bag against the laser pointer. You want the light to be bright, but spread out. Decide the number of layers you want to use.
Use tape to hold the pieces of the bag in front of the laser pointer.
Shine the light from the laser onto your film.

These figures show the same film in white light, and light from red, green, and purple laser pointers. The difference in thickness from one dark stripe to the adjacent stripe is one wavelength of light . In air, red lasers have a wavelength around 650 nanometers, green around 530 nm, purple around 450 nm. (The exact wavelength depends on the way the laser diode was made.) The wavelength in the film, is this value divided by the index of refraction of the film. Once you know the wavelength of your laser, you can use it effectively as a ruler to measure incredibly tiny distances.

This also lets you take advantage of thick films: films more than around 1000 nm thick produce interference colors that are very hard to see in regular light; but when lit by laser light (especially green), many dark and light stripes are very clear.

Step 8: References and Background

I'm certainly not the first to do this activity; many others have posted some very good instructions on the same topic. You can find some similar activities at:

All of the animations shown above assume the light goes perpendicular to the surface of the film. Things are a little different when you tilt at an angle, since the effective thickness that the light travels through changes. That's part of what makes these colors seem so magical - they shift as you look at them.

I hope this is a useful contribution to what others have done. I haven't read of others using this way of making "handles," nor of using plastic report covers; I like how flat and "finished" the results look when using them. And only one of these links (the one at sci-toys.com) emphasized the importance of letting the nail polish fully dry. I'd been confused about several failures before reading about that, and thinking about why that would matter.

And often, the focus is more in producing something that looks good, rather than on how it works.

With these tips, I've had consistent good success. I hope you find the links and animations to be helpful.