What can be the simplest way to find the thickness of a soap bubble? Is it possible to measure the thickness of a soap bubble without using any sophisticated instruments such that anyone can do it?
 A: One can try to use the interference colours: at least for the thickness range between the black spot and where they blend into fainter colours one should be able to make a map from colour to thickness when shining white light on it. Indeed, this has been proposed as a student experiment.
Thin-film interference is what gives the bubble its iridescent colours. Different wavelengths are reflected back from the bubble surface and the interior water-air interface and interfere: this makes the intensity of the reflected light vary with wavelength and bubble thickness. 
Using a relative intensity of $$I(\lambda, t)= (1/2)+(1/2)\cos(4\pi n_{water}t/(2\lambda) - \pi)$$ (see the link above for a derivation) one can make a plot of how much intensity of different wavelengths will show up for different thicknesses, and hence estimate the thickness from the resulting colour mixture.

Except that the above picture does not do justice to the colours, and is misleading for the thicker bubbles! For bubbles a micrometer thick the different wavelengths blend into each other, producing far less vivid colours than my plot. 
The reasons are twofold. First, representing exact colours on a computer screen is very tricky (your settings differ from mine, and there are colours that cannot be depicted by particular screen). More seriously, the above picture uses just three wavelengths rather than the full continuum of the light spectrum, and this is why the muddling of colours does not occur. I did this because the top plot would otherwise be hard to understand, and because converting from a full spectrum to a computer RGB color is again a tricky issue (the package ColorPy has some solutions, and uses soap films as one of the examples further down on the page). The chart on the soap bubble wiki is more accurate than the above, and it might at least give a hint at what is going on. 
A: Average thickness could be determined by observing a bubble machine consume soapy water and produce bubbles. The calculations require only arithmetic and the physical science concepts of length, area, volume, and time.
$$\text{average thickness} [L] = \frac V {\frac {\pi d^2} 3 \frac {n s} t}$$
$$V = \text{volume of solution consumed} [L^3]$$
$$d = \text{average diameter of bubble} [L]$$
$$n = \text{count of bubbles during bubble-counting period} [\#]$$
$$s = \text{duration to consume solution} [t]$$
$$t = \text{duration of bubble-counting period} [t]$$
Major error sources would be the uneven film thickness, globs of solution at the bottom of each bubble, and spittle made by the bubble machine.
A: I actually did this as an experiment. So you need a scale, a ruler, a paper towel, and a bubble wand. Blow a large bubble to catch it on the bubble wand. Measure it using the ruler. Now set the bubble aside and measure  the paper towel rolled up in a ball. Now try to fling the bubble so that it floats downward on the paper towel, go ahead and measure it (the change in mass). The change in mass will be the volume of the bubble which is approximately the density of water (mass x 1ml/ 1 g). Anyways, using geometric formula  for the area of the sphere one can close in on the thickness of a bubble, which turns out is around 1000 nanometers. 
A: One can measure temperature and pressure of the air used to blow  a bubble, the diameter of the bubble, and its vertical speed in air (using a camera). Then one can use the Stokes law, calculate the mass of the bubble and the mass of the air in the bubble, their difference is the mass of soap water, then one can calculate the thickness of the bubble. For example, if the densities of soap water and air are respectively 1000 kg/m^3 and 1.29 kg/m^3, the diameter and the thickness of the bubble are respectively 1 cm and 1 micron, the mass of the air in the bubble is about 0.7 mg and 0.3 mg, so they are of the same order of magnitude.
