Chemistry - Soaps come in different colors, but why is soap lather always white?
Solution 1:
Though @DHMO's answer is quite interesting, you shouldn't take it without a pinch of salt. I've to disagree with it in some aspects.
Soap colorants range from various kinds of Mica to dyes found naturally in plants. Now typically when you dye anything the quantity of dye used in comparison to the quantity of the substance to be dyed is very small. Too much dye, and it could possibly stain your hands/clothes, so soap manufacturers use as little dye as possible, but just enough to give the soap a good color.
Now for the rest of this answer, I will assume (reasonably enough) that by 'colored' soap you are referring to soap that goes by colors other than white.
Now when you lather using soap, only a really teeny-tiny bit actually goes into the water. As @DHMO correctly points out, the dye/pigment used to color the soap is greatly diluted. Why don't you carve off a piece of colored soap (having more or less the same size as as an almond) and dissolve it a mug of water by gently stirring it. I emphasize on "gently" so that you don't stir up a lather.
Have a look at the water. You'll see that the soap, apart from making it more cloudy, has not visibly imparted any particular color to the water. This is not unexpected, as I've already mentioned, the quantity of dye used is very small.
Now if you go ahead and agitate that soap solution, it will give rise to white lather, and this shouldn't be surprising anymore.
Now @DHMO's goes on to mention that Total Internal Reflection (TIR) is what imparts the white color to the foam. But this is grossly incorrect. While TIR can result 'white light', it is not the dominant phenomenon acting here (I'm not saying it's completely absent here either).
What is largely giving foam it's white appearance is another phenomenon called Scattering.
Now you might ask, 'Then why isn't soap water white?'. Well, since the foam is made up of lots of teeny tiny bubbles, light passing through it will have to encounter several surfaces, and it's these surfaces that scatter the light in so many directions.
So to say it straight DHMO's answer is incorrect. (No offence DHMO)
Remember I said you can't see any visible coloration in the water because of the dye is present in really small quantities? Well here's a way to validate that claim: Simply combine a teaspoon of red food-color with a bit of hand-wash (now that's really concentrated). Now you can lather the soap and lo behold! You have red foam.
[Credit to @ACuriousMind from Physics.SE, for that bit on why soap water isn't white. Also he confirmed that the white color of foam is due to scattering]
Edit- More kudos to @ACuriousMind for providing this amazing link on scattering.
Solution 2:
You might have observed that large soap bubbles are transparent.
This is because the color has been diluted to a great extent that it basically became transparent.
Now, the foam is just a multitude of tiny bubbles that are transparent.
You would observe that the unorganized mass of transparent particles (the bubble is quite organized) would appear white.
For example, $\ce{NaCl}$ crystal (organized) is transparent while as a powder (unorganized) it is white.
Another example; a small water column when you open the water tap (organized) is transparent, but when you open the water tap to a greater extent, the water no longer falls together, and it appears white.
This is because of total internal reflection.
When the particle is organized, the light is uniformly bent, so the image is not very distorted and it appears transparent.
However, when there are many transparent particles, a small change in the angle of incidence can cause a large change in both the position and the angle of the resultant light.
Therefore, the colors are mixed together, and you see white.
Edit: After a short debate with Aaron Abraham, I figured that I only mentioned total internal reflection, but forgot refraction. Therefore, I now clarify that refraction instead of total internal reflection plays a dominant role in bending the light.
Solution 3:
It is due to multiple scattering events of the incident light off the surface of the many small bubbles in the foam? Large bubbles (of the order of centimetres) do not scatter but show the typical colours of thin film interference fringes.
Common table salt or pure sugar crystals look white for the same reason. Even though the polished crystal is optically transparent, any roughened crystal surface causes scattering. Scattering occurs due to the difference in refractive index of the air, approx 1, and the material in the foam or crystal, which is in the range 1.3 to 1.5 for many substances. Scattering is sensitive to the size of the imperfections on a crystal surface or bubble sizes in foam. It increases with more imperfections or denser bubbles.
You can remove the scattering by placing crystals into a solvent of the same (or very similar) refractive index as the crystal: harder to do with bubbles. However, you can make surface roughened glass beads 'disappear' in the right solvent; water is quite effective.