| MadSci Network: Physics |
The question: When we hold two or more pieces of white paper (we tested this with several types of paper - printer paper, notebook paper, recycled paper - all gave the same result) in front of a source of white incandescent light (60W bulb) the paper appeared purple (although the shade varied from almost blue to deep purple depending upon the type of paper). Why is this?
"The answer" takes us into several areas of color perception. First, look at these previous answers from our archives, which I found by doing several searches with our search engine:
However, the last answer shows the 1931 CIE chromaticity diagram, while the 1976 CIELAB chromaticity diagram is most often used these days.
Here are some other Web references:
comprehensive article about color scales
more about different color gamuts
LAB color space from Answers.com
My specialty is optical physics, and in my lab at work I have a
spectrometer that can measure "color". I measured the "color" transmitted
through up to 8 sheets of white paper, with an incandescent bulb as the
source, on my spectrometer. The "color" values I then put into a
color-conversion program (see BabelColor) to determine and map the
"color" through different numbers of sheets. Here are the L*, a*, and b*
results I obtained with my spectrometer:
| # of sheets | L* | a* | b* |
| 1 | 99.7 | -0.32 | 0.77 |
| 2 | 67.1 | 1.31 | 3.96 |
| 3 | 50.1 | 2.40 | 4.86 |
| 4 | 35.2 | 3.00 | 7.21 |
| 5 | 22.1 | 5.60 | 2.39 |
| 6 | 11.6 | 5.57 | 3.16 |
| 7 | 5.30 | 7.49 | -1.97 |
| 8 | 2.60 | 6.91 | -4.65 |
The row with only one sheet is my reference "color", and it was, literally, referenced to itself, which accounts for the L* value near 100 and the small (almost zero) a* and b* values. The value L* is a measure of the amount of light, while a* and b* are color coordinates on the CIE a*b* chromaticity diagram. If a* is positive the color is toward the blue/red, while b* positive is toward the green/red. Only two of the results I obtained have either a* or b* negative, being the results from 7 and 8 sheets.
If one maps, as I did with BabelColor, the a*b* coordinates onto the CIE a*b* (CIELAB) diagram one finds that when there are a small number of sheets the color is slightly red, while with 7 or 8 sheets the color shifts toward the purple! It is a very dark purple, which is obvious from the small L* values. But our eyes are so good at being able to see an incredibly diverse range of luminances (amounts of light) that we can actually perceive a slight color. (I am not going to get into the differences between photopic and scotopic vision, but you can do some research into it yourself!) But the color is not very saturated, meaning that it is not very far from white. Saturated colors have a* and b* values in the tens rather than single digits. In fact, the CIELAB a* and b* scales run from -120 to +120, while the L* goes from 0 to 100 (see beezlebugbit). Also, the minimum discernible color difference on the CIELAB color space is roughly one unit (see isg.cs.tcd.ie).
So, the color is definitely red or purple, but why? The reduction in the amount of light getting through is primarily a scattering phenomenon, but there are other aspects at work, including absorption and frequency conversion by brighteners. Most modern white papers contain brighteners to convert ultraviolet to blue, making the paper less yellow and more "white". The makeup and function of brighteners can be read about at this page from Wikipedia and at this site from paperonweb (Look in the section called "Optical Properties".).
Scattering by small particles and small fibers tends to scatter the blue end of the visible spectrum more than the red end (Which accounts for the fact that the sky is blue!), so the very slightly red hue with up to 6 sheets can be accounted for by this. The (very small) turn toward the purple with 7 or 8 (or more?) sheets is probably due to the fact that most paper is slightly yellow (ignoring the brighteners), meaning that it reflects (or absorbs) more yellow than blue light, and causes a very slight preferential transmission of blue through the large number of sheets.
The perception of color is a very complicated subject, indeed. One of the subjects that I have not even discussed is the fact that not every person's eyes see exactly the same colors as other people. In fact, if you have a small group of people looking at the sheets of paper that you describe, I am surprised that some do not disagree with your saying that the color is purple! If I were to describe the color that I perceive through my 8 sheets of paper I would say that it is a very dark yellow! But my spectrometer tells me it is a very unsaturated (almost white) purple, and I will defer to the spectrometer.
John Link, MadSci Physicist
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