I
needed to paint the inside of an ambient light exclusion device for an
optical mensuration1 experiment. (To the layman, I was trying to
paint the inside of a box black.) I had decided on flat black mainly because
it would look cool. Flat black really gives A/B plywood an air of
scientificalness.
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The
trouble was, this was autumn and the temperature in my garage2 was
45°. The warning label on the spray paint can advised me against painting at
temperatures below 50°, but I threw caution to the wind. In single-minded
devotion to the greater cause of Science, I forged ahead, hoping that I did
not get caught by the Spray Paint Police.
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I
can look back on this today and laugh at my naiveté. I was quite frankly
surprised by the results. The flat black paint came out glossy.
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How can flat paint become glossy?
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Naturally,
my first reaction was to get out the microscope to investigate the
microstructure of the surface. This is what I saw.
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The image at the left is the surface that I had just
painted. The one on the right was a surface that looked flat black because I
had painted it at the regulation temperature. Clearly, the glossy surface on
the left is smoother than the matte surface on the right. Ironically, the
surface of “flat” black paint is not flat!
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My “flat black” spray paint became glossy because
the vehicle (the stuff that carries the pigment) evaporated much slower at
45°. This gave the surface of the paint time to smooth out.
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Changing color with colorless water
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Seeing
these images, I immediately had a flashback to one day when I was five years
old. I had found myself with a small plastic bucket filled with water and a
paint brush. The young scientist in me bloomed when I painted the wall of our
house with water, and found that it turned the house from a chalky light
green to a richer green.
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Some
adult wandered by and asked me what I was doing. When I said that I was
painting the house, they frantically went off to find my mom. My little ruse
had fooled even them. I probably got spanked before the truth was realized. If
only I had known Fresnel’s law at the time, I would have been able to explain
the phenomenon to my mother before her hand came down on my precocious little
butt.
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Fresnel’s Law
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Fresnel’s
Law3 describes what happens when light goes from one medium to another,
in this case from air to the surface of the paint or water. When light goes
from air to a surface that is optically “harder” (having a higher index of
refraction), some light enters the surface and other light reflects directly
from the surface, in billiard ball fashion – with angle of incidence equaling
angle of reflectance.
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Fresnel’s
law predicts what percentage of the light is reflected and what percentage of
light enters the second medium. The law takes into account the angle of
incidence, the indices of refraction of the two media, and the polarization
of the incoming light. All that is fabulously interesting, but all we need to
know is that somewhere between two and five percent of the photons act like little
billiard balls. We call this specular
reflection.
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I
brought my good friend Smeldon in to demonstrate. He reads his magazine4
with the light behind him, and the magazine tilted slightly away from him. Without
even thinking about it, he will orient the magazine so as to avoid the
specular reflection. Smeldon could orient the magazine so he sees only the
gloss of the magazine, as in the drawing on the right. If he were to do this,
the print on the paper would be largely washed out by the specular light.
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Smeldon’s
magazine was printed on a coated
stock. After the paper is formed, it goes through a second process where
various additives, like kaolin (a white clay) and calcium carbonate, are affixed
to the surface of the paper and then the paper is polished to a glossy finish.
The coating makes the surface glossy. Most magazines are printed on coated
stock. Newspapers and Sunday paper inserts are printed on uncoated stock.
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If
Smeldon were to try this same experiment with a newspaper, he would not see
the same results. In fact, he would be hard pressed to find a way to orient
the newspaper in such a way as to see gloss. (The interested reader will try
this before going on. Go ahead. I’ll wait.)
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Smeldon
is not an accomplished color scientist and applied mathematician like me (and
he is not nearly as good-looking as me) but he does have a bit of a
scientific bent. His conclusion is that newsprint is an exception to Fresnel’s
law. It would appear that newsprint
has very little surface reflection.
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Holding out on the dark side
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Smeldon
is inquisitive and intuitive, but in this case, he is wrong. A newspaper has plenty
of specular reflection; it’s just hiding in plain sight. I’ll get back to
that in a bit.
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Anyone
who has looked at a magazine and newspaper side by side will notice that the magazine
has much richer color. A solid black on newsprint looks almost gray when
sitting next to a solid black of a glossy glamour magazine.
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Why
is this? I have heard many otherwise intelligent people attribute this to “holdout”.
As the explanation goes, glossy stock will “hold out” because of its nice smooth
and hard surface. That is, it will impede the progress of ink that tries to
seep in. Newsprint has no protective coating, so ink will seep into the
paper, and some of the cute little pigment particles will hide behind paper
fibers.
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I
am sure this is explanation is true, but hey, flies
walk on the ceiling. I am not convinced that this is the predominant
effect. I submit the following image as proof. The image is of newsprint. I
borrowed my wife’s clear nail polish and painted over the word “FREE”. The
black ink with the polish is noticeably darker. I didn’t add pigment. This
was clear nail polish. This is not explained by the “ink hiding behind the
paper fibers” theory – the cute little pigment particles are still in hiding.
Why did it get darker?
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Newsprint with splotch
of nail polish
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The
next picture sheds some light on the quandary by shedding light from a
different direction. To take the next picture, I left the camera and the newsprint
where they were and moved the light over to the specular angle. The splotch of
nail polish has suddenly gotten much brighter because the specular reflection
has suddenly reappeared.
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Same sample, with
light at specular angle
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Going
back to the original pair of microscope images, we saw that the “flat” black
ink on the right had a rough texture. Photons hit this rough surface and reflect
specularly in all sorts of directions. Contrary to Smeldon’s conclusion, newsprint
still follows the magic of Fresnel’s law, it’s just that the specular reflection
goes in all directions.
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In
the first “free estimate” image, it’s not so much that the nail polish made
the black ink darker. It’s more that the specular reflection in the other
parts of the image made the black ink without the polish look lighter. The nail polish focused the specular
reflection so that it all bounced away from the camera.
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My
conclusion is that smoothness will make a surface appear darker in color.
This is not because there is less total light reflected. It is because the specular
reflection from a smooth surface generally bounces off in a direction where
we don’t normally notice it.
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2) Due
to certain previous incidents, I wasn’t allowed to paint in the basement like
other respectable mensurologists do. I guess we can see why I don’t have a
Nobel Prize. Yet.
3) In
my humble opinion, Fresnel’s Law is way cooler than Snell’s Law. By the way,
Snell’s Law was discovered by Ptolemy. I don’t know who discovered Fresnel’s
law, but we know from a previous blogpost that it probably wasn’t Fresnel. As
for the Fresnel lens? That idea came from Georges Louis Leclerc, and not Augustin-Jean
Fresnel.
4) Magazines
were a technology common in the 20th century that was similar to
the iPad. While articles could be read on these devices, you could only check
the status of a few celebrities, and one magazine could barely hold a few
dozen articles. To their credit, they were produced from a once common
renewable resource called “trees”. Ask your grampa to tell you about trees.
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Tuesday, July 3, 2012
Flat paint is not flat
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Actually what we call Snell's law was not accurately derived ny Ptolemy but by Ibn Sahl in 984 (Rashed, Roshdi (1990). "A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses". Isis 81 (3): 464–491. DOI:10.1086/355456.)
ReplyDeleteWhile you may consider Fresnel's law way cooler it is far less useful. Snell is used to undepin most ray tracing programs use to design focusing devices in all kinds of modern optoelectronic devices. Fresnel not required.
Fresnel lenses have nothing in common with the law assigned to his name.
Perhaps next time you will give more attention to the instructions from the coatings chemist concerning the reaction temperature required for his polymer resin to form a conformal coating instead of floculating the extenders and pooling a layer of unpigmented polymer at the surface of the coating.
ReplyDeleteAlso those in optics prefer the term metrology or metrological to mensuration, even though optics is highly dependent on geometry we prefer to reserve the term mensuration for the practice of measurement in geometric mathematics.
I love the comments! Thank you, Unknown. (Although I suspect you are not quote unknown to me. I think I recognize the lion by his paw.)
ReplyDeleteYou are correct that I have given too much credit to Ptolemy. He merely characterized the effect of Snell's law, and fit a quadratic to it. He did not analyze this from first principles, apply a trig function, or go beyond measurements of refraction in water.
Thanks for the info on ibn Sahl. I had not yet met the guy in my studies on applied math history.
You're right. Fresnel's law is not required when understanding Fresnel lenses.
I hope you don't think less of me for sometimes favoring "cool" over "useful". :)
This comment has been removed by the author.
ReplyDeleteAs for those darn flocculating extenders... One thing I have pondered about heatset presses... In order to maximize the amount of product out the door, the press guy tries to run the press as fast as possible, which means he needs to run the dryer at a higher temp. Doing that, he spends more money on natural gas, but (it seems to me) he also loses gloss. This means he needs to run more ink to get the same density.
ReplyDeleteI wonder how big this effect is. What are the hidden costs of running faster?
Time on a heatset web is much more costly than ink. (a total guess, knowing that cost is usually the determining factor over quality)
Delete