Spectrum of Spider Webs

forwarded to sci.astro.amateur
From Bob Eklund of MWOA:

I'm looking for some technical guidance that would help me in a writing
project I'm involved with, regarding colors of the solar spectrum seen
in nature.

You may be familiar with the wheel-shaped webs produced by the banded
garden spider (AKA "orange spider.") Today I was looking at such a
web, stretched across the sidewalk above my head, when I noticed that
the web was reflecting sunlight, but pink and green only. The color
would shift from pink to green as I changed my position a few inches
backward and forward. I was looking more or less toward the sun, with
the sun perhaps 20 degrees to the side of the web.

My question is this: Is the effect I'm seeing here produced by
reflection, refraction, or a combination of the two (as in a rainbow);
or is it diffraction (as with a grating), or the thin-film effect (as
with an oil slick), or what? I'm tempted to think it's related to the
oil slick, only because the colors are the same. I have also seen this
pink-and-green effect in middle-level clouds made of water-droplets,
seen near the sun (not the same as the familiar halos seen in higher,
ice-crystal clouds).

My eyelashes, as well as scratches in my eyeglasses and windshield,
also produce somewhat similar effects, when I'm looking near the sun,
except that there I see a full spectrum, not just pink and green.

If anyone would care to enlighten me on this, I would much appreciate
it.

Thanks,
Bob Eklund
Chairman, Publications and Programs
Mount Wilson Observatory Association (MWOA)

"Matthew Ota" wrote in message
oups.com...
[snip]

You may be familiar with the wheel-shaped webs produced by the banded
garden spider (AKA "orange spider.") Today I was looking at such a
web, stretched across the sidewalk above my head, when I noticed that
the web was reflecting sunlight, but pink and green only. The color
would shift from pink to green as I changed my position a few inches
backward and forward. I was looking more or less toward the sun, with
the sun perhaps 20 degrees to the side of the web.

My question is this: Is the effect I'm seeing here produced by
reflection, refraction, or a combination of the two (as in a rainbow);
or is it diffraction (as with a grating), or the thin-film effect (as
with an oil slick), or what?

It's because of diffraction, as in "diffraction grating". The diffraction
"grooves" are the consecutive silken strands. The formula for gratings still
applies:

d*sin(phi_k) = k*lambda (1),

where d = distance between grooves,
phi_k = angle of spectrum of order k,
k = order of spectrum, k in Z,
lambda = wavelength

Using lambda = 5500 A = 5500*10^(-10) m (green light)
and assuming that the silken strands are at a distance of d = 1/10 mm =
10^(-6) m,

then,

sin(phi_k) = k*lambda/d = k*5500*10^(-4) = k*0.55,

so the strands will generate first order spectra (k=1) at an angle:

phi_1 = sin^(-1)(0.55) ~= 33.3 degrees.

which should be what you see, unless I made a typo somewhere.

Thanks,
Bob Eklund
--
Ioannis

Ioannis wrote:
It's because of diffraction, as in "diffraction grating". The diffraction
"grooves" are the consecutive silken strands... [snip]
Using lambda = 5500 A = 5500*10^(-10) m (green light)
and assuming that the silken strands are at a distance of d = 1/10 mm =
10^(-6) m,

First of all, I have a hard enough time believing that the strands are
even 0.1 mm apart, but even if they were, 0.1 mm is not 10^(-6) m, but
10^(-4) m. Thus, your path difference is not 0.55 wavelength, but 100
times more, or 55 wavelengths. Your diffraction grating should yield
effects in infra-red or microwaves.

--
Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

"Ioannis" wrote in message
news:1152901092.935015@athnrd02...
[snip]

Using lambda = 5500 A = 5500*10^(-10) m (green light)
and assuming that the silken strands are at a distance of d = 1/10 mm =
10^(-6) m,

Ooops! Here's the typo: 1/10 mm = 10^(-4) m, so the angle is wrong.

Correct value should be:

sin(phi_k) = k*lambda/d = k*5500*10^(-6),

so the strands will generate first order spectra (k=1) at angles:

phi_1 = sin^(-1)(5500*10^(-6)) ~= .31 degrees,

second order spectra,

phi_2 ~= 0.63 degrees,

third order spectra,

phi_3 ~= 0.94 degrees, etc

Note that because the phi_k angles are really small, you should get some
overlapping between the spectra, explaining why you see pink, and perhaps
other non-pure colors.

Sorry for the typo!
--
Ioannis

"Brian Tung" wrote in message
...

Ioannis wrote:
It's because of diffraction, as in "diffraction grating". The
diffraction
"grooves" are the consecutive silken strands... [snip]
Using lambda = 5500 A = 5500*10^(-10) m (green light)
and assuming that the silken strands are at a distance of d = 1/10 mm =
10^(-6) m,

First of all, I have a hard enough time believing that the strands are
even 0.1 mm apart, but even if they were, 0.1 mm is not 10^(-6) m, but
10^(-4) m.

Yeap, that was a typo. Sorry, I posted a correction.

Thus, your path difference is not 0.55 wavelength, but 100
times more, or 55 wavelengths. Your diffraction grating should yield
effects in infra-red or microwaves.

I don't know if such nets have these effects, but I've been studying spiders
for quite some time. I've seen nets with distances between the threads
between a tenth of a mm, all the way to 1-1.5mms. I have also examined the
light at various blazing angles and to me it seems that the spectra (when
they exist) are generated by the threads themselves. Finer and smaller nets
generate more intense spectra, which leads me to believe that the nets act
as gratings when the spacing is small enough.

--
Brian Tung
--
Ioannis

Here's a photograph of the diffraction from the little beads of stickum
on the strands. Clearly the diffraction is in a direction parallel to
the strand as one would expect from a one-dimensional grating:

http://www.engl.paraselene.de/html/d...in_a_spid.html

and,

http://www.engl.paraselene.de/html/d...n_a_spid1.html

also:

http://www.sciencemusings.com/
"The capture threads of an orb web are especially remarkable. As the
spider spins these threads it coats the silk with a viscous liquid.
Surface tension causes the liquid to contract into droplets, the way a
thin stream of water from a faucet breaks up into drops. As the drops
coalesce along the thread, some of the silk is gathered up in bunches
within the drops. When the thread is stretched, the silk unwinds from
the droplets, like tiny key chains on spring-loaded reels, and then
pulls tight back into the drops. The result is a product wonderfully
suited for holding insects with virtually unbreakable bonds."

I am still looking for a reference showing a photomicrograph of the
beads with a scale to determine their spacing.
Clif Ashcraft

Here's another ref. with a photomicrograph of the beads and a scale for
determining spacing:
(tiny url)
http://tinyurl.com/kxby5

The photograph shows equally spaced beads about 75 microns apart. I
have no idea how much this varies from species to species or from
strand to strand in web woven by a single spider, however this is close
enough to form a one dimensional grating which accounts for the colors
of spider orbs.
Clif Ashcraft

On 15 Jul 2006 08:38:41 -0700, wrote:


Here's another ref. with a photomicrograph of the beads and a scale for
determining spacing:
(tiny url)
http://tinyurl.com/kxby5

The photograph shows equally spaced beads about 75 microns apart. I
have no idea how much this varies from species to species or from
strand to strand in web woven by a single spider, however this is close
enough to form a one dimensional grating which accounts for the colors
of spider orbs.
Clif Ashcraft

The problem with this explanation is that the spectra are on the
support threads, which have no beads.