Optical effects on spider webs

German version

Under favourable conditions (dark background, but against the light) the strands of spider webs may be seen shining in vivid colours. Figure 1 shows the web of Zygiella x-notata approximately in natural size.


Figure 1	Figure 2

The next two images are enlarged details from figure 1. The colours are caused by interference of the rays scattered by the arrays of tiny sticky droplets on the catching threads. The colours are rendered best when the strands are slightly out of focus.


Figure 3	Figure 4

What can be found in the World Wide Web?
First of all, there are some fascinating images on the pages of Eva Seidenfaden, which are mainly devoted to astronomy and atmospheric optics.
And then an article by H. Joachim Schlichting, "Farbenspiel im Spinnennetz" (in German) with an explanation which only covers part of the observable phenomena.

Spider silk

Strong, non-sticky silk is used for the frame and the spokes of an orb web, while the catching silk is softer and carries small sticky droplets.
On the diameter of the silk threads one finds something like 1–4 μm, or 2.5–4 μm. I have looked at catching silk thread of a cross spider (Araneus diadematus) under the microscope and determined the diameter of the sticky drops as 25 μm approximately, estimating that of the thread in between as one tenth of that, i.e. 2–3 μm. There were 12 to 13 drops per millimeter. Presumably, the size as well as the density of the droplets vary within wide limits.
Colours can be seen both on the dry and on the sticky threads. Figures 6 to 13 show webs or strands of cross spiders.

Figure 5: A radial spoke silk strand and a catching thread carrying drops of glue, taken from the orb web of Zygiella x-notata shown in figures 1 to 4, magnified ca. 150 times. Between two drops with about 15 μm diameter there is mostly a much smaller one.

Investigations using electron microscopy (see Fritz Vollrath, Spider webs and silks. Scientific American 266, March 1992, 46–52) have shown that the glue droplets also serve to keep the threads taut while allowing considerable stretching: the surface tension tends to concentrate the glue into droplets, the strong adhesive forces let it stick to the silk. By this, the silk thread is drawn into the droplets where it curls.

The dry strands

We consider first the dry (non-sticky) silk. Figure 6, intentionally out of focus, shows the gloss of threads in the centre of a cross spider's web, figure 7 shows radial spokes and in the background framing strands. The bluntness in the middle is due to motion in the wind.


Figure 6	Figure 7

The light producing the thread's image has partly been reflected at the surface, partly it has gone through the silk, being refracted, and some has gone around it, being diffracted. The thread, however, is so thin that the three effects cannot be separated. The cross section is neither circular nor constant along the thread. The silk is secreted as a liquid by the spinnerets and hardens in the air – presumably the surface is wrinkled. For our considerations here it is important that the silk is not smooth on a microscopic scale, and this affects reflection, refraction as well as diffraction. The corresponding phenomenon seen on mat surfaces is discussed extensively elsewhere. Here we see, so to say, the one-dimensional variant.
A plane surface of water shows the mirror image of the sun only on one spot. If the surface is ruffled by the wind, many small glittering reflections are distributed over a much larger area. If a thread were smooth and cylindrical, the reflection of the sun would be seen on a very short section as a very bright gloss. If the thread is wrinkled, there are many small reflections along a much longer section. In the eye of the observer, more precisely: on its retina, the light waves coming from the partial reflections are interfering, and as they have travelled different paths, a pattern of enhancement and extinction arises, which, moreover, is different for different wavelengths.
Thus, this is the one-dimensional case of speckle (granulation). On a two-dimensional mat (= microscopically wrinkled) surface a pattern of coloured speckles would arise. Here the speckles are lined up on a thread, and in an unsharp image they become stripes or curls, looking like beads on a string.

The sticky capture threads

In the case of the capture threads we have to discriminate between those parts where the silk itself is shining and the other parts where only the droplets glitter and the thin silk between them is almost invisible, see figures 8 to 11.

Aside of the shining parts of the threads

When the threads themselves are not shining, their optical properties are almost exclusively determined by the droplets sitting on them.
On both pictures 7 and 8, the web was moving in the wind, thus also the parts in focus are not sharp. Where in figure 8 and in the following pictures single droplets become discernible, there are no colours. In contrast to this, the play of colours on the dry strands remains if they are in focus (figure 7).


Figure 8	Figure 9


Figure 10	Figure 11

On the threads which are in focus, in many cases single droplets are discernible. These are, however, much smaller in reality. What is seen is the larger diffraction image due to the small opening of the diaphragm of the digital camera.
The thread between the droplets is nearly invisible.
Where the image is in focus, there are no or only very weak (unsaturated) colours to be seen. The colours become vivid where the light of neighbouring droplets is superposed on the retina of the eye, on the film or on the sensor of the camera. Thus, clearly it is the interference of two or more rays which gives rise to the colours. The underlying physics is dealt with in the section on "multiple beam interference".

The ideal case

What is to be seen in the ideal case of a string regularly beaded with droplets? There is one spot of the thread which shines brightly. This spot would also shine if there were no droplets; it is the spot where the direct reflection of the sunlight is seen. From there, all rays interfere constructively, as their paths all have the same length. A small distance aside from this, the light paths over the different droplets already differ sufficiently so that the sum of the waves becomes very small. Proceeding in that direction, a point is reached where the difference between neighbouring paths is equal to the wavelength of blue light which then interferes constructively while the green, yellow and red light is still weakened, the thread shows blue lustre. Next, the path differences match the wavelength of green light which is enhanced while yellow and red are still suppressed and blue is suppressed again. Then Yellow and red follow and after that, there comes a dark region where all wavelengths are suppressed. In figure 12 – again in an out-of-focus closeup – there are several glossy sections, the sides of which are flanked by colours in just this spectral sequence. One of them is zoomed in in figure 13.

Figure 12

Figure 13

Seen from large distances, each piece of the catching thread between two radial spokes only shows a small part of the full colour sequence. As the density of the droplets along the thread is not constant, in most cases more or less random colours occur.

Freshly spun catching thread

Figure 14

An attempt to take a picture of a small spider just building its orb web, resulted in the image shown above. The spider was hastily moving, the sun was dazzling and on the display of the camera almost nothing to see. The autofocus system of the camera chose to focus on the grass in the background; the spider is seen blurred and over-exposed somewhat below the centre. The freshly spun catching threads are seen in the upper part as light stripes – completely out of focus. The threads are shining in the sunlight. The lowest of them is the newest one, there is only one reflection, the thread above it also shows only one reflection. On the other threads, from bottom to top with increasing intensity, to the left and the right other, coloured reflections appear. This can be seen better in the next figure.

Figure 15

Note that only on the uppermost thread there is an almost complete spectrum from blue to red at the side of the "zero order" reflex. Second order diffracted images are missing (cf. e.g. a multiple slit diffraction pattern).
All details of the picture are easily explained at least qualitatively. Assume that the thread leaving the spinneret is in the beginning covered uniformly with the viscous sticky fluid. Then it will reflect the sunlight like an ideal cylinder in a single sharply defined spot – as seen on the lowest thread.

Driven by the surface tension, the viscous cover starts to get alternatingly narrower and wider, similar to the small stream of water starting to divide into droplets shown on the left. Now, instead of a single reflection of the sun, on each widening ("belly") and on each narrowing ("neck") there is a small glossy spot, a small, distorted image of the sun. Looking at the same part of the thread while moving the head to one side, one would see pairs of belly- and neck-reflections approach each other until they eventually join to form flank-reflections, and then disappear.
As long as belly- and neck-reflection are separated, the beams coming from there can interfere destructively, depending on the path length difference. By this the missing colours of the diffraction spectrum might be explained, as well as the relatively low intensity of the central (zero order) reflection and also its colour.
The narrower the necks, the smaller are the neck-reflections and the smaller their influence on the intensity of scattered light. When the droplets are completely separated there are no neck-reflections any more.
Of course, there is also refraction which directs some light to the observer. But this may be discussed in much the same way; what counts is the sum of reflected and refracted light.

Figure 16: A flashlight picture of a thin stream of water starting to divide into droplets as an illustration of belly- and neck-reflections. Only the white patches immediately to the right of the middle line are reflections from the front surface; all others arise due to refraction and reflection at the back surface.
Proceeding from top to bottom, first there is a flank-reflection on the hardly widening or narrowing stream, then follow alternating belly- and neck reflections, the latter becoming very small at the narrow necks.

The shining parts of the capture threads

Looking at a capture thread under the microscope and changing the illumination such that the thread itself shines in the light, one can hardly see the small droplets any more. This means that to a first approximation the droplets may be ignored when the threads themselves are shiny.
Figures 17 and 18 show once more the orb web of the same spider as Figures 1 to 4; this time, there are many glossy parts on the capture threads. They are very bright and partly over-exposed in figure 17; in figure 18 with shorter exposure the corresponding spots are light blue or yellow-green. The sequence of hues – light blue, greenish, yellow, orange, purple, blue, green – resembles that of soap films.


Figure 17	Figure 18

This is not so by accident, but a hint for the correct interpretation: the hues of soap films are quite similar to those which appear in the diffraction image of a slit or of thin, absorbing line-shaped obstacles. Apparently, under the present conditions, diffraction of light is most important for the appearance of the threads.

Figure 19: Colours appearing in the diffraction pattern of a slit or of a black thread. The brightness has been chosen so intense that the image is "over-exposed" up to the 14th tick of the scale below, which means that it should be brighter than can be displayed on the screen. The scale gives the radius (in μm) of the cylindrical thread or half the width of the slit, respectively, multiplied by the deflection angle (in degrees). The hues between the 17th and the 35th tick are found in glossy spots of figures 17 and 18. One could use this to estimate the thickness of the thread if the deflection angle is measured. It is, however, to be expected that the transmitted light as well as the true reflection at the surface will somewhat change the results – not qualitatively, but quantitatively a little bit.

Large deflection angles

Why are the colours visible against the light and not under larger angles, having the sun in the back?
Clearly, diffraction is seen only at small angles. But multiple beam interference could also occur in the light reflected from the sticky droplets also at large angles. But there are two effects opposed to vivid colours in backward direction.
If the size of the droplets is not very uniform, this has little effect in forward direction, but can destroy coherence in backward direction. The following two sketches illustrate this. The thread is assumed to be perpendicular to the screen, and there are two droplets of different sizes. Two reflected rays are shown, and the path-length difference is emphasized in red. It is small in forward (fig. 20) and large in backward (fig. 21) direction.
Figure 20

Figure 21

However, if the sizes and mutual distances of the scattering centres are uniform, interference colours do appear also in backward direction, as the following two pictures show. I have taken them in the morning with the sun behind me.


Figure 22	Figure 23

In the left, only slightly defocused picture, only faint, unsaturated colours are seen. The right figure shows the same threads (only the uppermost two are missing) at a slightly changed observation angle and more out of focus. Now there are saturated colours, but rather dark and therefore not very conspicuous. The intensity of the scattered light is too weak!

Are there still other phenomena?

In the paper cited in the beginning "Farbenspiel im Spinnennetz" there is a picture with interference colours in backward direction (figure 3, a photograph by W. Schneider) and the remark

"Aufmerksame Beobachter können nämlich unter günstigen Bedingungen ein ähnliches Farbenspiel in Reflexion beobachten (Abbildung 3). Dieses Phänomen ist nicht abschließend geklärt. Es liegt aber nahe, dass hier ein Regenbogeneffekt vorliegt."
(Attentive observers namely can under favourable conditions observe a similar play of colours in reflection (figure 3). This phenomenon is not yet definitely clarified. However, the presence of a rainbow effect suggests itself)

Rainbows from very small drops (called fogbows) or from filaments as thin as spider silk are not colourful but white. This is due to the fact that pronounced diffraction effects completely outweigh dispersion. Rainbows can be seen on cobwebs if (comparatively large) drops of dew have condensed there, and are easily identified. Rainbow-effects are certainly not the correct explanation.
The picture in question has little in common with the pictures shown here. There one can see an orb web with capture threads in several sectors shining in the sun, not white but pink. The surroundings are gleaming green. Except of this bright pink and dark green no other colours are seen (at least in the reproduction of the photograph). This is quite different from the appearance if seen against the light.
The correct explanation might be the following: The light reflected from the silk strands and from the droplets interferes so that the intensity of green light is somewhat reduced, which makes the reflections pink. Constructive interference of green light occurs at slightly different angles, so that the neighbouring areas appear green. This is essentially two-beam interference, and, as seen on thin films, for larger path-length differences (= higher orders), pink and green are the predominant hues.

Conclusion

The phenomena which have been discussed separately rarely occur so well separated: Often, on sticky threads, the interferences seen also on dry ones are not fully hidden by the additional ones, or irregularities in the distribution of droplets produce similar small scale changes of colour. The shining parts of the catching threads can be affected by interference with the light scattered from the droplets, similar to the reflections in figures 14 and 15. The pattern produced by the wrinkled surface of the dry threads is superposed with the "normally" expected diffraction colours of thin filaments. Thus a puzzling complexity may arise which seems to defy all attempts of explanation. Only under favourable lighting and observing conditions a single phenomenon prevails and is then more easily interpreted.

Some more images:

Links to other pictures

Fantastic photos by Trevor Roberts
A wonderful small image by Ágnes Őri shown on an "Optics Picture of the Day" page of of the Atmospheric Optics site.

Back to multiple beam interference

or back to the index origins of colour