Observations of Nature in Art

May 23rd 2012, Please read this DISCLAIMER before proceeding. Today's edits are in red.

RAINBOWS:

A. What is wrong with this picture?

(Thanks to Shailesh S for motivating the following.) 

Have you ever seen an elliptical rainbow? No? Let's ask ourselves why not? Imagine looking at a circle, a child's hula, or a hoop-earring in a 3/4 profile photo of a beautiful woman looking out over a seascape (just saying!). The hula-hoop appears as a circle only from one particular angle, out of 2 Pi steradians. To anyone else looking at it, it appears as an ellipse. This becomes clear when they are as far to one side of you as you are from the hula-hoop. Now imagine that there is a big evening rainfront about 20 miles to your East, and you see a rainbow (in the East, why?), and your friend who lives 20 miles to your North texts you, "i c byu t ful rnbo, do u?". You respond, "Yes, i c it 2, as circle, so u must c it as ellipse." She txts bak, "No way, mine is circle 2! ;-?"

Now, the only way the same real object can appear as a circle to all viewers is if it is a ... sphere! Let's accept that a rainbow is not a sphere (in four dimensional space, it would be! Isn't just that a reason one would wish String Theory to be true?). Then we have to conclude that a rainbow is not real! What one means by "not real" is that you can't project it on a screen. Such images are called "virtual images", like the image you see through a magnifying glass. 

We see the rainbow, because the lens of our eye collects the light reflected and refracted from all the raindrops and projects a real image onto our retina. If we consider "seeing an object" to mean sensory perception of light emanating or reflected or otherwise having interacted with that object, then what we are seeing when we "see a rainbow" is all the raindrops!

So the only real image of the rainbow is the one that is projected onto your retina and which is then processed by your brain. Now since that is just as true for your friend as it is for you, what that means is that each and every person has their own personal rainbow, and she or he is at the center of it!   That is a pretty good analogy for consciousness of the universe.

You'll never see a rainbow as an ellipse, less so as co-axial elliptical bands. If we insist on imagining what it would look like to another observer far to the left of us, it would still not look like the above where the red arc remains on the left edge and the blue arc remains on the right edge. The colors form concentric annular discs, so the red arc should be imagined to stay on the outside edge of the elliptical form, and the blue arc on the inside edge.

B. What is wrong with this picture?

 The three rainbows have three different centers, implying three sources of light! On a planet with three or more spectrally identical suns, this landscape is possible. However, since rainbows are virtual images, they would not obscure one another.

Ignoring the rainbow on the right, non-concentric double rainbows are in principle possible. The lower one (whose center is the shadow of your head and is below the horizon) is the normal one formed by light from the sun refracting and reflecting off the raindrops. The upper rainbow, with its center above the horizon, is formed by sunlight which is first reflected by the body of water in the foreground, and then impinges at an upward angle on the raindrops! The center of the reflection rainbow is where the shadow of your head would appear to be after reflection from (a continuation of) the expanse of water. Because of the landforms, the upper rainbow should be incomplete except where there is water directly below the lower rainbow. What a thought-provoking painting!

Now, just as we can see multiple shadows due to multiple lights, for example at night in an illuminated parking lot, with some luck and lots of practice with a hose spraying water, one might be able to see three rainbows as well. 

C. What is wrong with this picture?

The sun is under the rainbow? Whatever the artist is smoking, I want some! This was seen by some of my readers as being derisive towards the artist. By no means! I really really do want some! A rather prosaic way of achieving the same effect would be to have a filtered mirror in front and just to the side of you while looking at the rainbow. By the way, even if the sun was above the rainbow it would still be wrong. Here is an excerpt from the page of an observant artist : "On a showery day, one may be blessed with the appearance of a rainbow. It is visible in an area of the sky opposite the light source."

D. What is wrong with this picture?

The order of the colors is inverted, as the artist could have ascertained by umm ...  looking. But hey! Why look at nature when you can do an art project? Or go online to check whether it is raining? What I think bothers me here is that young children, even when they see a rainbow, are perhaps missing the time with an adult who could help them look at the rainbow. By which I mean observe and mindfulness, which is a first step towards both science and art.

The angles for the first maximum, or the primary rainbow, are proportional to the wavelength. A rainbow, or anything else with a spectrum, requires dispersion, i.e. wavelength dependence of the relative refractive index of the material of the drops (water) in the atmosphere (air). In water, shorter wavelengths (blue) are dispersed more than longer wavelengths (red). Hence one might expect that red be on the inside and blue be on the outside, as in the above painting.  However, the light is also reflected from the back wall of the droplet and purely due to the geometry of this reflection, the colors cross each other and are inverted. See the wikipedia rainbow article.

E. What is wrong with this picture?

This is more subtle! Again, all the artist need have done is look! From inside to outside, the colors in the secondary rainbow go from red to blue! The secondary rainbow is formed when the light is reflected inside the rainbow twice! This causes the order of the colors to be inverted yet again and back to the original "blue is dispersed more". I'll confess that I haven't figured out the geometry of this, and neither has wikipedia.

F. What is i) right and ii) wrong with this picture?

i) The two rainbows are concentric, and the shadows cast by objects are consistent with the position of the sun. That is, the line joining the observer to the center of the rainbow is parallel to the lines joining objects to their shadows.
ii) However, I would have expected to see the shadow of the artist's head at the geometric center of the rainbow, near the bottom, but by my reckoning within the frame of the painting. This is a minor quibble.

G. In contrast, what is right with this picture?

The order of the colors of the secondary rainbow. An artist actually looked at nature! (Okay, the last sentence is unneccesary.)

G. What are two things wrong with this picture?

First, the only way the rainbow can be seen in front of the background trees is if there is rain or mist between the artist and the trees, which, from the clarity of appearance of the sheep and houses near the "pot-of-gold" point, does not appear to be the case. Second, from the artist's viewpoint one can see close to 180 degrees worth of the rainbow, implying that the sun is at the horizon. This is inconsistent with the rather short length of the children's shadows, which indicate the sun to be about halfway to the zenith, or about 45 degrees above the horizon, in which case the rainbow shouldn't be visible at all! (The sun has to be less than 42 degrees above the horizon, since that is the outer conical angle of the rainbow.)

 SNOWFLAKES: The next time I see non-C6 symmetry snowflakes I'll scream.

Scream 1

Scream 2

Scream 3

The USPS, which tends not to be particularly science friendly, did use actual photos of snowflakes for their stamps.

To which one can only say,
"Naught immortal hand nor eye
  could frame thy C6 symmetry"

Next up: descriptions of nature in Turgenev.