With water, dish-washing detergent and a laser pointer—the kind used in presentations—the married physicists Adriana and Alberto Tufaile have developed an experimental model and provided a new explanation for a natural phenomenon that has fascinated mankind for at least 2300 years, since Aristotle’s time: the appearance of a set of luminous patterns around the Sun, scientifically known as the parhelia. In cold regions, sunlight interacts with small ice crystals suspended in the atmosphere and, under certain conditions, gives rise to pairs of bright spots (also known as mock suns or sun dogs), a halo (parhelic circle) and straight lines (sun pillars) around the Sun. On even rarer occasions, these formations also occur around the moon.
In 2013, the pair of professors in the Soft Matter Laboratory of the University of São Paulo (USP) School of Arts, Sciences and Humanities, on the East Campus, carried out tests involving light scattering in soap bubbles, one of their fields of research, when they noticed the same patterns projected on the background of the experiment. “We had no idea what it could be,” says Alberto. “We did extensive research and the only similar phenomenon was solar parhelia, which we had not known about previously.” The discovery was reported in an article published on December 9, 2014 in the electronic version of the journal Physics Letters A. “Before, explanations for the atmospheric phenomenon depended only on geometric optics, in which light is treated as a particle and obeys Newton’s laws,” states Adriana. “Our study, however, suggests that the parhelic circle is principally due to the wave nature of light.”
Figures practically analogous to the bright spots, straight lines and circle that form around the Sun were observed in the laboratory when the physicists illuminated the Plateau border—the intersection of three thin films in detergent bubbles—with a laser beam. The region of the intersection bears this name in honor of the Belgian physicist Joseph Plateau. In the 19th century he observed that bubbles always meet in threes and form a sort of corner that sustains their tenuous walls. Changing the angle of incidence of light on the Plateau border, formed inside a closed acrylic box (a Hele-Shaw cell) containing a water-detergent solution, Adriana and Alberto noted that more or fewer shapes appeared, of different sizes and with different degrees of sharpness. Intrigued by the light pattern generated by the laser in the experiment done at USP’s East Campus, Adriana decided one day to try to reproduce the experiment at home. She placed soapy water in a saucer, stirred the mixture to form bubbles and pointed a laser pointer at a Plateau border, where three soap films meet. The same thing happened: the bright spots, lines and circle appeared on the wall at home. “In an open environment the Plateau border breaks down faster,” explains the physicist. “That is why we use a Hele-Shaw cell.”
One of the keys to understanding the similarity between the two phenomena—atmospheric and in soap bubbles—is linked to the extremely similar symmetry of snow crystals and Plateau borders, according to the couple from USP, whose studies are part of the National Institute for Complex Fluid Science and Technology (INCT-FCx), funded by FAPESP and the National Council for Scientific and Technological Development (CNPq). The crystals have a hexagonal shape and the borders are triangular. These two geometrical figures have a close relationship: a regular hexagon can also be seen as the junction of six equilateral triangles. Therefore, when striking these two structures, sunlight or laser light is scattered according to the same principle. “It is very difficult to study the formation of images in this rare atmospheric phenomenon in detail,” explains Alberto. “And capturing the ice crystals involved in the phenomenon is practically impossible.” Having identified an analog of Sun parhelia in their experiments with detergent bubbles and a laser, the researchers decided to do an in-depth investigation of the mechanism behind the formation of this pattern of bright images.
After repeating the experiment several times in the laboratory, including using three different-colored lasers (green, blue and red) to make sure that the wavelength of light does not change the result, and studying the scientific literature on the atmospheric phenomenon, Adriana and Alberto came to the conclusion that the explanation for the figures was essentially based on the wave nature of light. More specifically, they believe that as the light strikes the junction of the three soap bubbles, the laser beam scatters light through two similar processes, interference and diffraction, especially the latter. Diffraction is a phenomenon seen in the propagation of different types of waves, such as sound, electromagnetic and even water waves. It occurs when sound or light encounters an obstacle or a tiny slit approximately the same size as its wavelength and the interaction changes its angle of propagation. The result of diffraction is to shift the path of the beam of waves or how it is scattered. The phenomenon is easier to measure when created using sound waves, which are larger than those of visible light.
In the case of a laser illuminating soap bubbles, the beam of light strikes the Plateau border, a region a few nanometers in length forming a small triangular tube capable of scattering light. The light reaches the junction of the three bubbles in the form of a single straight, focused laser beam. After striking the thin obstacle, it becomes a series of weaker, thinner beams that form the light pattern associated with the phenomenon. One part of the initial laser beam passes in a practically straight line through the border and causes a brighter spot to appear on the white background behind the experiment. It corresponds to the Sun seen in the atmospheric version of the phenomenon. The light from this spot is reflected in the soap bubbles and produces two or four mirror images that are fainter than the original, known as mock suns in the celestial version. “Note that these bright spots always form on a line delimiting a circle,” states Adriana.
Up to this point, the Brazilian duo’s explanation is roughly equivalent to how other researchers account for solar parhelia. Their contribution is unique because they introduce the issue of light diffraction caused by thin soap films. There are usually three straight lines cutting through the principal spot—the “original Sun”—that result from diffraction of the part of the light that strikes the triangular structure of the Plateau border. It is as if the walls of each of the three bubbles squished against each other give rise to a straight line. In order to obtain the halo of the phenomenon, an extra requirement must be met: the laser must strike the Plateau border obliquely. Thus another fraction of the diffracted light wave scatters in a conical shape, forming a perfect circle. “Our explanation is simpler than that of other theories that use only reflection and refraction of light, not its wave nature, to explain the atmospheric phenomenon,” says Alberto.
This celestial event—the Sun and its fainter replicas—has fascinated man for some time, according to written records and even pictorial representations. In the 4th Century Aristotle referred to this type of event in his text Meteorologica. Regarded as the first representation of Stockholm, the painting Vädersolstavlan, from 1535, portrays the complete phenomenon in the skies over the Swedish capital. Later, in the 16th century, the English playwright William Shakespeare mentions solar parhelia in the play Henry VI, Part 3. The Frenchman René Descartes went to Rome in 1629 to see the phenomenon and also wrote about it. In some periods, certain cultures associated the occurrence of solar parhelia with impending war. When Adriana and Alberto saw the laser and soap bubble version of the phenomenon in their laboratory on the USP East campus, they realized that they had found an interesting—and ancient—research topic.
National Institute of Science and Technology for Complex Fluids (NICT-FCx) (No. 2008/57685-7); Grant Mechanism Thematic Project; Principal investigator Antônio Martins Figueiredo Neto (IF-USP); Investment (in the INCT) 2,522,238.07 (FAPESP) and 2.5 million (CNPq).
TUFAILE, A. and TUFAILE, A. P. B. Parhelic-like circle from light scattering in Plateau borders. Physics Letters A. Dec. 4, 2014