Buddha's fingers. Sun drawing water. Ropes of Maui.
These phrases are descriptions of the same phenomenon, crepuscular rays. The image above is an example of what crepuscular rays look like-- beams of sunlight radiating from the sun. Why do they form? Why do they appear to diverge from the sun? The answers to these questions originate in two processes: a physical process called scattering and an optical process called perspective.
A key component for crepuscular rays is a shadow. This shadow can be cast by almost anything-- clouds, a row of trees, or, a window. The result is sunlight broken into darkened areas in the shadow and lighted areas outside. Put simply, the object has forged beams of light.
However, these sunbeams are not visible without aid. Their light needs particles to reflect off of, or scatter, to our eyes. If you have ever driven a car with its lights on during a cloudy day, you may have noticed this- the road itself and street signs are brighter, but the volume of air in front of car does not seem to be more lighted. If, for example, you then drove through an area of dust or fog, you would be able to observe the light scattering off the particles of dust or water droplets, forming a bright cone emanating from each lamp. In the first instance, there were not enough particles for appreciable amounts of the light of the headlights to return to you eyes. But, once a higher concentration of particles was in front of the lamps, the increased scattering became apparent.
Many different particles can act as scatterers. Snow, rain, and dust are all capable of scattering light. In addition, the atmosphere itself can scatter enough light to see the sunbeams by way of Rayleigh scattering. Whatever the method of scattering, the visible beams will appear to diverge from the sun and spread out over a portion of the sky. You will notice in the above image that the rays appear to converge to a point in the lower right-hand corner. Also note from the image that the rays become less apparent the farther they are from the solar point. In fact, the upper left-hand portion of the image is free of rays. Once the rays become visible, contrast between the rays and shadows make them more apparent.
Given that crepuscular rays arise from virtually parallel rays of sunlight that are partially blocked by an object, it may seem counterintuitive that they appear to diverge from the solar point. However, a brief lesson in perspective will shed light on the nature of the path of sunbeams.
Gauging physical size and distance of objects is a process that involves seeing an object with our eyes and letting our brain do the processing. The brain can only process the angular size of an object; how large (in some angular measure) is it in our field of view. Sure, we have experience to guide our minds in making decisions about the physical size of an object, but the use of that experience can be easily in error.
To illustrate this point, imagine you are standing on a set of railroad tracks. To one side of the tracks are regularly spaced telephone poles. Both the tracks and the line of poles are following a straight path and are visible to the horizon. Although you know that the tracks are the same width where you are standing as they are at the horizon, the farther away they are, the smaller they seem. Also, the telephone poles seem to be shrinking as they approach the horizon. What's happening here?
Let's look at a scene containing crepuscular rays from a geometric perspective.
Figure 1 is a simplified version of the railroad setting viewed from above. Points A and B are arbitrary distances away from you, while line H is the horizon. As you can see, angle a' is smaller than that of b'. Thus, you see the tie at A as being smaller than the one at B.
Figure 2 depicts the same scene, but viewed from the side. This helps determine the relative placement of the objects in your field of view. The angle of declination to point A is smaller than the corresponding angle to point B. In addition, the angle of declination of the horizon, h', is almost zero. Thus, the tie at point B will be below the tie at point A with both ties lying below the horizon line.
Applying similar logic to the telephone poles, it is deduced that the farther away a pole is, the smaller its angular size.
Utilizing the information from Figures 1 and 2, a basic view of what you would see by looking down the tracks toward the horizon can be constructed; Figure 3 is the result of this construction. The light grey lines represent the railroad tracks, with the location of points A and B noted. Lines K and J are imaginary constructs connecting the tops of the poles and the bottom of the poles. Notice here that the scene has four parallel lines extending to the horizon, yet these same lines converge to a single point, indicated by point X; a point commonly
called the vanishing point. This optical process, called perspective, is why crepuscular rays appear to diverge.
If you look at the image above, you notice that all the rays appear to extend upward and outward from the sun-- just like the tops of the poles in Figure 3 extend upward and outward from Point X. However, since we know all rays are virtually parallel and they extend from the sun to your eyes, they must be descending in altitude the closer they become to you. It is just perspective that makes them seem to ascend.
We interact with scattering and perception in many facets of our lives. Even when we understand them in depth, when they come together in crespuscular rays, they still can produce awe-inspiring results.