Corona Formation

Corona Formation: Exploring the Phenomenon of Light Diffraction

Have you ever marveled at the beautiful rings of light that appear around the Sun or Moon during certain atmospheric conditions? This captivating optical phenomenon is known as a corona. In this article, we will delve into the intricacies of corona formation and explore the underlying principles of light diffraction that give rise to this awe-inspiring spectacle.

Unraveling the Science Behind Corona Formation

Coronas are formed when light is diffracted by small particles in the atmosphere, such as droplets, ice crystals, pollen grains, or dust particles. Each point on the surface of these particles acts as a source of scattered outgoing spherical waves, according to the Huygens-Fresnel Principle. These waves interfere with each other, resulting in regions of enhanced brilliance (constructive interference) and darkness (destructive interference).

To understand the formation of coronas, let's consider the scattering of light by a droplet. When light interacts with a droplet, it scatters from multiple points on the droplet's surface. The scattered waves overlap and interfere, leading to an intricate diffraction pattern - a corona. The intensity of the light varies depending on the coincidence or cancellation of wave crests.

The Delicate Dance of Light Waves

As we move away from the central axis, which aligns with the incident light direction, we observe a fascinating play of light and darkness. In specific directions, the wave crests coincide, resulting in beams of enhanced brightness at an angle to the incident light. Conversely, in other directions, the crests of one wave coincide with those of opposite amplitude of another wave, leading to cancellation and darkness.

This alternation between bright and dark regions continues as we increase the angular distance from the axis, creating a mesmerizing diffraction pattern. It is important to note that this phenomenon arises not only from scattering at two points on the droplet's surface but also from the combined effects of scattering, reflection, and transmission throughout the particle.

The Role of Droplet Size, Shape, and Light Wavelength

Corona formation primarily depends on the size, shape, and light wavelength interacting with the droplet. Surprisingly, the interior of the droplet plays a minimal role in corona formation, as the surface-scattered waves predominate. This means that whether the droplet is transparent or opaque, and regardless of its composition, be it water, ink, or coal, the resulting corona pattern remains similar.

Furthermore, coronas are not limited to spherical droplets alone. They can also form around small ice crystals, pollen grains, and large dust particles. The ability of various particles to produce coronae highlights the universal nature of this captivating optical phenomenon.

The Kaleidoscope of Colors in White Light Coronas

When it comes to coronas, white light reveals its true colors. A white light corona is the sum of all the contributions from each spectral color. This amalgamation creates a stunning display of vibrant hues encircling the central region of enhanced brightness. The presence of multiple colors further enhances the visual appeal of coronas and adds to their allure.

The Intricate Balance: Spacing and Size Uniformity

Contrary to what one might expect, the spacing between cloud particles does not significantly affect corona formation. Even though cloud particles are typically separated by 50 or more diameters, mutual interference occurs only when droplets are closer than two diameters. Thus, for a corona to form, each light ray reaching the observer's eye must have been scattered by a single droplet.

To observe a sharp corona with distinct rings, it is crucial that the cloud droplets are of similar size. If the droplets vary significantly in size, the resulting coronae from different droplets may merge, leading to a blurred appearance rather than a well-defined corona with multiple rings.

Surprising Connections: From Droplets to Telescopes

Interestingly, the principles governing corona formation find unexpected parallels in other areas of physics. The diffraction pattern observed from a droplet is remarkably similar to that produced by an opaque disc. This similarity extends further to the diffraction pattern generated by a circular aperture of the same diameter, as revealed by Babinet's principle.

Intriguingly, when we look at a star through a telescope, we may observe a corona surrounding the small disk-like image of the star. This corona corresponds to a 'droplet' with dimensions similar to the telescope objective. The magnification provided by the telescope optics allows us to witness the corona in greater detail, with larger telescopes yielding sharper, point-like stars and smaller droplets producing more extensive coronae.

Embracing the Wonders of Corona Formation

Coronas are undoubtedly one of nature's most captivating displays, offering a glimpse into the fascinating world of light diffraction. Whether we encounter these ethereal rings around the Sun, Moon, or even artificial light sources, understanding the underlying principles enriches our appreciation of this enchanting atmospheric optics phenomenon.

Next time you find yourself gazing at a corona, take a moment to ponder the intricate dance of light waves, the delicate balance of droplet size and spacing, and the surprising connections between droplets and telescopes. Let the beauty of coronas inspire awe and curiosity as you delve into the wonders of our atmospheric optics.

Light diffracted by a droplet.

The diagram illustrates how two points on a droplet surface can scatter light and act as sources of outgoing spherical waves.

The scattered waves overlap and interfere.

Where wave crests of the same sign coincide the light intensity is increased. Where the waves have opposite amplitudes they destructively interfere to give low intensity.

Scattered light from the whole droplet surface plus smaller contributions from reflected and transmitted waves combine to form a diffraction pattern - a corona

A corona is produced by small particles diffracting light. Every point on the particle's illuminated surface is a source of scattered outgoing spherical waves ( Huygens-Fresnel Principle ). These waves mutually interfere to give regions of enhanced brilliance, constructive interference, and darkness destructive interference. ( Interference or Diffraction? )

Scattering from only two points is shown on the diagram. Along the central axis, the incident light direction, the crests of the two scattered waves always coincide to form a region where the light is strong.

Moving away from the axis, there is a direction where the crests again coincide to give beams of enhanced brightness at an angle to the incident light. In between there is a region where crests of one wave coincide with those of opposite amplitude of the other. The two waves cancel and there is darkness in those directions.

There is a another coincidence of wave crests at a larger angle and the light intensity is again enhanced. With increasing angular distance from the axis there are alternating bright and dark regions, a diffraction pattern.

In reality, light is scattered from all around the droplet periphery and other low intensity waves arise from reflection and transmission through the particle. The net wave amplitude at any point is the sum of the amplitude vectors, not intensities, of all the individual waves. The result is a very bright central region surrounded by less bright rings, a corona.

Corona formation, to a good approximation, needs no knowledge of the droplet interior because the surface scattered waves predominate. It could be water, ink or coal - the pattern is almost the same. It depends primarily on the droplet size, shape and the wavelength of the light.

There is no need for the droplet to be transparent nor even spherical. Small ice crystals, pollen grains and large dust particles all form coronae.

A white light corona is the sum of all the coronae contributions from each spectral colour.

The spacing of the cloud particles does not matter. Cloud particles are separated by 50 or more diameters and mutual interference as in a diffraction grating only takes place if the droplets are closer than two diameters as in condensation on a window pane. A corona is produced when each light ray reaching the eye has been scattered by a single droplet.

If the corona is to be sharp with many rings, the cloud droplets must all be of similar size otherwise all the different size coronae produced by the droplets produce merely a blur.

The solution of one physics problem is often the solution of another one apparently quite unrelated. The diffraction pattern from a droplet is almost the same as that from an opaque disc. In turn, the diffraction pattern from a disc is the same as that from a circular aperture of the same diameter (Babinet's principle). A telescope lens or mirror is just such an an aperture. A star seen through a telescope is a small disk surrounded (if the lens is good and the air steady) by one or two delicate rings. This is a corona, one for a 'droplet' the size of the telescope objective and only visible because it is magnified a few hundred times by the telescope optics, but a corona nonetheless. Large telescopes make sharp point-like stars. Small droplets make large coronae.

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Reference Atmospheric Optics

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