The rainbow that appears in the sky after rain is an optical phenomenon. It is caused by the refraction, internal reflection, and scattering of light in water droplets, resulting in a continuous band of colors across the sky. A rainbow appears as a circular arc with multiple colors. A rainbow formed by sunlight always appears in the sky directly opposite the sun. Rainbows can also be formed by various forms of water in the air, including not only rain, but also mist, spray, and dew.
A rainbow can be a complete circle. However, usually, a person can only see a portion of the rainbow, appearing above the ground and centered along the line connecting the observer's eye to the sun.
In a primary rainbow, the outer edge of the arc appears red, and the inner edge appears violet. This rainbow is formed when light enters a water droplet, refracts, is internally reflected off the back of the droplet, and then refracts again upon exiting.
In a secondary rainbow, a second arc appears outside the primary arc, and its color sequence is reversed, with the inner edge being red. This occurs because the light is reflected twice inside the droplet before exiting.
Rainbow visibility
A rainbow appears when water droplets are present in the air and sunlight shines on them from a low angle behind the observer. Therefore, rainbows are usually seen in the west in the morning and in the east in the evening. The most beautiful rainbows occur when half the sky is covered with rain clouds and the observer is facing away from the sun. This creates a bright rainbow against a dark background. Often, a larger but fainter secondary rainbow also appears. It is located about 10° outside the primary rainbow and has its colors in reverse order.
This rainbow effect is also common near waterfalls or fountains. Additionally, this effect can be artificially created by spraying water droplets into the air on a sunny day. On a moonlit night, a lunar or night rainbow sometimes appears. In low light, humans see fewer colors, so lunar rainbows often appear white.
Capturing the entire rainbow in a single frame is difficult, as it requires a 84° viewing angle. For a 35mm camera, this requires a wide-angle lens with a focal length of 19mm or less. However, software that combines multiple overlapping images to create panoramas now makes it easier to capture the entire rainbow and secondary arc.
From above the Earth, such as from an airplane, a rainbow sometimes appears as a complete circle. This can resemble the glory phenomenon, but the glory is usually much smaller, only 5-20°. The sky inside the primary rainbow is brighter than the sky outside. This is because each water droplet is spherical and scatters light across a complete circular disc in the sky. The radius of this disc depends on the wavelength of light; red light scatters at a larger angle than blue light. Across most of the disk, the scattered light of all wavelengths combines to produce the white light that illuminates the sky. At the edge of the disk, the varying wavelengths of the scattered light create the colors of the rainbow.
The light from the primary rainbow is 96% polarized, with the polarization direction parallel to the tangent of the arc. The light from the secondary arc is 90% polarized.
The number of colors in a spectrum or rainbow
For the colors visible to the human eye, the most common and memorable sequence is Isaac Newton's seven-color system—red, orange, yellow, green, blue, indigo, and violet. To remember this sequence, one can use the mnemonic phrase "Richard of York Gave Battle in Vain" or the name of a fictional character (Roy G. Biv). This sequence is sometimes reversed and referred to as VIBGYOR. These days, rainbows are often described as having seven colors: red, orange, yellow, green, cyan, blue, and violet. The distinct categorization of primary colors is a characteristic of human perception, and the precise number of primary colors is somewhat arbitrary.
Newton, who believed his own eyesight was not particularly good at distinguishing colors, originally (in 1672) divided the spectrum into five primary colors: red, yellow, green, blue, and violet. He later added orange and indigo, resulting in seven primary colors, matching the number of notes in a musical scale. Newton's decision to divide the visible spectrum into seven colors was based on the beliefs of ancient Greek philosophers, who believed in a connection between colors, musical notes, the known objects in the solar system, and the days of the week. Scholars have noted that the color Newton called "blue" at that time is now called cyan, and "indigo" is now called blue.
The color pattern of a rainbow seen after rain differs from the spectrum, and its colors are less vibrant. Spectral blurring in a rainbow occurs because there is a distribution of exit angles for a given wavelength, rather than a single, fixed angle. Furthermore, a rainbow is a blurred version of a rainbow formed from a point source, since the angular size of the sun (0.5 degrees) is not negligible compared to the width of the rainbow (2 degrees). Therefore, the number of colors in a rainbow can differ from the number of colors in the spectrum, especially if the raindrops are very large or small. Thus, the number of colors in a rainbow varies. However, if the term "rainbow" is used incorrectly to refer to the spectrum, it generally means the number of primary colors in the spectrum.
Besides the red and violet bands, a rainbow also contains bands in the near-infrared and ultraviolet regions, although these bands are not visible to humans. The rainbow only includes frequencies near the visible spectrum because water and air become more transparent to these frequencies, causing the light to scatter. The UV band can sometimes be seen with a camera using black and white film.
The question of whether everyone sees seven colors in a rainbow is related to the theory of linguistic relativity. It has been suggested that there is a universal way of perceiving a rainbow. However, recent research suggests that the number of distinct colors perceived and their names depend on the language used; people who speak languages with fewer color terms perceive fewer distinct colors.
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