Atmospheric Refraction

The phenomenon of refraction is responsible for our ability to focus images with a lens or our eye. The refraction, or bending of light, depends upon the index of refraction of the transmitting medium. The amount of bending can be very large at the surface of a lens because of its large index of refraction, typically about n= 1.5.

A number of refraction phenomena can be observed in the atmosphere, but the conditions are quite different because the index of refraction of the air is very small, it being a nearly transparent medium. The index of refraction of air at standard temperature and pressure (STP) is n= 1.00029 compared to exactly 1 for a vacuum. The interesting observations of refraction effects in the atmosphere arise from the fact that the index of refraction varies with temperature and pressure, and the fact that distances for observation can be very large so that a small amount of refraction produces observable effects. Refraction leads to bending of the light rays toward the slower medium at an interface, so in air the light will tend to bend toward the area of greater pressure since the light speed decreases with increasing pressure. It will also tend to bend toward the area of lower temperature since the light speed will be slightly lower.

For light coming from outside the Earth's atmosphere, the biggest influence on the light speed is the atmospheric pressure. Incoming light rays from the Sun or stars will be bent downward by refraction toward the Earth. The bending is significant mainly when the light is coming from near the horizon when the light will travel through a long pathway of air. For the Sun near sunset, the refraction will cause the Sun to appear higher in the sky than it is. Because of this refraction, the Sun is actually past the direction tangent to the Earth when you see the big red Sun effect and, on rare occasions, the green flash. Stars near the horizon will likewise appear higher in the sky than they are because of this refraction.

Some of the visible effects of refraction in the atmosphere are mirages, looming, a flattened Sun near the horizon, the green flash, red sunsets, and twinkling of stars

Mirages

Mirages are produced by atmospheric refraction and are mainly seen in settings where there are large variations in the air temperature, such as in deserts or over cold bodies of water. The refraction which occurs near the Earth's surface is mainly due to temperature gradients where the light rays will be bent toward the cooler side of a given interface.

The photograph above was taken on a hot Arizona highway in summer. Refraction bends the light rays from the bright sky upward from the hot surface producing a mirage which has the appearance of a wet surface. Gallant refers to this kind of mirage as a "puddle mirage". The light from the vehicles ahead which moves toward the hot surface is refracted back upward, producing mirage images below the vehicles.

The inferior mirage is produced when light rays from an object approach a hotter region and are refracted away from the hot area. In the desert mirage, the rays approaching the hot surface are turned upward away from the surface. If those upward rays are intercepted by your eye, you see the mirage image appearing below the actual object. Following the pattern of Greenler to demonstrate this kind of mirage, the amounts of curvature shown in the illustration are greatly exaggerated. Such inferior mirages are typically seen from a large distance and the curvatures are much less that those illustrated.

The Vanishing Line

Considering the desert example, the rays from an object will be refracted upward toward the cooler air region. There can be a level on the object such that all rays from points below that level will be refracted over the observer's position. Points below that "vanishing line" on the object will not be seen by the observer. The observer can see both the object above the vanishing line, and corresponding points in the inferior mirage below that level.

The above illustration is patterned after one in Greenler, based on his observations of lakes in northern latitudes. The vanishing line limits the amount of the distant shore line that is visible, and an inferior mirage is exhibited below the vanishing line. The above illustration shows the inferior mirage at the same vertical scale as the object, but that is not necessarily the case. Greenler notes that the inferior mirage is often vertically compressed. With a greater viewing distance, the vanishing line will rise so that less of the object is seen. Greenler notes that with a small change in viewing height, like stooping down, a dramatic change in the vanishing line may occur. Thanks to Travis Finley for photography and discussion of mirages and the nature of mirages of the sky.

Some aspects of the above graphic are hypothetical - that is, I have never seen one like it. But the link above to Atmospheric Optics shows that the refracted light from the sky does refract to make the mirage, replacing the view of the water below the geometrical horizon. As depicted above, the refracted light from the sky matches in brightness and hue the direct light from the sky, which seems unlikely. I would expect a discernable border between the direct view of the sky and the refracted light from the sky. The extent of the mirage of the sky is placed at the extent of the trees in the mirage of the islands, but that extent would presumably depend on the temperature profile of air around the islands.

While it is difficult to anticipate the detailed appearance of a mirage, it does appear that those details arise from the nature of the profile of air temperature vs height. Again making use of the work of Robert Greenler with his permission, consider the proposed set of light pathways leading to one of the interesting sailing ship images from northern seas.

These remarkable sketches of the mirages associated with sailing ships were published by S. Vince, "Observations on an Unusual Refraction of the Air, with Remarks on the Variation to Which the Lower Parts of the Atmosphere Are Sometimes Subject", Philosophical Transactions of the Royal Society of London 89, 436 [1799].

The illustration below, which is redrawn with permission from Greenler, shows how the left hand image above might have been produced by refraction from the vertical variation of the air temperature. An increase in temperature produces a slight decrease in the index of refraction, corresponding to a slight increase in light speed in the air. From a table published by NIST the decrease in the index is from n=1.0002718 at 20°C to 1.000243285 at 50°C. The tiny change in light speed over large distances produces the visible refraction effects.

Superior Images and False Horizons

A superior image can be produced when warm air exists over cold water. Again, using the pattern from Greenler, the vertical scale and the curvature are greatly exaggerated to show the effect. Such images are often seen at great distances in the arctic region when the air is significantly warmer than the water. Since the geometry of the mirage images depends on the details of the temperature contour, a great variety of mirage images can be formed.

The superior mirage may appear as an inverted image above the view of the real object. Examples from the 高级海市蜃楼可能表现为真实物体上方的倒立影像。Gurney旅程中的例子 Gurney Journey

An image like this ship that appears to be floating in midair, from Explorersweb may not be classified as a mirage, but as a missing horizon. The refraction plus reflection and haze may obscure the view of the horizon, although in this case with close examination you can find the subtle horizon. 这种看起来像在空中漂浮的船，可能不被归类为海市蜃楼，而是一个缺失的地平线。折射加上反射和尘雾可能遮挡了地平线的视线，尽管在这种情况下，仔细观察可以发现细微的地平线。

A YouTube video on boats floating in air and another describing the same phenomenon show examples of false horizons. Such superior images are sometimes referred to as "looming" or as fata morganas. Looming may be distinguished from the missing horizon phenomenon by the fact that the water level rises with the ship. Looming is the phenomenon which can allow you to see a distant ship when it is geometrically below the horizon. YouTube上关于船在空中漂浮的视频以及描述相同现象的视频展示了虚假的水平线。这类超现实的图像有时被称为‘隆起’或‘费塔·莫根斯’。隆起可以与缺失水平线现象区分开来，因为水位随着船只的升高而升高。隆起是一种现象，允许你看到一艘在几何学上位于水平线以下的远处船只。

Looming

The looming effect is the result of a superior mirage. A typical example is a mirage of a ship formed over cool water in an area where the temperature increases with height. Refraction bends light down toward the water in this case.

Sailors have long been aware that under the proper conditions they could see a ship which was geometrically over the horizon, just as we can see the red Sun after it has set below the horizon because of atmospheric refraction. They would say that the ship is "looming" over the horizon. Since the visability of this mirage depends upon the details of the temperature contour of the air over the water, there can be great variety in these mirage images. The sailors observed that the mirages were sometimes stretched in the vertical direction, which they called "towering", and were sometimes compressed, which they called "stooping".

There is a rich literature of the varieties of looming mirages, particularly from the Arctic region. Gallant relates some of these stories. Looming mirages may appear to be nearby, and may appear to be greatly magnified (towering). The polar explorer Fridtjof Nansen once nearly shot one of his sled dogs, thinking it was a polar bear because it formed an enlarged mirage. A ship's captain off Newfoundland saw what he thought was a white boat ahead and way about to turn to avoid ramming it, when it flapped its wings and flew away. That is dramatic "towering" when a seagull appears like a boat!

"The crew of a Canadian ship in the Arctic reported the mirage of a sailing ship off in the distance, upside down. The image was so sharp that the crew could make out the ropes in the rigging and could see people moving about on the deck. Two months later, the ships actually met. When the captains compared their ships' logs, they found that at the time of the sighting the two ships had been 80 miles apart!" (Gallant) The suggested explanation for a visible mirage at such a great distance is the observation of light traveling a long distance when a layer of cooler and denser air is sandwiched between two layers of warmer air (a temperature inversion). 一艘加拿大船队在北极地区报告说，他们看到远处一艘帆船的海市蜃楼，而且是倒置的。那张影像非常清晰，船员们能够辨认出桅杆上的绳索，甚至能看到甲板上人们活动的身影。两个月后，两艘船实际上相遇了。当船长们比较各自的航海日志时，发现当时两艘船相距80英里！（Gallant）对于如此远距离可见的海市蜃楼，一个可能的解释是，当一层较冷且密度较大的空气夹在两层较温暖的空气中时，光在长距离传播时产生的现象（温度倒置）。

The ship mirage image above is from a 1799 article by S. Vance titled "Observations on an Unusual Horizontal Refraction of the Air, with Remarks on the Variations to Which the Lower Parts of the Atmosphere Are Sometimes Subject", Philosophical Transactions of the Royal Society of London 89,436.

This illustration of how light can be trapped in a cold layer of the atmosphere is after Robert Greenler. He gives an example of a photograph of the Alaska Range of mountains from the University of Alaska, which is over a hundred miles away.

Looming mirage images have also been called the "fata morgana" (see wiki). "It is an Italian term named after the Arthurian sorceress Morgan le Fay, from a belief that these mirages, often seen in the Strait of Messina, were fairy castles in the air or false land created by her witchcraft to lure sailors to their deaths."

"Morgana (Breton equivalent of sea woman) according to a Celtic legend and Arthurian romance, was a fairy, half-sister of King Arthur, who exhibited her power by the mirage. Italian poets represent her as dwelling in a crystal palace beneath the waves. Hence, presumably, the name Fata Morgana (Italian for Morgan le Fay, or Morgan the fairy) was given, centuries ago, to those complicated mirages that occasionally appear over the strait of Messina ... molding the bluffs and houses on the opposite shore into wondrous castles that, alike, tower into the sky and sink beneath the surface; nor is it strange that this poetical name should have become generic, as it has, for all such multiple mirages, whenever they occur." (Humphreys, W. J., "Physics of the Air", 3rd Ed, Dover, 1940. Reprint 1964, pp 474-5.)

Below are links to posted examples of looming mirages:

Looming Sun mirage 日轮海市蜃楼	Green flash and towering island mirage 绿闪和高岛海市蜃楼	Towering arctic mirage, Alaska 阿拉斯加的高耸极地海市蜃楼	Ships in midair - Wiki 空中船 - 维基

Twinkling

Star twinkling is caused by nonuniformity in the index of refraction caused by turbulence of the air through which the light from the stars travel. Any boundary where the index of refraction changes will experience bending, or refraction, of the light. Stars are so distant that they appear as points of light, so that point of light will appear to dance about as it encounters different "cells" of the atmosphere which have different temperatures and/or densities. Planets are close enough that they appear as disks of light which tend to average the light over multiple cells of the atmosphere and they appear as steadier, even though they are not perceived to be larger than stars by the unaided eye.

Pillars

Sun pillars are caused by reflection from falling ice crystals, unlike the 22° halo and sun dogs which are also associated with such ice crystals, but are refraction phenomena. Ice crystals in the atmosphere often form hexagonal flat crystals. As such crystals fall through the atmosphere and interact with the air, they tend to orient parallel to the Earth, but have enough variation in their angles to reflect a low Sun's rays downward to an observers eyes from various heights. This gives the appearance of a pillar of light in the sky.

Pillars can also produced by the bright lights of a city at night, but those are divergent sources and the light columns are much narrower - like vertical lines of light. Only those ice crystals in a very narrow vertical column from the light source can reflect to a viewer's eyes.

Below are links to posted examples of Sun pillars and other light pillar images:

Astronomy Picture of the Day 天文图片每日	Weather Online 天气在线	Light Pillar wiki 光柱维基	EarthSky 地球天空

Crepuscular Rays

Rays or beams of light may appear to fan out radially from a low sun when the cloud structure is right. The rays from the sun, 93 million miles away, are parallel - but in the setting of the crepuscular rays they appear to diverge because of perspective narrowing over the long path on which they are visible (like the apparent converging of railroad tracks when you look down a long straight track.) Under rare conditions the crepuscular rays extend all the way across the sky and appear to converge back together on the horizon opposite the sun.

This sketch attempts to match the perspective of the image of crepuscular rays over Reno, Nevada below.

Below are links to posted examples of crepuscular rays:

Rays over Reno from Wiki 来自维基的雷诺斯射线	Rays over Plymouth Sound, UK from Wiki UK Plymouth Sound rays from Wiki	Space rays over India, wiki 印度上空的射线，维基	Astro Bob Astro Bob（专名或术语）