The Science of Mirages.

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The more one looks into the circumstances of how these odd lights appear, and the geometry involved with cars on distant roads, the more one thinks of mirages as a possible contributing factor to many of the reports. I have looked at a number of articles about the physics of mirages during April, 2002, and here are some of the interesting facts I have collected about them.

 There are three types; Inferior, Superior and Lateral. The atmospheric optics involved are a bit different.

 INFERIOR MIRAGES: When the ground is warmer than the air just above, the index of refraction is lower near the ground where the air density is lowest. This causes a dely in the wavefront propagating through the cooler air relative to the ground, and the wavefront tilts upwards. As it arrives at the viewer, the viewer sees an image of the object BELOW where the object is located on the local ground. This causes the familiar 'water on the roadway' effect because the light from sky near the horizon is reimaged to a point just below the 'horizon' making the Inferior Mirage.

 SUPERIOR MIRAGES: When the road is colder than the air, an image forms that is ABOVE the actual location of the source. This is called a SUPERIOR MIRAGE and is very common at sea. Spits of land and ships near the horizon are seen ABOVE the water level.

 LATERAL MIRAGES: Both of these mirages involve image displacements that are perpendicular to the the ground. A lateral mirage occurs when a temperature gradient is present in the horizontal direction, as on the side of a building. This causes distortions of objects in 'superior or inferior' orientations relative to the source location in the horizontal direction.


 TEMPERATURE CONDITIONS: Mirages can happen at all times of the year, not just on hot days or under arid conditions. This caught me by surprise, but after numerous observations on the beltway driving to and from work at Goddard, I verified that I have seen 'roadway' mirages even on days when the temperature was near 50 degrees on April 26, 2002 on Ceder Lane. All it takes is the right temperature gradient.

 MIRAGE DISTANCES: The distance to the mirages I have seen while in a car depends on the radius of curvature of the roadway as I crest the peak of the hill. For severely curved roadways like Ceder Lane in Kensington, the distance to the mirages can be about 4 seconds at 30 mph or 4x44 = 176 feet. On the Beltway where the hills are more gradual, the typical distances on 65 degree days is 5s at 60mph or 5x88 = 440 feet. When we drove to Salsbury on Saturday, April 27 where the roadways were very flat with extremely gentle rises, the distances were as much as 15s at 60 mph = 15x88 = 1300 feet. Once the distances become in excess of 1000 feet, oncoming traffic headlights become duplex and with the naked eye you can see the entire roadway to the horizon covered in 'water'. Its very dramatic, but needs a telephoto lens to really study in detail.

 CURIOUS PLAYFULNESS: In the book 'Color and Light in Nature' by Lynch and Livingston (1995 QC355.2 L96) their description of inferior mirages in section 2.24 gives another quality of these mirages. "Everyone is familiar with the sight of shimmering water on a highway, and how that water miraculously 'evaporates' as we approach. Were we to look in the rear view mirror, we could find that the water reappears behind us. " I have seen this as I drive as well.

 NIGHT TIME MIRAGE: In 'Color and Light in Nature' Section 2.25 they mention "Mirages can also occur at night. Before dawn, while driving through a high inter-mountain valley in Colorado, we saw a string of vertical lights which flickered and varied in spacing. A comparison with the full moon allowed us to gauge tha the display subtended less than 1/2 degree. Eventuall we passed the car whose headlights were the probable cause of this superior mirage. Mirages can also occur 1000 feet above the ground.

 ATMOSPHERIC DUCTS: In the book 'Physical Meterology' by John Johnson, (1954 QC861.J67) a more detailed description of atmospheric optics at multi wavelengths including radio, discusses how 'atmospheric ducts' can form in which 'At optical frequencies, complicated ducts may exist near the surface of the ground, leading to extremely complicated optical effects' The author doesn's describe what these might be, but one can imagine by analogy to radio ducts that the possible range of distortions might be considerable. To make a duct, the index of refraction must increase with distance from the road, then decrease again, before resuming its normal adiabat. This causes the light wavefront to bend upwards, then downwards again...possibly several times depending on the horizontal length of the duct. For visible light, the minimum duct thickness can be about 1 centimeter ( Table 1.2 page 23)

  OPTICAL SKIPPING: In "Physical Meterology' by Johnson, page 10, he says that if the gradient is equal to 6.3 degrees per 100 feet, the curvature of the light ray matches the curvature of the earth and a mirage can form from an image that may be well over the horizon. Some spectacular images have been reported from several hundred kilometers. For larger temperature inversions, says Johnson (pg 10) the rays can actually bend back to earth and be reflected from the earth into the atmosphere again. The light ray 'skips' with multiple reflections like a radio signal at the critical frequency of the ionosphere. This would probably cause multiple 'ghost' mirages based on whatever image is 'transmitting' at the skip points on the earth. They would probably arrive at the observer as overlapping images I think. Like a radio receiver picking up multiple radio stations near the same frequency.

 THIN REFLECTION REGION: In 'The Climate Near the Ground' by Rudolf Geiger (1965, QC861.G31) says that when the lapse rate is -3.42 degrees/100 meters, the density of air is constant with height and no mirages occur. If the lapse rate is more negative than this which happens when the surface is warmer than the air relative to the normal lapse rate, then you get inferior mirages due to atmospheric refraction. (p135). This causes the apparent horizon to bent upwards relative to the actual horizon. The region over which most mirage images are formed may be only a few centimeters thick above the ground, and that is why roadway mirages seem so thin in the vertical direction. This is also why wind and traffic do not disturb the mirage-creating region. (p. 138) and he quotes S. E. Ashmore's work as saying that mirages can be observed anytime during the year so long as snow and water backsplash do not interfere. Also, the height of the layer of air causing a roadway mirage is about 18 millimeters.

 WEIRD IMAGES: In the book 'Pagentry of the Sky' (QC 863.O75) page 115, the author notes; Mirages 'may transmit the lights of a city far beyond the horizon. They have been known even to reflect weird, zigzagging images of light that were nothing more than the headlights of an automobile winding up a moluntaneous road.' They may also explain some UFO accounts.

 HORIZON DISTANCE: In 'Physics of the Air', by W. Humphreya (1964, QC ...), Gives formula for calculating the distance to the horizon for various observer elevations. For an evelation of 1.6 meters, the distance is 5 kilometers! (p. 469). The formula is h = 6366000(sec(a) -1) - 36286200 (sec(a/5.7) -1)sec(a) where r = 6366a and a is in radians. h is the observers height. the units of r are in kilometrs and h is in meters.

 ROADWAY MIRAGES: In 'Light and Color in the Outdoors' by Len Seymore (1993). P.66 Discusses inferior roadway mirages over asphalt roads. 'The thermometer shows a fall in temperature of as much as 20 or 30 degrees in the first centimeter above the surface, after which the fall becomes a few degrees per centimeter. 'My experience is that the mirage is still finer above concrete roads'.

 VIEWING ANGLE: The viewing angle to a mirage is very sensitive and generally it is only a few degrees to the horizontal. For example, on our roadtrip to Hebron MD, I saw mirages about 1300 feet ahead of me at their nearest edge and my eyes were about 3 feet above the roadway inside the car. This angle is only about 8 arcminutes! On Ceder Lane where I was seeing mirages 170 feet ahead, the angle is a bit larger at 1 degree, so my experience is that you need angles less than 1 degree to the local horizon to see them.

 NIGHT TIME MIRAGES: There may be a critical sun angle involved in roadway mirages .The 1955 article by S. E. Ashmore (Weather, vol 10 p. 336) describes in great detail the 'Wrexham Road mirage' which he observed from mid-February to October 30, and during very strong wind conditions. Once the sun had reached an angle of 24.5 degrees the mirage would materialize, and dissappear once the sun sank below this angle in the afternoon. 'Once the required temperature gradient is established it persists for a long time in the absense of insolation. In the evening the mirage is often visible until darkness makesfurther observation impossible, and at night experiments have been performed using a bicycle lamp placed on the site of objects seen in the daytime mirage, and the effect was beautiful in the surrounding darkness. This has been done up to 4 hours after sunset. On 4 October 1953, I observed the same effect by chance near Trefnant, where a road lamp gave the source of light, and a mirage of it was seen at 20:30 almost 3 hours after sunset. The dry bulb about a quarter of an hour before was 42 degrees F and the temperature on the grass was 33degrees F. I believe that is a hot summer day is followed by a cloudy night which enables the daytime temperature gradient to persist long enough, the Wrexham mirage may last all night"