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Briefly explain the process of mirage formation

 A traveler has lost his way in the desert. Enduring thirst and hunger, he suddenly saw an oasis, so the overjoyed man quickly ran towards it. To his great disappointment, it was just an illusion produced by a mirage. Such an episode was often pictured in movies, yet the optical magic that the nature plays with us - mirage - really exists in reality. Its formation is a result of the refraction and the total internal reflection of light in the air. 

To investigate the formation of a mirage, we firstly need to understand why light is refracted in the air. Regions of air at different temperatures have different refractive indexes, just like many different mediums. The closer the air is to the ground, the hotter it will be, and its refractive index will be smaller. We could imagine the air as many layers of medium with a particular refractive index for every layer, and the refractive index is smaller for those that are closer to the ground. Thus when light travels in air, its path is as shown in Fig.1. 

On the other hand, we should also understand what total internal reflection is. If light travels from glass to the air with a small incident angle, part of the light will be reflected back while the remaining part will be refracted, passing out from the glass. As the refractive index of glass is larger than that of the air, the refracted angle is always larger than the incident angle (Fig. 2). When the incident angle becomes larger, the refracted light will get closer and closer to the interface between the air and the glass. When it is larger than the critical angle, the light will only be reflected but not refracted. This phenomenon is called total internal reflection (Fig. 3). 

Fig. 4 shows the path of light when a mirage happens. Suppose there is an oasis and the light it emits at point A is refracted by the air, the light will travel through a curved path. Total internal reflection occurs at point B and will cause the light to travel upwards. Then the light is refracted by the air again. At last, it will enter the eyes of the observer at point C, producing an illusion that the oasis is close to him. 

Total internal reflection has been discovered for a long time already. Some of its broad applications include optical fibre, single lens reflex camera and binocular telescope.

Fig. 4  The path of light when a mirage happens.

 

Fig. 2 Refraction occurs when a light beam travels from glass to the air. The angle of incidence i is smaller than the angle of refraction r.

Fig. 3 Total internal reflection occurs when the incident angle i is larger than the critical angle c.

Fig. 1 In regions of air with temperature decreases with altitude, light will travel in a curved path due to refraction.

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Driving down the highway on a recent hot day, I saw the pavement ahead of me appeared to be covered with water. I never ever reached that wet pavement because what I observed was a true mirage commonly known today as a highway mirage.

Before highways spider-webbed the national landscape, people would likely have called such a sight a desert mirage. By either name, the vision is an example of a mirage type known as the inferior mirage. The adjective inferior refers to the position of the perceived image in relation to the actual position of the object -- seen below or inferior to it -- rather than a commentary on the mirage's quality. An inferior mirage may be either a normal or an inverted image of the original and greatly distorted.

The term mirage generally conjures up images of thirsty, lost cowboys or French Legionnaires crawling across desert sands toward pools of "cool, clear water" to quote a popular country/western song. Many believe mirages to be delusions of an overstressed mind, a pure figment of the imagination, but the mirage is a real image that can be photographed. They are optical illusions, images seen by our eyes but incorrectly interpreted by our mind. What our mind interprets as "water" are actually images formed by light rays from clouds and blue sky above and ahead of us that are refracted by large variations in air density near the surface. Since these rays are bent upward toward our eyes, our brain interprets them as having come up from the ground.

Inferior mirages form when light rays passing through a relatively hot layer of air are bent or refracted upward from their descending straight-line path. [Note: many references incorrectly call mirages reflected images.] In general, when light waves travel from one medium into another, they are bent from their straight-line path to a degree and direction that depends on the density difference between the two media. Refractions in the atmosphere occur whenever light passes through air layers of different densities. Light rays traveling through air layers of differing temperature will bend toward the colder air.

Strong solar heating usually produces large air density variations near the surface. Highway mirages will form when the air near the ground is much hotter than that above it -- the hotter the air, the greater the effect. To give some idea of how much hotter the air can be above a paved road in the full sun, measurements have shown surface temperatures 11 to 17 C degrees (20-30 F degrees) hotter than the temperature measured 1 cm (less than half an inch) above the surface. The most important factor for inferior mirage formation is the temperature difference between surface air layers rather than their absolute temperatures. Thus, highway mirages can be as commonly seen over dry pavement on sunny winter days as during the summer months.

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In deserts and in hot climate, the air near the ground becomes more hotter than air at higher levels.The refractive index of air increases with its density.Hotter air is less dense, and has and has small refractive index than cooler air.If the air currents are small,that is the air is still,the optical density of different layers of air increases with height.As a result, light from a tall object such as a tree, passes through a medium whose refractive index decreases toward the ground. thus, a ray of light from such an object successively bends away from the normal and undergoes total internal reflection, if the angle of incidence of air near the ground exceeds the critical angle. To a distant observer, the light appears to be from somewhere below the ground.the observer naturally assumes that light is being reflected from the ground, say, by a pool of water near the tall object. Such inverted image of distant tall objects cause an optical illusion to the observer. This phenomenon is calledMirage..

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In deserts and in hot climate, the air near the ground becomes more hotter than air at higher levels.The refractive index of air increases with its density.Hotter air is less dense, and has and has small refractive index than cooler air.If the air currents are small,that is the air is still,the optical density of different layers of air increases with height.As a result, light from a tall object such as a tree, passes through a medium whose refractive index decreases toward the ground. thus, a ray of light from such an object successively bends away from the normal and undergoes total internal reflection, if the angle of incidence of air near the ground exceeds the critical angle. To a distant observer, the light appears to be from somewhere below the ground.the observer naturally assumes that light is being reflected from the ground, say, by a pool of water near the tall object. Such inverted image of distant tall objects cause an optical illusion to the observer. This phenomenon is calledMirage..

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IT IS AN EXAMPLE OF OPTICAL PHENOMENA
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