Figure 1. On the left, a ship appears to be floating in the sky above the sea (Source: Colin McCallum, Facebook Post Capture). On the right, it looks like there is water on the road on a hot day (Source: Broken Inner Glory, Wikimedia Commons)
Recently, it was a hot topic in the UK when a ship was seen floating in the air above the sea. However, there is virtually no possibility that a ship of this size would actually be in the air above the sea. Although it looks like this, the phenomenon in which there is no substance in the visible position is called a’miracle’. When driving on a highway on a hot day, there are times when the road in the distance is covered with water, and the surrounding landscape appears to be reflected in the water. This is also a kind of mirage. Why does this happen? It is a phenomenon that occurs because light bends or bends at the boundary of a material.
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How a mirage is created
In an empty vacuum, light flies the fastest at 300,000 kilometers per second. The speed of light in air is slightly slower than this. In water, the speed of light slows by 25%, 225,000 km/sec, and in glass, it slows by 33% to 200,000 km/sec. Light breaks at the interface where two materials with different speeds of light meet. This is called Snell’s law. For example, light breaks on the water surface, which is the interface between water and air, or the glass surface, which is the interface between glass and air. There is a simple experiment to check the phenomenon of the light being bent. Prepare two identical cups, and put a coin in each cup. Leave one cup as it is, and fill the other with water. Looking down from above, you can see the coins in both cups. (Picture 2, above picture) If you change the viewing position from the top of the cup to the side of the cup, the rim of the cup begins to cover the coins from the cup without water. Then, the coins in the cup without water are completely covered by the rim of the cup, and the coins in the cup filled with water can be found at the viewing angle. (Middle picture of’Picture 2′) In a cup without water, the light that starts from the coin at the bottom of the cup and goes to the eyes passes through only the same air, so it is straight. Looking at the picture in the middle of’Picture 2′, in the case of the left cup, the light path from the coin to the eye is blocked by the frame of the cup, so you cannot see the coin. On the other hand, in the case of a cup filled with water, coins are visible even when viewed from the same angle. Looking at the path of light coming from the coin to the eye, the light passes in a more upward direction in the water, and then the light breaks from the surface of the water and goes to the eye. (Blue solid line in the right picture below’Picture 2′) The light from the coin bypasses the border and is seen as the light touches the eye. Without water, it should be invisible, but it is visible, so it looks like a coin is floating in the middle of the water. However, the actual coin is at the bottom of the cup, so there is no coin where the coin can be seen. It appears to be where it shouldn’t be. When comparing the left cup without water and the right cup filled with water in the picture in the middle of’Figure 2′, the bottom of the cup filled with water and the coin appear as if they are in the middle of the cup.
Figure 2. Top: A coin was put in the right cup without water, and the left cup was filled with water and a coin was put. Center: When viewed from the side at an appropriate angle, the coins in the cup without water are not visible, only the coins in the cup filled with water are visible. In a cup without water, the rim of the cup is covered and coins are not visible, but in a cup filled with water, the light breaks from the surface of the water, bypassing the rim of the cup and reaching the eye. Compared to the waterless cup on the left, the coin appears to be in the middle of the cup. Bottom: A picture showing the path of light when looking at a cup without water and a cup with water. The blue solid line indicates the direction of the light, and the red dotted line indicates the visible position of the coin recognized by the brain.
It is a similar phenomenon that the ship appears to be floating in the air above the sea. For this to occur, a material with a relatively slow speed of light, such as a cup filled with water, must be located on the bottom, and a material with a relatively high speed of light must be on the top. The difference from looking at a coin in a cup full of water is that there must be layers of different speeds of light only with air. This is because the ship is floating rather than submerged. In other words, the layer of air with the slower speed of light must be at the bottom and the layer of air with the speed of light must be above. When the air pressure is high and the air is cold, the air becomes more dense and the speed of light is slightly slower. Conversely, when the air pressure is low and the air is warm, the density of the air decreases and the speed of light increases slightly, making it closer to the speed of light in a vacuum. Thus, when cold air is placed under high pressure and hot air is above low pressure, a situation similar to a cup filled with water is created. It creates a condition in which a distant ship can be seen from a higher position than it actually is. The phenomenon that appears to be above reality under these conditions is called’superior mirage’. However, weather conditions in which the’upper mirage’ phenomenon occurs are not common. In the water surface, the direction of light changes rapidly on the surface of the water in a way that the light bends because the material changes rapidly from water to air. However, in the area where the two air layers meet, the density of air does not change rapidly, but changes relatively slowly. Because of this, the direction of the light gradually changes, so it is appropriate to regard the light as bent. Conversely, if enough hot air is placed underneath, the direction of the light bends in the opposite direction. It may appear to be further down. This situation can be easily encountered unexpectedly. This is the case when you drive on a road on a hot day, and it looks like water is spreading over the distant part of the road. It is a phenomenon that occurs when the heat of the road heats the air on the road, creating a layer of hot air directly above the road. In this situation, with enough hot air below and relatively cold air above, the landscape above the road is visible on the road below the actual position. It seems as if there is water on the road and the landscape on the road reflects on it. This phenomenon seen below the real thing is called an’inferior mirage’.
Figure 3. Simulating’upper mirage’ and’lower mirage’ with a prism at the same time: Place the prism so that the center of one side of the prism is above the letter’Y’, and look down on the other two sides of the prism. Each letter appears to be in a position rather than where it should be, one on each side of the prism. On one side of the prism where the slow light speed glass is positioned above the air, a’superior mirage’ phenomenon is created in which the object appears higher than it actually is, and the other side of the prism where the slow light speed glass is positioned below the air. In the’inferior mirage’ phenomenon, the object is seen further below than it actually is. Light breaks off the surface of the prism, the interface between air and glass. In the figure below, the blue solid line indicates the direction of light travel, and the red dotted line indicates the visible position of the letters recognized by the brain.
Using a prism, you can simulate the two mirages described above at the same time. Write a small letter on the paper, and place the prism on the paper so that the letter is centered on one side of the prism. And look down towards the apex made by the other two sides of the prism. Then, although there is only one letter under the prism, two letters are visible, one on each of the two sides of the prism. The letters on the top of the prism appear to be above the actual position of the picture, and the letters on the bottom of the prism appear to be below the actual position of the picture. Each mimics the’upper mirage’ and’lower mirage’. As can be seen in the figure below of’Fig. 3′, when the letters are visible on the top, the glass of the prism, which slows the speed of light, is located under the air. In this case, it can be seen that the light path from the letters to the eyes goes upward at first and then bends downward at the prism glass surface. This is the typical shape of the light path when the’upper mirage’ was created. When the letters are visible below, the glass of the prism is above the air. In this case, the light goes down and then bends up. It is the shape of the path of light when the’lower mirage’ is created.
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A mirage made with a gravitational lens
There are situations in which the direction in which the light flies changes even if the speed of the light does not change. This is the case when there is gravity. According to Einstein’s theory of general relativity, where there is no gravity, light flies in a straight line, but when there is gravity, light bends in the direction that gravity pulls. The difference is that light bends or bends at the interface between air and water or air and glass because the speed of light changes. The first time we observed the bending of light due to gravity was the total solar eclipse on May 29, 1919. By observing a star that should not have been seen by the sun at the moment of a total eclipse, it was confirmed that the sun’s gravitational force bends the light. This observation is called the’Eddington Experiment’ after one of the observers. Later, as astronomical observation technology developed, special astronomical phenomena were observed due to the bending of light under gravity. One of them is the’Einstein ring’ that can be seen in the upper left photo of’Figure 4′. In reality, celestial bodies of this shape do not exist on this scale. There is another celestial body in the middle, and the light is bent due to the gravitational force of the celestial body. It is a kind of mirage that looks different from the actual location. It is also called a gravity lens because gravity acts as a lens. The glass ball can be used to simulate the Einstein ring without gravity. As in the picture on the lower left of’Figure 4′, if you place the glass ball appropriately on the small black circle, you can see that a round ring shape is additionally created. The shape of a ring is an image in which the direction of light changes while the light originating from a point passes through the glass ball.
Figure 4. An astronomical photograph captured with a gravitational lens and a photograph mimicking it as a glass ball and a glass pyramid. Top left: The galaxy in the middle acts as a gravitational lens, making the galaxy behind it appear like a ring. It is called the’Einstein Ring’ (Source: ESA, NASA). Bottom left: A picture of a glass ball placed a little over the dot, one dot creates another ring-shaped image. Top right: One quasar appears to be four quasars under the influence of a gravitational lens. It is called the’Einstein Cross’ because it is in the shape of a cross. Bottom right: If you place the glass pyramid on top of a dot, you will see all 4 dots, one on each of the 4 sides of the pyramid.
In some cases, as in the picture on the upper right of’Figure 4′, four stars are seen up, down, and both sides. However, these four stars are light from a single quasar. A quasar is a very large black hole at a very long distance, absorbing the surrounding material and emitting a strong light. The quasar light bends due to the gravity pulled by the third celestial body between the quasar and the Earth, making one quasar light appear like four different lights. It looks like a cross, so it is also called the Einstein cross. The Einstein cross can also be imitated as a pyramid made of glass. When a glass pyramid is placed on a dot, one dot appears as four dots, as in the picture on the lower right of’Figure 4′.
Figure 5. Above: Virtual image of a black hole seen up close. The ring shape of the black hole, similar to the original Saturn’s ring shape, looks different. The rings at the front of the black hole are almost intact, but the rings at the back of the black hole bend up and down to form two semicircles (source: NASA). Bottom: A picture of a glass ball placed on a straight line. One straight line appears as two semicircular rings at the top and bottom. Because light passes through the center of the glass ball, it looks like a straight line in the middle, but the black hole in the middle absorbs all the light, so the middle straight line is not visible as in the picture below.
In the movie Interstellar, a look at a black hole up close appears. The ring that glows around the black hole is similar to the original Saturn’s ring, but the black hole in the middle acts as a gravitational lens, making it look like the picture above in’Fig. 5′. It is not an actual observed image, but a virtual image created based on several scientific principles. The ring in front of the black hole looks almost the same as it was. This is because the black hole is behind the front ring, so the effect of acting as a magnifying lens is not large. However, the rings behind the black hole look completely different. The black hole in front of it acts as a gravitational lens, and the back ring looks bent upwards and downwards. It looks as if two rings were made above and below the black hole. The upper ring corresponds to the’upper mirage’, and the lower one corresponds to the’lower mirage’. A similar situation can be simulated with a glass ball. The picture below in’Figure 5’is a scene where a glass ball is placed at a suitable distance on a straight line. It appears to be one semicircle curved upward and two semicircles curved downward. In a virtual black hole image, the ring at the back is quite similar to what appears as a semicircle above and below. The difference is that the glass ball has a straight line shape in the middle because light passes through it, but nothing is visible because it absorbs all the light in the center of the black hole. Bok-Won Yoon/Georgia Institute of Technology, USA (Computational Materials Science Center·Physics) [email protected]