Mirrors in the air: mirages in nature and in the laboratory

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M Vollmer Figure 16. Two-fold and three-fold superior mirage images, observed on 1 August 1798 by Reverend S Vince in Ramsgate (after [10]). Figure 17. Inferior mirage in the laboratory using a 1.8 m long metal plate, covered by sand and heated using gas flames. should not be exposed to vibrations, since rapid diffusion decreases the period for observations. Without disturbing the solution, experiments for demonstration of curved light beams may be performed for a couple of hours, those of three part superior mirages (see below) for even longer times, and some mirage distortions like towering or stooping may be seen for one or two days. After preparation of the layered liquids in the tank, the curvature of a laser beam in the inhomogeneous solution can be easily demonstrated by illuminating from below and varying the angle of incidence. Figure 18 depicts a photograph of a curved laser beam directed through the tank and viewed from the side. Even a horizontally incident beam will be curved downward due to the vertical gradient of the index of refraction. This is due to the finite dimension at the beam waist: the upper and lower portions see different values of refractive index and will be bent differently. Consequently, the whole ray will be curved. Once the solution is prepared and curved light paths are observed, one should also be able to observe superior mirages when looking through the water tank. The size of the objects depends on the height of the salt solution and fresh water layers. Dimensions of several centimetres work 172 P HYSICS E DUCATION March 2009
Mirrors in the air: mirages in nature and in the laboratory Figure 18. A laser beam is illuminating a layered solution from below. It illustrates a curved light ray. well. Parameters for the observation are: relative height of the object and the boundary (diffusion) layer, the distance of the object behind the water tank, and the distance of the observer as well as the angle of incidence of light rays with respect to the eye of the observer. Once the solution is prepared, optimum observation conditions are usually found within a few minutes. For better results, one may illuminate the objects and observe through the smaller dimension (width) of typically 10 cm rather than the length of the tank. Depending on the observation angle, one can readily observe three-fold images (see figure 19). As mentioned above, in nature, typical dimensions are of the order of hundreds of metres, and changes of the index of refraction are of the order of several 10 −5 . In the water tank experiment, the distances are only of the order of 10 cm, but this is compensated by the change of the index of refraction of the order of 10 −2 . Among the most fascinating properties of mirages in nature are transient effects due to air fluctuations. They can be demonstrated by introducing water turbulence: for example, by slowly stirring the system. Wavelike disturbances in the artificial inversion layer lead to similar wavelike patterns in the mirages. More experiments More water tank experiments are possible using different liquids. Besides layered salt solutions, sugar solution also works very well [13], although it is more messy to clean up. However, sugar allows the preparation of multilayer solutions which can help to understand more complex mirages in nature. Quite a few more complicated chemical recipes have also been reported in the literature; however, most are with controlled substances which are not suited for teaching purposes. Using the salt water tank set-up with the three-image mirage, it is also possible to observe colourful effects from black and white objects which are due to dispersion effects within the artificial inversion layer [14]. In nature, one may also observe lateral mirages, for example, as mirages from heated walls. Experiments along these lines were realized in the laboratory, by using a U-shaped, flameheated channel [4, 14]. This allowed observation of three lateral images of the object. Finally, it is possible to observe mirages with hot plates as small as 14 cm diameter, although the image effects are small. However, hot plates are also ideally suited to demonstrate what we might call the deflection of light beams by human breath [14]. A laser is set up to illuminate a hot plate at grazing incidence such that some of its light is scattered by the surface. In addition, one also observes the position of the light beam on a distant wall. Blowing onto the hot plate results in an easily observable upward deflection of the beam spot on the wall while, simultaneously, the scattered light on the surface of the plate is no longer visible. Acknowledgments Special thanks go to Pekka Parviainen for letting me use his photograph (figure 14) and in particular March 2009 P HYSICS E DUCATION 173
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Mirrors in the air: mirages in nature and in the laboratory

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