Laboratory Simulation of Inferior and Superior Mirages

Robert G. Greenler Vol. 4, No. 3/March 1987/J. Opt. Soc. Am. A 589

Laboratory simulation of inferior and superior mirages

Robert G. Greenler

Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201

Received May 5, 1986; accepted August 29, 1986 A small scene, viewed over a heated plate, exhibits many of the typical inferior-mirage effects. As the viewing point is lowered, a mirage lake appears, and a vanishing line rises on the scene, showing objects apparently reflected in a rising surface of water. Several kinds of superior mirages are simulated by viewing objects through a water tank containing fresh water layered over salt water. The system simulates towering, stooping, various forms of the Fata Morgana, and the three-part mirage.

aperture. A piece of cardboard with a horizontal slit about 1 INTRODUCTION cm wide was placed in front of the camera lens to reduce the Mirages come in a wide variety of forms. For simplicity, we blurring from this effect. Plate Va shows a photograph divide them into two classes. Over a region of space where taken from a relatively high viewpoint, such that the light the air temperature decreases with height (as over a hot road rays pass high enough above the aluminum plate to give a or a heated desert floor), light rays follow curved paths that relatively undistorted view of the desert scene. In Plate Vb are concave upward. Such paths yield an upright image of a the vanishing line is located on the desert floor in front of the distant scene that appears to be below its actual position and scene. The apparent reflection about this line shows desert hence is called an inferior mirage. Where the air tempera- sand at the horizon but sky below the horizon, giving the ture increases with height (as when warm air flows over a convincing appearance of a lake located in front of the desert cold body of water), light-ray paths are concave downward. scene. As the viewing point is lowered for Plates Vc and Vd, An upright image of a distance scene, in this case, appears the vanishing line rises and lower features in the scene disap- above its real position, which we indicate by calling it a pear. The desert sand in front of the scene is below the superior mirage. Of course, more-complicated mirage ef- vanishing line, and so the trees, oil derrick, etc. appear to be fects can be observed when we look through a layered atmo- projecting out of a water surface. These are all effects that sphere that has a positive temperature gradient at some are seen in the typical desert or hot-road mirage. elevations and a negative gradient at others. Such compli- Just as the vanishing line on an object will rise as the cated mirages may not fit neatly into our two classes. I will observer's viewpoint is lowered, so will it rise as the obser- not discuss the elementary theory of the mirages here. Two ver's distance from the object is increased. Plates VIa-VId Scientific American papers" 2 describe new ways to under- are photographs of a truck on a hot road (not a simulation) stand mirage phenomena, and the classical treatment can be for a fixed camera viewpoint but different truck distances. found in a variety of books; for example, see Refs. 3-7. The images can be understood by considering a vanishing This paper describes two laboratory models that show line rising on the red truck as it recedes into the distance. many of the commonly observed features of the two classes of mirages. SUPERIOR MIRAGE A tank is constructed with sides of glass and ends of clear INFERIOR MIRAGE plastic 60 cm long, 30 cm high, and 8 cm wide. The tank is In 1889 Wood published a description of an apparatus for filled about half full of saturated salt water, and then a layer demonstrating the desert mirage.8 The apparatus demon- of fresh water in introduced on top. If fresh, hot water is strated here is essentially the same as he described. A plate poured onto a floating board, it can be introduced without of aluminum about 3 m long and 20 cm wide is heated from much mixing with the salt layer. The boundary can be beneath by gas flames. The flames come from a pipe with broadened by careful stirring or by letting the tank sit for a holes spaced 2.5 cm apart, connected to a gas line. A desert few days. Rays passing near the boundary (from below) scene of objects a few centimeters high is placed at one end of move in curved paths that are concave downward, the condi- the heated plate and viewed from the other end. To ensure tion that produces superior mirages. Plate VII shows the that there is no actual reflection from the metal plate, it is obvious curvature of a laser beam in passing through the covered with a layer of sand. tank. With a suitable placement of an object and the obser- Plates Va-Vd are a sequence of photographs taken by ver's eye, a wide variety of superior mirages can be simulat- successively lowering the camera position. The lens used ed. for these photographs was a 500-mm focal-length lens. Be- Plate VIIIa is a drawing of a ship, photographed directly, cause the appearance of the scene changes with the height of without the water tank. Different placements of the ship the camera, a particular photograph incorporates all the and observer relative to the "inversion layer" simulated by image variations that occur over the spread of vertical di- the salt-fresh-water boundary give a vertical magnification mensions corresponding to different points in the camera or demagnification of the ship (Plates VIIIb and VIIIc) that

are known in the terminology of sailors as towering and all the rays that end at the observer's eye. Any object that stooping, respectively. Special cases of the vertical magnifi- lies below the caustic surface cannot be seen. The caustic cation of a superior mirage can produce a variety of forms of surface rises in the distance, and its intersection with any the Fata Morgana. 7 A horizontal line across an ice surface object is what I have called the vanishing line. The base of can be drawn upward to produce a wall (Plate IXa); small the salt-fresh-water mirage tank can cut off parts of the surface features can be vertically magnified into spires lower mirage images, as in the simulation shown in Plate (Plate IXb); or the surface feature can be magnified and XIIId. This is similar to the obscuration of the lower part of connected to an inverted image to produce the capped col- a ship by the horizon, as in Vince's drawings appearing in umns of the Fairy Morgan's illusionary castles (Plate IXc). Plate XIIIb, although the short length of the simulation Plate X shows the drawing of an ice surface (Plate Xa) and tank makes the analogue less than perfect. Some of the its appearance through the water tank (Plate Xb), resem- Fata Morgana effects could be more accurately modeled by bling the wall. Plate XIa is a drawing of a rough surface and having the object consist of a rough horizontal plane located its appearance through the tank (Plate XIb) to resemble beyond the tank. It should also be possible to simulate Plate IXc. more-complicated 9 superior mirages by adding additional In 1799 Vince published sketches of mirage images of layers of liquids. However, the results obtained from these ships that he had observed when looking out from Ramsgate, two simple systems give insight into the conditions neces- England, over the North Sea. Several of his sketches are of sary for the formation of a variety of mirage effects. three-part mirages, as is, perhaps, Plate XII. It was argued, qualitatively (Ref. 7, p. 163), that Vince's three-part mirage could result from a simple temperature inversion. From the REFERENCES way that the salt-fresh-water mirage tank is prepared, it is 1. W. Tape, "The topology of mirages," Sci. Am. 252, 120-129 clear that the index of refraction is a monotonic function of (1985). height; the boundary between the salt and fresh water pro- 2. A. B. Fraser and W. H. Mach, "Mirages," Sci. Am. 234,102-111 vides a negative gradient of the refractive index with no (1976). multiple 3. W. J. Humphreys, Physics of the Air, 3rd ed. (1940; reprinted, layering. With this simple system, I can reproduce Dover, New York, 1964). Vince's drawings in rather surprising detail by viewing (and 4. M. Minnaert, The Nature of Light and Colour in the Open Air, photographing) the ship of Plate VIIIa through the mirage translated by H. M. Kremer-Priest, revised by K. E. Brian Jay tank. Plates XIIIa and XIIIb are two of Vince's drawings, (Dover, New York, 1954). and Plates XIIIc and XIIId are the mirage-tank photo- 5. A. B. Fraser, "Meteorological optics," in R. A. Anthes, H. A. Panofsky, J. J. Cahir, and A. Rango, The Atmosphere (Merill, graphs. Columbus, Ohio, 1975), Chapter 9. 6. A. B. Fraser, "Theological optics," Appl. Opt. 14, A92-A93 (1975). DISCUSSION 7. R. Greenler, Rainbow, Halos and Glories (Cambridge, New York, 1980). To simulate both the inferior and the superior mirages dis- 8. R. W. Wood, "Some experiments on artificial mirages and torna- cussed in this paper, I use objects located in a plane, all at the does," Phil. Mag. 47, 349-353 (1899). same distance from the observer. For the desert mirage, it 9. S. Vince, "Observations on an unusual horizontal refraction of would be simple to have objects located at different dis- the air, with remarks on the variations to which the lowerparts of the atmosphere are sometimes tances to show how the vanishing line rises with distance. subject," Philos. Trans. R. Soc. 6 London 89, 436-441 (1799); or see some of Vince's drawings Fraser discusses this situation by considering the caustic of reproduced in Ref. 7, p. 164.