$VLPSOHH[SHULPHQWWKDWGHPRQVWUDWHVWKH³JUHHQIODVK´ -RKDQQHV&RXUWLDO
&LWDWLRQ $P-3K\V GRL 9LHZRQOLQH KWWS G[GRLRUJ 9LHZ7DEOHRI&RQWHQWV KWWS DMSDDSWRUJUHVRXUFH$-3,$6YL 3XEOLVKHGE\WKH$PHULFDQ$VVRFLDWLRQRI3K\VLFV7HDFKHUV
5HODWHG$UWLFOHV 5HIOHFWLRQRIDSRODUL]HGOLJKWFRQH $P-3K\V (QHUJ\DQGPRPHQWXPHQWDQJOHPHQWLQSDUDPHWULFGRZQFRQYHUVLRQ $P-3K\V 7KH³UDLQERZ´LQWKHGURS $P-3K\V 1RYHOFDVHVRIGLIIUDFWLRQRIOLJKWIURPDJUDWLQJ 7KHRU\DQGH[SHULPHQW $P-3K\V 7KH2SWLFVRI/LIH $%LRORJLVW¶V*XLGHWR/LJKWLQ1DWXUH $P-3K\V
$GGLWLRQDOLQIRUPDWLRQRQ$P-3K\V -RXUQDO+RPHSDJH KWWS DMSDDSWRUJ -RXUQDO,QIRUPDWLRQ KWWS DMSDDSWRUJDERXWDERXWBWKHBMRXUQDO 7RSGRZQORDGV KWWS DMSDDSWRUJPRVWBGRZQORDGHG ,QIRUPDWLRQIRU$XWKRUV KWWS DMSGLFNLQVRQHGX&RQWULEXWRUVFRQW*HQ,QIRKWPO
Downloaded 11 Jan 2013 to 81.194.35.225. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission A simple experiment that demonstrates the “green flash” Johannes Courtial School of Physics & Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom (Received 9 January 2012; accepted 2 August 2012) The green flash occurs when, under certain atmospheric conditions, the top segment of the low sun is visibly green. It is surrounded—in at leastafewminds—byanairofmystery.Idescribea simple experiment that demonstrates different aspects of the green flash. The experiment uses an odd-shaped, water-filled, fish tank to simulate therefractivepropertiesoftheatmosphere;milk powder added to the water mimicks the atmosphere’s scattering properties. A circular white- light source is viewed through the fish tank and the combination of refraction and scattering makes one end of the light source look green. The setup also allows experimentation with mirage effects, thereby drawing attention to their often neglected contribution to the green flash. VC 2012 American Association of Physics Teachers. [http://dx.doi.org/10.1119/1.4746384]
I. INTRODUCTION demonstrating either the mechanism that colors the setting sun’s upper and lower edges (e.g., Ref. 3), or the mechanism There are many colors in the sky: white and various by which the atmosphere scatters purple and blue light.12–16 shades of gray come from the clouds; blue comes from the A lengthy literature search uncovered very few experiments cloudless daytime sky; and yellow, orange, and red come that demonstrate both at the same time.17,18 Here I describe from the sun as it traverses the sky from sunrise to sunset. an experiment that demonstrates both of these aspects of the The sky is not normally green, which makes it all the more green flash, and arguably other, less well-known aspects. surprising when part of it appears green. Such a situation 1 2 The experiment uses only inexpensive, commercially avail- occurs in rainbows and during the green flash. able equipment; namely, a non-cuboid aquarium, water, milk The green flash can occur during sunset, just before the top powder, and a bicycle light. This experiment was developed segment of the sun disappears behind the horizon, or during to demonstrate the green flash for an episode of the BBC sunrise, just after the sun’s top segment appears above the ho- documentary series “Coast.”19 rizon. During a green flash, the top segment of the sun— indeed, all of the sun that is visible—is green. Whether or not the green flash occurs depends on location and atmospheric II. OPTICS OF THE GREEN FLASH conditions. Normally, the sunrise or sunset needs to be visible This section provides a brief explanation of the green flash low on the horizon, which is one of the reasons why the sea- followed by some refinements on different aspects of this side is a good place to observe it. Also, the sky needs to be explanation. sufficiently clear so that the setting sun is yellow and not red.2 When the green flash occurs, the length of time it is visible A. Brief explanation of the green flash depends on the rate at which the sun sets or rises, which in turn depends on the observer’s latitude and the time of year. The green flash can be explained in two steps: During the polar summer, a green flash has been observed to last for more than 30 min.2 A more typical duration for the 3 (1) When looking at the sun at sunset, an observer is looking green flash at temperate latitudes is on the order of a second. through an “atmospheric prism”—a prism-shaped piece of Relatively few people have seen the green flash, which is the atmosphere. Just like looking through a glass prism of perhaps why it has acquired something of an air of mystery 4 suitable orientation, the observer sees displaced images and a fair number of nonsensical associations. One such of the sun in all colors of the rainbow, with the red image example is “one of the numerous inexplicable legends of the at the bottom and the blue/purple image at the top. As the Highlands” apparently invented by Jules Verne for his novel 4 sun sets, these images disappear behind the horizon, one “The Green Ray” (French “Le Rayon vert”), which asserts by one, and the last one to disappear is the blue/purple that “this ray has the virtue of making him who has seen it image. (At sunrise, the time sequence is reversed, and so impossible to be deceived in matters of sentiment.”5 Perhaps 3,4,6 the blue/purple image of the sun is the first to appear surprisingly, the green flash actually occurs frequently; above the horizon.) When it is visible, the light from this the relative scarcity of its observers is due to the fact that in top, blue segment of the sun is called a blue flash. non-polar regions it requires looking from the right place,7 in 8 (2) But the green flash is green, not blue. This is because the right direction, at the right time. Even when it is under green-flash conditions much of the blue light has observed, it is sometimes unclear whether what was seen been scattered out of its original path by the atmosphere. was actually a green flash or merely appeared green due to Thus, no blue image of the sun will be visible, which physiological effects, specifically bleaching of the cone pho- 9 10 means that the top image—the last to disappear behind topigments. To be certain, one can record spectra, take the horizon at sunset (or the first to appear at sunrise)—is photos (taking special care with white-balance settings), or green. observe the green flash at sunrise.3,11 A number of experiments that demonstrate aspects of In the brief explanation above, there are a number of points the green flash have been previously described, usually that require clarification—a number of details ranging from
955 Am. J. Phys. 80 (11), November 2012 http://aapt.org/ajp VC 2012 American Association of Physics Teachers 955
Downloaded 11 Jan 2013 to 81.194.35.225. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission interesting to important have been left out in the interest can be calculated approximately from Snell’s law using the of brevity. These details are discussed in Secs. II B to II H. refractive index of the vacuum of space on one side (n1 1), and the refractive index of the atmosphere at the ¼ observer (n2 1:0003 for green light and pure air at sea B. The atmospheric prism level24)ontheother. Let us refine our model of atmospheric refraction slightly. The first clarification concerns the “atmospheric prism” We still consider only refraction at one interface between through which any observer of a green flash views the sun. vacuum and the atmosphere at the observer, but we now Unlike the material of a prism, the atmosphere does not end 20 allow this interface to be angled. From the deflection angle in a sharp outer boundary but instead becomes thinner with of rays from the sun at sunset (approximately 40 arc altitude. This lack of a sharp boundary is reflected in the min24,25) and the refractive index of air at sea level, it is pos- multitude of definitions relating to the edge of the atmos- sible to calculate an inclination angle with respect to the hor- phere. For example: the US definition of an astronaut is any- 21 izontal of 1:8 . If the prism shown in Fig. 1 was made from a one who has flown more than 50 miles above sea level; the material with a refractive index the same as that of air at sea Karman line, 100 km above sea level, is the approximate alti- level, the interior angle of the prism’s left corner (when ori- tude at which aircraft must travel faster than orbital velocity 21 entated as shown in Fig. 1) must be very acute, namely, 1:8 , for the aerodynamic lift to support their weight; and during to mimic atmospheric refraction. atmospheric reentry of spacecraft, atmospheric effects 22 As an aside, it is worth mentioning another effect of become noticeable at an altitude around 120 km. atmospheric refraction. When the sun’s upper edge disap- The thinning of the atmosphere with altitude gives rise to pears behind the horizon, its light rays reach the atmosphere a refractive index that varies with altitude. Refraction due from a direction that is well below the horizon. When seen to such an atmosphere can be described mathematically in 23 near the horizon, the sun appears approximately 40 arc min considerable detail, but for the purposes of this paper a higher in the sky than its actual position.24 For comparison, simplified description suffices. The atmosphere is actually the angular diameter of the sun when it is high in the sky is much thinner than the sketch in Fig. 1 would suggest, so about 30 arc min ( 0:5 ), and when it is low in the sky it much so that the layers of constant refractive index are appears flattened to a vertical angular extent of around 24 almost parallel. But the angle change on transmission arc min.26 Thus, by the time the sun’s lower edge first through such a structure is very simple. When a light ray touches the horizon, all light rays from the sun (including its arrives from space (refractive index n0)atananglea0 with upper edge) reach the Earth from a direction below the respect to the vertical direction (which is also the normal to horizon. the layers of constant refractive index) and enters the first atmospheric layer (refractive index n1), Snell’s law states C. The images of the sun in the colors of the rainbow that its new angle with the vertical direction a1 is given by the equation n0 sin a0 n1 sin a1.Inthesameway,the ¼ According to the brief explanation in Sec. II A, the atmos- direction change upon entering the next atmospheric layer pheric prism creates displaced images of the sun in all colors is governed by the equation n1 sin a1 n2 sin a2.Oneside ¼ of the rainbow. This point can benefit from clarification. of these two equations is the same, namely, n1 sin a1,andso The displaced images of the sun in the colors of the rain- we can directly write n0 sin a0 n2 sin a2. In other words, ¼ bow an observer sees do not actually look like a rainbow, as the intermediate layer does not have any effect on the over- the brief explanation might suggest. Instead, only the top and all light-ray-direction change. This is true not only for one bottom of the sun appear colored. An observer with narrow- intermediate parallel layer but also for any number of such band filters would see that the images of the sun seen in dif- layers. Therefore, the angle by which sunlight is deflected ferent wavelengths appear vertically displaced; the shorter the wavelength the higher the corresponding image of the sun. These images in different wavelengths are displaced very little, so they mostly overlap and their colors add up to the color of the setting/rising sun (they would add up to white if there was no absorption or scattering in the atmos- phere). Only at the very top and bottom is the overlap of images incomplete, so this is where the sun appears colored, respectively, like the inside (blue) and outside (red) of a pri- mary rainbow.
D. Atmospheric scattering The change in color of light as it travels through the atmosphere is more complicated than the brief explanation Fig. 1. (Color online) Light rays from the sun’s top edge pass through a in Sec. II A suggests. The dominant effects are absorption of segment of the atmosphere that is approximately equivalent to a prism, yellow light by water vapor and ozone, and Rayleigh scatter- resulting in refraction and dispersion such that light rays with different ing, especially by aerosols.2,4 We concentrate on these domi- colors reach the observer from different vertical angles (blue on top, red nant effects here. on bottom). Under green-flash conditions, red and yellow rays have disap- Rayleigh scattering is particularly important; it affects all peared below the horizon and almost all blue and purple light has been scattered out of their original path by the atmosphere. Only green light rays light, but blue light is scattered much more than red light reach the observer. The diagram is not drawn to scale. (Image of Earth from because the intensity of scattered light varies inversely as the 4
956 Am. J. Phys., Vol. 80, No. 11, November 2012 Johannes Courtial 956
Downloaded 11 Jan 2013 to 81.194.35.225. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission intensity of the incident light. In any direction away from the mirage—as described in Sec. II A—is inversely proportional sun we see the sky in scattered light, which is the reason why to the vertical speed of the sun at the horizon.29 This speed, the (clear) daylight sky is blue.27 When the sun is seen in turn, depends on the latitude of the observer’s position through a thick atmosphere—at sunrise or sunset—it typi- and the time of year. In polar regions during summer, the cally looks orange or red because much more blue light has sun can graze along the horizon with a very small vertical been scattered away than red light. speed. The resulting green flash will be correspondingly Different atmospheric concentrations of the contributing long, so the half-hour on-off green flash mentioned in the scatterers and absorbers will lead to a different color of the introduction is perhaps not terribly surprising. In central top segment of the sun and a flash of a different color. Too Europe (or similar latitudes), the top segment of the setting little scattering, due to extremely clear air or a shorter path sun is green for about 1.5 s.29 through the atmosphere when a flash is observed looking This duration also appears to be the typical duration for a upwards,28 leads to a blue or violet flash;2 too much scatter- mirage-enhanced green flash seen by naked-eye observers. ing leads to a not-so-surprising red flash. As a rule of thumb, For example, regarding the duration of the green flash, a pale orange (not red) setting sun is a good candidate for Ref. 2 states that “[i]t only lasts for a second or two.” On the producing a green flash.2,18 other hand, a mirage-enhanced green flash can also last significantly longer. According to Ref. 9, which presumably E. Enhancement through mirage effects refers to the latitudes and conditions of California, “real green flashes can last as long as 15 s (although this is possi- A very important detail that has been left out of the brief ble only for certain rare types of flash).” explanation in Sec. II A is the role mirages play in the green Note that physiological effects (Sec. II G) can make a flash. As described above, the green flash is not visible to a green flash appear significantly longer than it actually is. naked-eye observer without being enhanced in some way.29 The only natural phenomenon that can cause such an G. Physiological effects enhancement appears to be a mirage4,29—the bending of light rays during transmission through the atmosphere that It is worthwhile to expand briefly on the theme of physio- results in the apparent displacement and distortion of logical effects mentioned in the introduction. objects.30 As a suitably strong mirage occurs only occasion- Physiological effects can alter the color perceived by a green-flash observer, resulting in flashes that are not actually ally, this is consistent with observations that the green flash 9 is “notoriously capricious in its appearance,”17 and specifi- green despite being perceived as such. For example, a yel- cally that it is not visible with the naked eye in many sunsets low flash can appear green due to visual adaptation. This is but that it is visible when mirages of other objects are appa- caused by photobleaching of the pigment in an observer’s rent.31 There are two aspects to consider: retina that is sensitive to red light, which reduces sensitivity to red light and can therefore make yellow light appear (1) In the absence of a mirage, the green segment of the 4,9 rising or setting sun cannot be resolved by the unaided eye. green. Given that the refractive index of pure air at sea level is The effects of photobleaching typically persist for several minutes. Photobleaching can therefore give the illusion of a about nair 1:0003 (green light) compared to nvac 1 for ¼ ¼ green flash that lasts minutes, a timescale that is too long to be the vacuum of space, the different colored discs of the sun 9 are very close together, being dispersed by approximately 1 an ordinary green flash at temperate latitudes. Reference 9 arc min.29 As a result, the angular extent of the unenhanced lists a number of reports of observations of extraordinarily green rim is of order 10 arc sec,32,33 significantly smaller long green flashes which appear to be due to this effect. than the angular resolution of the unaided eye ( 1 arc min).2,17 A mirage can stretch the width of the green rim to H. Green ray, green flash, green segment several arc minutes, thereby making it resolvable to the The final clarification concerns the term green flash itself. unaided eye.4 The terms “green flash” and “green ray” are widely used for This is consistent with the following quote from Ref. 4: a number of effects that are related but slightly different. “Perhaps one sunset in five or six offers a naked-eye green There is green-ness in all of them, but neither are all of them flash from the California coastline; with modest magnifica- flash-like nor do all of them possess ray characteristics. tion, nearly all sunsets do. So go ahead and look!” It is At least three effects can easily be distinguished: worth noting that looking at the setting sun through binoc- ulars is considered safe, provided the sun is sufficiently low.4 (1) When hazy air is illuminated by a beam of light, the col- (2) The previous point only prevents a naked-eye observer umn of air the beam intersects is visible. If the column of from resolving the green flash, but it does not stop the ob- air is illuminated by sunlight, this is called a crepuscular server from seeing the green light. However, calculations ray.34 The very rare green ray is probably a crepuscular show that the unenhanced green light from the top segment ray that is illuminated by a particularly bright green of the low sun is too faint to be visible against the sunset flash.4 sky.29 By partially focussing light from the green rim onto (2) The effect for which the term green flash seems entirely the observer, a mirage can increase the power of green light appropriate is the brief appearance to the naked-eye ob- that enters the observer’s eye to visible levels. server of green light during a mirage-enhanced sunset. (3) There is also the more frequent green rim of the setting F. Duration of the green flash sun that is visible only through binoculars or on photo- graphs. In an attempt to differentiate it from related phe- It is interesting to discuss briefly the duration of the green nomena, it has been called—and perhaps should be flash. The duration of a green flash that is not enhanced by a called more often—the “green segment.”29
957 Am. J. Phys., Vol. 80, No. 11, November 2012 Johannes Courtial 957
Downloaded 11 Jan 2013 to 81.194.35.225. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission III. DEMONSTRATION EXPERIMENT The demonstration experiment described here uses an odd-shaped, inexpensive aquarium (Marina Aqua Alien Goldfish Tank Starter Kit 17L) to demonstrate a number of aspects of the green flash. Figure 2 shows a top view of the aquarium partly filled with slightly scattering water. The sur- face of the water indicates a horizontal cross-section of the aquarium, which changes slightly with height. The horizon- tal cross-section forms roughly an isosceles trapezoid, but with three of the edges curved. Two numbered light paths are sketched in Fig. 2. Ignoring for the moment the curvature of the aquarium’s sides, each light path intersects a wedge of water that acts like part of a prism. The wedge angles are different for the two paths, approximately 60 for path 1 and 37 for path 2. Just like a prism-shaped piece of glass or atmosphere, this prism- shaped volume of water produces displaced images in the colors of the rainbow of any broad spectrum white-light source when seen through the water. In the experiment shown here, a mountain-bike light (Lupine Edison 5) was placed approximately 50 cm behind the aquarium. This light is a high-intensity discharge (HID) lamp, chosen for its brightness and wavelength spectrum.35 The lamp’s bright and relatively compact beam allows the scattered and non- Fig. 3. (Color online) Images of the light source taking path 1 in Fig. 2. scattered light to be observed with the naked eye over a wide Image (a) was taken with the aquarium filled with clear water, image (b) range of scatterer concentrations; the lamp’s wavelength was taken with some milk powder added, and image (c) was taken after yet spectrum subjectively gives the beam the color of daylight, more milk powder had been added. Image (d) was taken with the same con- and it contains significant amounts of red, blue, and green centration of milk powder as in (c), but a piece of black card was inserted wavelengths so that all aspects of the demonstration experi- between the aquarium and the camera to simulate the horizon. ment can be observed. The scattering properties of the atmosphere are simulated amounts of milk powder to the water.15 Here, with the aquar- by adding sub-wavelength-sized scatterers to the water in the ium filled to roughly three liters of water, the milk powder is aquarium. One easy way of doing this is to add small added in successive small pinches (about 10 pinches per tea- spoon) until the desired effect was achieved. Note that the blue glow of scattered light can be seen in the photo shown in Fig. 2, which was taken with the light source illuminating the aquarium from the right. Figures 3 and 4 show a series of photographs of the light source taking different paths through the aquarium with increasing quantities of milk powder added to the water. The camera (Canon EOS 450D with Canon EF 100-mm f/2.8
Fig. 2. (Color online) Top view of aquarium. Light paths 1 and 2, and the corresponding angles of the traversed water prism, are indicated. Note that Fig. 4. (Color online) Images of the light source taking path 2 in Fig. 2. As the photo was taken with the white light source illuminating it from the in Fig. 3, the series of images from (a) to (d) shows the view with increasing right, and with some milk powder added to the water. The light scattered in amounts of milk powder added to the water, beginning with no milk powder the water is blue for the same reason that the clear daytime sky is blue. at all. In image (d) the green segment is no longer visible.
958 Am. J. Phys., Vol. 80, No. 11, November 2012 Johannes Courtial 958
Downloaded 11 Jan 2013 to 81.194.35.225. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission USM lens used at f/32) was placed as close as practical (about 3 cm) to the aquarium to minimize distortion of the image. The key to this demonstration is that the camera re- cord color in the same way throughout the experiment so that all changes in the apparent color of the light source can be attributed to physics and not image processing in the cam- era; this was ensured by using the same white-balance setting for all images.36 Figure 3(a) shows the light source viewed along path 1 in Fig. 2, through a (slightly curved) water prism with a 60 prism angle and no milk powder added to the water. The main part of the image is white, although purple and red seg- ments can be seen on the left and right sides. These colors correspond, respectively, to the top and bottom segments of the sun near the horizon under exceptionally clear conditions (i.e., with almost no atmospheric scattering). As further milk powder is added to the water, the light source first appears pale yellow and then turns to a shade of Fig. 5. (Color online) Green segment, enhanced by an artificial mirage (left orange/yellow, as shown in Figs. 3(b) and 3(c). Importantly, side of front of tank); orange light of non-scattered light (remainder of beam seen through front of tank); blue glow of scattered light (seen through right note that the purple segments seen on the left in Fig. 3(a) first side of the tank); and light source, seen directly to the right of the tank. shrink and then disappear. At this point, as shown in Fig. 3(c), the leftmost segments of the image are now green. This situation represents the conditions under which the top addition of a cylindrical lens (with a vertical axis) to the segment of the low sun is green. prism formed by the water in the aquarium. Moving the Figure 3(d) represents the situation when the sun is so low camera away from the aquarium results in the image that only the green segment and a small portion of the yellow being stretched sideways.38 This stretching is significant segment are visible above the horizon. The artificial horizon enough that only a small part of the image can be seen in in our experiment was a black card that was inserted by the left part of the aquarium in Fig. 5. It is to minimize hand between the aquarium and the camera.37 The situation such distortion that the images in Figs. 3 and 4 were taken represented by Fig. 3(d) is an example of when the green with the camera as close as possible to the aquarium. flash would be seen if it were not too dim to be visible29 (3) The distortion of the image, in combination with reflec- (see Sec. II E); it therefore demonstrates the physics of the tion off the flat side of the aquarium (the top side in Fig. 2), is a crude simulation of a mirage that is seen to green flash at the level of the brief explanation in Sec. II A. magnify the green(ish) part of the image. Figure 4 shows the light source viewed along path 2 in Fig. 2, through a prism angle of 37 and again, with different amounts of milk powder added to the water. Because the IV. POSSIBLE EXERCISES prism angle is smaller than in Fig. 3, the dispersion angle is smaller. The green segment can still be seen in frames (b) The theoretical and practical details of the demonstration and (c) but it is smaller than in Fig. 3; its angular size is experiment outlined above provide numerous opportunities now slightly closer to the low sun’s green segment that has for students to explore related topics. I outline a few possibil- not been enhanced by a mirage—so small that it requires ities below. binoculars or other optical instruments to be resolvable (see Sec. II E). In frame (d), so much milk powder has been A. Observations in nature added to the water that almost all colors other than red have been scattered out of the transmitted light. The image of the First and foremost, students should keep an eye out for the light source now looks uniformly orange and the green real thing—the green flash occurring naturally. I would go so segment is no longer visible, a fact that is consistent with the far as to say that the demonstration experiment has suc- rule of thumb that a red sunset is not a good candidate for ceeded if students look for the green flash the next time they producing a green flash.2,18 see a setting or rising sun (or better yet whenever they see a Figure 5 shows an image of the aquarium taken from a dis- setting or rising sun for the rest of their lives). Of course, tance of a few meters. The aquarium is orientated such that instructors should encourage their students to do so. In this context it is worth reiterating that looking at a very low sun light from the source travels along path 2 to reach the cam- 4 era. This image shows a number of things. is considered safe. Another effect that is readily observable in nature, and which students should be able to explain from what they (1) The colors of the light source, the scattered light, and the know about atmospheric refraction, is the apparent flattening unscattered light are clearly different: the light source, of the low sun (or moon) due to a higher deflection of the visible to the right of the aquarium, is white; the scat- sun’s (moon’s) lower part compared to its upper part.26 tered light, visible in the right part of the aquarium, is I hope that the experiment described here raises students’ blue (although not very bright in the image); and the awareness of atmospheric optical phenomena, and more gen- unscattered light, visible in the left part of the aquarium, erally of optical phenomena in the outdoors and in nature. is mainly orange. Numerous amateurs and professionals have a particular fas- (2) The curvature of the aquarium sides is now important. cination with this area of optics, and many wonderful books The effect of this curvature can be approximated as the are devoted to it.39,40
959 Am. J. Phys., Vol. 80, No. 11, November 2012 Johannes Courtial 959
Downloaded 11 Jan 2013 to 81.194.35.225. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission B. Atmospheric refraction demonstrates that small objects scatter waves with smaller wavelengths more strongly.49 A number of possible exercises relate to atmospheric refraction. Approximating the atmosphere for the purposes of refraction by a prism with the same refractive index as air D. Other exercises at sea level, as was done in Sec. II B, simplifies the discus- The green-flash demonstration experiment described here sion of many related effects. As an introduction to these can be used as the starting point for more in-depth explora- related effects, students could be asked to work out, from the tions of other topics. Students could, for example, be asked deflection angle of rays and the refractive index of air at sea to observe and explain what happens if the knife edge that level, the geometry of this equivalent prism and hopefully simulates the horizon is placed not between the aquarium arrive at the results listed in Sec. II B. and the observer, but between the light source and the By comparing the deflection angle of light from the low sun aquarium. to the sun’s angular size, students should be able to work out The demonstration, especially if it is performed using a that the low sun (or moon) is actually completely below the camera, also provides an opportunity to learn about a cam- horizon even when its visible bottom edge is still above the era’s white balance. It is worth mentioning how remarkable horizon. In this context, it might also be worth discussing it is that our visual system does this automatically so that we the so-called moon illusion, which makes the moon appear do not normally notice that artificial light has a completely 41 unusually large when it is close to the horizon. different color from natural light. Finally, mirages42 are an interesting atmospheric- refraction topic of special relevance to the green flash. Some V. CONCLUSIONS interesting theory, for example, about the formation and ori- entation of multiple images produced by mirages, can be The experiment described here demonstrates—and allows worked out and even illustrated by producing an artificial mi- experimentation with—the basic physics of the green flash. rage using sugar solutions.30,43,44 If the demonstrator is will- It uses everyday, non-toxic ingredients and it touches upon ing to compromise the (relative) simplicity of the experiment the important mirage aspect of the green flash. described here, and if a suitable container can be found such The special appeal of this demonstration lies in the overlap that the water prism can be turned through 90 without the of a number of interesting areas (green flash, blue sky, red water spilling out, then perhaps the green-flash and artificial- sunset, mirages, etc.) and the fact that the experiment can be mirage demonstrations could even be combined. performed using simple everyday pieces of equipment and ingredients. C. Atmospheric scattering Almost everybody has seen the blue color of the clear day- ACKNOWLEDGMENTS light sky and the red(ish) color of the low sun. Here, there is Thanks to Richard Bowman and Nong Chen for useful dis- an opportunity to experiment with the relevant parameters. cussions related to optics. Many thanks to Beth Paschke and Specifically, it is possible to vary the concentration of scat- Adrian Lapthorn for help and advice on chemistry. terers, and to vary the length of liquid intersected by the line of sight. There are a number of alternative ways of simulating the 1D. K. Lynch and W. Livingston, Color and Light in Nature, 2nd ed. (Cam- bridge U.P., Cambridge, United Kingdom, 2001), Chap. 4.2, p. 103ff. scattering properties of the atmosphere. One such experi- 2 ment, sometimes called a “chemical sunset,” is particularly D. K. Lynch and W. Livingston, Color and Light in Nature, 2nd ed. (Cam- bridge U.P., Cambridge, UK, 2001), Chap. 2.20, p. 48ff. memorable; it simulates not just a static situation, but also 3G. Johnson, “Experiments with flasks, prism and lamp explain rainbows the typical time evolution of the color of the setting sun. The and sun’s green flash,” Pop. Sci. Monthly, 118, 52–53 October (1934). colors produced in this experiment can be very vivid and re- 4A. T. Young, “Green flashes and mirages,” Opt. Photonics News 10, 31– alistic—I still remember seeing this demonstration when I 37 (1999). was an undergraduate student (many setting suns ago). The 5J. Verne, The Green Ray (Sampson Low, Marston, Searle and Riving, experiment involves a chemical reaction that creates the London, 1883). 6B. E. Schaefer, “The green flash,” Sky Telesc. 83, 200–203 (1992). scattering particles, and increases their concentration on a 7 The green flash is normally observed from the coast, as the horizon is then timescale that allows a reddening of the artificial sun to be 12–14 particularly low and the light path through the atmosphere particularly observed on the timescale of a natural sunset. It uses so- long. But it can also be seen over land, best from places with a low horizon dium thiosulfate (Na2S2O3, also known as “hypo”) and either such as airplanes, mountain tops, and tall buildings (see Ref. 4). 8 hydrochloric or sulfuric acid (HCl or H2SO4). In the case of Looking in the right direction at the right time is more difficult during sun- the mixture involving HCl, the ingredients combine to form rise, which is why “sunrises” shown on TV are often sunsets played colloidal sulphur according to the reaction backwards. 9A. T. Young, “Sunset Science. III. Visual adaptation and green flashes,” J. Opt. Soc. Am. A 17, 2129–2139 (2000). Na2S2O3 2HCl 2NaCl SO2 H2O S : 10 þ ! þ "þ þ # T. S. Jacobsen, “On the spectrum of the green flash at sunset,” J. R. Astron. Soc. Canada 46, 93–102 (1952). 45,46 A simpler alternative that uses Dettol instead of special- 11C. J. P. Cave, “The ‘green flash’,” Nature 120, 876 (1927). ised chemicals is also available.47 A recent, spectrometer- 12R. M. Sutton, Demonstration Experiments in Physics (McGraw-Hill, New enhanced experiment that explores Rayleigh scattering is York, 1938), pp. 387–388. 13 described in Ref. 48. M. H. Moore, “Apparatus for teaching physics: Blue sky and red sunsets,” Phys. Teach. 11, 436–437 (1973). The mechanism for the color change of light scattered by, 14 E. Zhu and S. Mak, “Demonstrating colors of sky and sunset,” Phys. or transmitted through, the atmosphere is mostly Rayleigh Teach. 32, 420–421 (1994). scattering. This can be the topic for a separate experiment 15H. Kruglak, “Apparatus for teaching physics: A simplified sunset demon- with water waves, normally in a ripple tank, which stration,” Phys. Teach. 11, 559 (1973).
960 Am. J. Phys., Vol. 80, No. 11, November 2012 Johannes Courtial 960
Downloaded 11 Jan 2013 to 81.194.35.225. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission 16D. Pye, Polarised Light in Science and Nature (IOP Publishing Ltd., 34D. K. Lynch and W. Livingston, Color and Light in Nature, 2nd ed. (Cam- Bristol, 2001), Chap. 6. bridge U.P., Cambridge, UK, 2001), Chap. 1.9, p. 15ff. 17R. J. Strutt (Lord Rayleigh), “Normal atmospheric dispersion as the cause 35See
961 Am. J. Phys., Vol. 80, No. 11, November 2012 Johannes Courtial 961
Downloaded 11 Jan 2013 to 81.194.35.225. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission