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A Simple Experiment That Demonstrates the “Green Flash”

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A Simple Experiment That Demonstrates the “Green Flash” $VLPSOHH[SHULPHQWWKDWGHPRQVWUDWHVWKH³JUHHQIODVK´ -RKDQQHV&RXUWLDO &LWDWLRQ$P-3K\V GRL 9LHZRQOLQHKWWSG[GRLRUJ 9LHZ7DEOHRI&RQWHQWVKWWSDMSDDSWRUJUHVRXUFH$-3,$6YL 3XEOLVKHGE\WKH$PHULFDQ$VVRFLDWLRQRI3K\VLFV7HDFKHUV 5HODWHG$UWLFOHV 5HIOHFWLRQRIDSRODUL]HGOLJKWFRQH $P-3K\V (QHUJ\DQGPRPHQWXPHQWDQJOHPHQWLQSDUDPHWULFGRZQFRQYHUVLRQ $P-3K\V 7KH³UDLQERZ´LQWKHGURS $P-3K\V 1RYHOFDVHVRIGLIIUDFWLRQRIOLJKWIURPDJUDWLQJ7KHRU\DQGH[SHULPHQW $P-3K\V 7KH2SWLFVRI/LIH$%LRORJLVW¶V*XLGHWR/LJKWLQ1DWXUH $P-3K\V $GGLWLRQDOLQIRUPDWLRQRQ$P-3K\V -RXUQDO+RPHSDJHKWWSDMSDDSWRUJ -RXUQDO,QIRUPDWLRQKWWSDMSDDSWRUJDERXWDERXWBWKHBMRXUQDO 7RSGRZQORDGVKWWSDMSDDSWRUJPRVWBGRZQORDGHG ,QIRUPDWLRQIRU$XWKRUVKWWSDMSGLFNLQVRQHGX&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.
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