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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 least a few minds—by an air of mystery. I describe a
simple experiment that demonstrates different aspects of the green flash. The experiment uses an
odd-shaped, water-filled, fish tank to simulate the refractive properties of the atmosphere; milk
powder added to the water mimicks the atmosphere’s scattering properties. A circular whitelight 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.
C 2012 American Association of Physics Teachers.
V
[http://dx.doi.org/10.1119/1.4746384]
I. INTRODUCTION
There are many colors in the sky: white and various
shades of gray come from the clouds; blue comes from the
cloudless daytime sky; and yellow, orange, and red come
from the sun as it traverses the sky from sunrise to sunset.
The sky is not normally green, which makes it all the more
surprising when part of it appears green. Such a situation
occurs in rainbows1 and during the green flash.2
The green flash can occur during sunset, just before the top
segment of the sun disappears behind the horizon, or during
sunrise, just after the sun’s top segment appears above the horizon. 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
conditions. Normally, the sunrise or sunset needs to be visible
low on the horizon, which is one of the reasons why the seaside is a good place to observe it. Also, the sky needs to be
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
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.
During the polar summer, a green flash has been observed to
last for more than 30 min.2 A more typical duration for the
green flash at temperate latitudes is on the order of a second.3
Relatively few people have seen the green flash, which is
perhaps why it has acquired something of an air of mystery
and a fair number of nonsensical associations.4 One such
example is “one of the numerous inexplicable legends of the
Highlands” apparently invented by Jules Verne for his novel
“The Green Ray” (French “Le Rayon vert”),4 which asserts
that “this ray has the virtue of making him who has seen it
impossible to be deceived in matters of sentiment.”5 Perhaps
surprisingly, the green flash actually occurs frequently; 3,4,6
the relative scarcity of its observers is due to the fact that in
non-polar regions it requires looking from the right place,7 in
the right direction, at the right time.8 Even when it is
observed, it is sometimes unclear whether what was seen
was actually a green flash or merely appeared green due to
physiological effects, specifically bleaching of the cone photopigments.9 To be certain, one can record spectra,10 take
photos (taking special care with white-balance settings), or
observe the green flash at sunrise.3,11
A number of experiments that demonstrate aspects of
the green flash have been previously described, usually
955
Am. J. Phys. 80 (11), November 2012
http://aapt.org/ajp
demonstrating either the mechanism that colors the setting
sun’s upper and lower edges (e.g., Ref. 3), or the mechanism
by which the atmosphere scatters purple and blue light.12–16
A lengthy literature search uncovered very few experiments
that demonstrate both at the same time.17,18 Here I describe
an experiment that demonstrates both of these aspects of the
green flash, and arguably other, less well-known aspects.
The experiment uses only inexpensive, commercially available equipment; namely, a non-cuboid aquarium, water, milk
powder, and a bicycle light. This experiment was developed
to demonstrate the green flash for an episode of the BBC
documentary series “Coast.”19
II. OPTICS OF THE GREEN FLASH
This section provides a brief explanation of the green flash
followed by some refinements on different aspects of this
explanation.
A. Brief explanation of the green flash
The green flash can be explained in two steps:
(1) When looking at the sun at sunset, an observer is looking
through an “atmospheric prism”—a prism-shaped piece of
the atmosphere. Just like looking through a glass prism of
suitable orientation, the observer sees displaced images
of the sun in all colors of the rainbow, with the red image
at the bottom and the blue/purple image at the top. As the
sun sets, these images disappear behind the horizon, one
by one, and the last one to disappear is the blue/purple
image. (At sunrise, the time sequence is reversed, and so
the blue/purple image of the sun is the first to appear
above the horizon.) When it is visible, the light from this
top, blue segment of the sun is called a blue flash.
(2) But the green flash is green, not blue. This is because
under green-flash conditions much of the blue light has
been scattered out of its original path by the atmosphere.
Thus, no blue image of the sun will be visible, which
means that the top image—the last to disappear behind
the horizon at sunset (or the first to appear at sunrise)—is
green.
In the brief explanation above, there are a number of points
that require clarification—a number of details ranging from
C 2012 American Association of Physics Teachers
V
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955
interesting to important have been left out in the interest
of brevity. These details are discussed in Secs. II B to II H.
B. The atmospheric prism
The first clarification concerns the “atmospheric prism”
through which any observer of a green flash views the sun.
Unlike the material of a prism, the atmosphere does not end
in a sharp outer boundary but instead becomes thinner20 with
altitude. This lack of a sharp boundary is reflected in the
multitude of definitions relating to the edge of the atmosphere. For example: the US definition of an astronaut is anyone who has flown more than 50 miles above sea level;21 the
K!arm!an line, 100 km above sea level, is the approximate altitude at which aircraft must travel faster than orbital velocity
for the aerodynamic lift to support their weight;21 and during
atmospheric reentry of spacecraft, atmospheric effects
become noticeable at an altitude around 120 km.22
The thinning of the atmosphere with altitude gives rise to
a refractive index that varies with altitude. Refraction due
to such an atmosphere can be described mathematically in
considerable detail,23 but for the purposes of this paper a
simplified description suffices. The atmosphere is actually
much thinner than the sketch in Fig. 1 would suggest, so
much so that the layers of constant refractive index are
almost parallel. But the angle change on transmission
through such a structure is very simple. When a light ray
arrives from space (refractive index n0 ) at an angle a0 with
respect to the vertical direction (which is also the normal to
the layers of constant refractive index) and enters the first
atmospheric layer (refractive index n1 ), Snell’s law states
that its new angle with the vertical direction a1 is given by
the equation n0 sin a0 ¼ n1 sin a1 . In the same way, the
direction change upon entering the next atmospheric layer
is governed by the equation n1 sin a1 ¼ n2 sin a2 . One side
of these two equations is the same, namely, n1 sin a1 , and so
we can directly write n0 sin a0 ¼ n2 sin a2 . In other words,
the intermediate layer does not have any effect on the overall light-ray-direction change. This is true not only for one
intermediate parallel layer but also for any number of such
layers. Therefore, the angle by which sunlight is deflected
can be calculated approximately from Snell’s law using the
refractive index of the vacuum of space on one side
(n1 ¼ 1), and the refractive index of the atmosphere at the
observer (n2 " 1:0003 for green light and pure air at sea
level24) on the other.
Let us refine our model of atmospheric refraction slightly.
We still consider only refraction at one interface between
vacuum and the atmosphere at the observer, but we now
allow this interface to be angled. From the deflection angle
of rays from the sun at sunset (approximately 40 arc
min24,25) and the refractive index of air at sea level, it is possible to calculate
an inclination angle with respect to the hor#
izontal of 1:8 . If the prism shown in Fig. 1 was made from a
material with a refractive index the same as that of air at sea
level, the interior angle of the prism’s left corner (when ori#
entated as shown in Fig. 1) must be very acute, namely, 1:8 ,
to mimic atmospheric refraction.
As an aside, it is worth mentioning another effect of
atmospheric refraction. When the sun’s upper edge disappears behind the horizon, its light rays reach the atmosphere
from a direction that is well below the horizon. When seen
near the horizon, the sun appears approximately 40 arc min
higher in the sky than its actual position.24 For comparison,
the angular diameter of the
sun when it is high in the sky is
#
about 30 arc min (" 0:5 ), and when it is low in the sky it
appears flattened to a vertical angular extent of around 24
arc min.26 Thus, by the time the sun’s lower edge first
touches the horizon, all light rays from the sun (including its
upper edge) reach the Earth from a direction below the
horizon.
C. The images of the sun in the colors of the rainbow
According to the brief explanation in Sec. II A, the atmospheric prism creates displaced images of the sun in all colors
of the rainbow. This point can benefit from clarification.
The displaced images of the sun in the colors of the rainbow an observer sees do not actually look like a rainbow, as
the brief explanation might suggest. Instead, only the top and
bottom of the sun appear colored. An observer with narrowband filters would see that the images of the sun seen in different 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 atmosphere). 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 primary rainbow.
D. Atmospheric scattering
Fig. 1. (Color online) Light rays from the sun’s top edge pass through a
segment of the atmosphere that is approximately equivalent to a prism,
resulting in refraction and dispersion such that light rays with different
colors reach the observer from different vertical angles (blue on top, red
on bottom). Under green-flash conditions, red and yellow rays have disappeared 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
reach the observer. The diagram is not drawn to scale. (Image of Earth from
<http://en.wikipedia.org/wiki/File:The_Earth_seen_from_Apollo_17.jpg>.)
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Am. J. Phys., Vol. 80, No. 11, November 2012
The change in color of light as it travels through the
atmosphere is more complicated than the brief explanation
in Sec. II A suggests. The dominant effects are absorption of
yellow light by water vapor and ozone, and Rayleigh scattering, especially by aerosols.2,4 We concentrate on these dominant effects here.
Rayleigh scattering is particularly important; it affects all
light, but blue light is scattered much more than red light
because the intensity of scattered light varies inversely as the
fourth power of wavelength: I / I0 k$4 , where I0 is the
Johannes Courtial
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956
intensity of the incident light. In any direction away from the
sun we see the sky in scattered light, which is the reason why
the (clear) daylight sky is blue.27 When the sun is seen
through a thick atmosphere—at sunrise or sunset—it typically looks orange or red because much more blue light has
been scattered away than red light.
Different atmospheric concentrations of the contributing
scatterers and absorbers will lead to a different color of the
top segment of the sun and a flash of a different color. Too
little scattering, due to extremely clear air or a shorter path
through the atmosphere when a flash is observed looking
upwards,28 leads to a blue or violet flash;2 too much scattering leads to a not-so-surprising red flash. As a rule of thumb,
a pale orange (not red) setting sun is a good candidate for
producing a green flash.2,18
E. Enhancement through mirage effects
A very important detail that has been left out of the brief
explanation in Sec. II A is the role mirages play in the green
flash. As described above, the green flash is not visible to a
naked-eye observer without being enhanced in some way.29
The only natural phenomenon that can cause such an
enhancement appears to be a mirage4,29—the bending of
light rays during transmission through the atmosphere that
results in the apparent displacement and distortion of
objects.30 As a suitably strong mirage occurs only occasionally, this is consistent with observations that the green flash
is “notoriously capricious in its appearance,”17 and specifically that it is not visible with the naked eye in many sunsets
but that it is visible when mirages of other objects are apparent.31 There are two aspects to consider:
(1) In the absence of a mirage, the green segment of the
rising or setting sun cannot be resolved by the unaided eye.
Given that the refractive index of pure air at sea level is
about nair ¼ 1:0003 (green light) compared to nvac ¼ 1 for
the vacuum of space, the different colored discs of the sun
are very close together, being dispersed by approximately 1
arc min.29 As a result, the angular extent of the unenhanced
green rim is of order 10 arc sec,32,33 significantly smaller
than the angular resolution of the unaided eye (%1 arc
min).2,17 A mirage can stretch the width of the green rim to
several arc minutes, thereby making it resolvable to the
unaided eye.4
This is consistent with the following quote from Ref. 4:
“Perhaps one sunset in five or six offers a naked-eye green
flash from the California coastline; with modest magnification, nearly all sunsets do. So go ahead and look!” It is
worth noting that looking at the setting sun through binoculars is considered safe, provided the sun is sufficiently
low.4
(2) The previous point only prevents a naked-eye observer
from resolving the green flash, but it does not stop the observer from seeing the green light. However, calculations
show that the unenhanced green light from the top segment
of the low sun is too faint to be visible against the sunset
sky.29 By partially focussing light from the green rim onto
the observer, a mirage can increase the power of green light
that enters the observer’s eye to visible levels.
F. Duration of the green flash
It is interesting to discuss briefly the duration of the green
flash. The duration of a green flash that is not enhanced by a
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Am. J. Phys., Vol. 80, No. 11, November 2012
mirage—as described in Sec. II A—is inversely proportional
to the vertical speed of the sun at the horizon.29 This speed,
in turn, depends on the latitude of the observer’s position
and the time of year. In polar regions during summer, the
sun can graze along the horizon with a very small vertical
speed. The resulting green flash will be correspondingly
long, so the half-hour on-off green flash mentioned in the
introduction is perhaps not terribly surprising. In central
Europe (or similar latitudes), the top segment of the setting
sun is green for about 1.5 s.29
This duration also appears to be the typical duration for a
mirage-enhanced green flash seen by naked-eye observers.
For example, regarding the duration of the green flash,
Ref. 2 states that “[i]t only lasts for a second or two.” On the
other hand, a mirage-enhanced green flash can also last
significantly longer. According to Ref. 9, which presumably
refers to the latitudes and conditions of California, “real
green flashes can last as long as 15 s (although this is possible only for certain rare types of flash).”
Note that physiological effects (Sec. II G) can make a
green flash appear significantly longer than it actually is.
G. Physiological effects
It is worthwhile to expand briefly on the theme of physiological effects mentioned in the introduction.
Physiological effects can alter the color perceived by a
green-flash observer, resulting in flashes that are not actually
green despite being perceived as such.9 For example, a yellow flash can appear green due to visual adaptation. This is
caused by photobleaching of the pigment in an observer’s
retina that is sensitive to red light, which reduces sensitivity
to red light and can therefore make yellow light appear
green.4,9
The effects of photobleaching typically persist for several
minutes. Photobleaching can therefore give the illusion of a
green flash that lasts minutes, a timescale that is too long to be
an ordinary green flash at temperate latitudes.9 Reference 9
lists a number of reports of observations of extraordinarily
long green flashes which appear to be due to this effect.
H. Green ray, green flash, green segment
The final clarification concerns the term green flash itself.
The terms “green flash” and “green ray” are widely used for
a number of effects that are related but slightly different.
There is green-ness in all of them, but neither are all of them
flash-like nor do all of them possess ray characteristics.
At least three effects can easily be distinguished:
(1) When hazy air is illuminated by a beam of light, the column of air the beam intersects is visible. If the column of
air is illuminated by sunlight, this is called a crepuscular
ray.34 The very rare green ray is probably a crepuscular
ray that is illuminated by a particularly bright green
flash.4
(2) The effect for which the term green flash seems entirely
appropriate is the brief appearance to the naked-eye observer of green light during a mirage-enhanced sunset.
(3) There is also the more frequent green rim of the setting
sun that is visible only through binoculars or on photographs. In an attempt to differentiate it from related phenomena, it has been called—and perhaps should be
called more often—the “green segment.”29
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957
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 surface of the water indicates a horizontal cross-section of the
aquarium, which changes slightly with height. The horizontal 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 prismshaped 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 nonscattered light to be observed with the naked eye over a wide
range of scatterer concentrations; the lamp’s wavelength
spectrum subjectively gives the beam the color of daylight,
and it contains significant amounts of red, blue, and green
wavelengths so that all aspects of the demonstration experiment can be observed.
The scattering properties of the atmosphere are simulated
by adding sub-wavelength-sized scatterers to the water in the
aquarium. One easy way of doing this is to add small
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
the photo was taken with the white light source illuminating it from the
right, and with some milk powder added to the water. The light scattered in
the water is blue for the same reason that the clear daytime sky is blue.
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Am. J. Phys., Vol. 80, No. 11, November 2012
Fig. 3. (Color online) Images of the light source taking path 1 in Fig. 2.
Image (a) was taken with the aquarium filled with clear water, image (b)
was taken with some milk powder added, and image (c) was taken after yet
more milk powder had been added. Image (d) was taken with the same concentration of milk powder as in (c), but a piece of black card was inserted
between the aquarium and the camera to simulate the horizon.
amounts of milk powder to the water.15 Here, with the aquarium filled to roughly three liters of water, the milk powder is
added in successive small pinches (about 10 pinches per teaspoon) 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. 4. (Color online) Images of the light source taking path 2 in Fig. 2. As
in Fig. 3, the series of images from (a) to (d) shows the view with increasing
amounts of milk powder added to the water, beginning with no milk powder
at all. In image (d) the green segment is no longer visible.
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958
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 record 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 camera; 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 segments 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
orange/yellow, as shown in Figs. 3(b) and 3(c). Importantly,
note that the purple segments seen on the left in Fig. 3(a) first
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
segment of the low sun is green.
Figure 3(d) represents the situation when the sun is so low
that only the green segment and a small portion of the yellow
segment are visible above the horizon. The artificial horizon
in our experiment was a black card that was inserted by
hand between the aquarium and the camera.37 The situation
represented by Fig. 3(d) is an example of when the green
flash would be seen if it were not too dim to be visible29
(see Sec. II E); it therefore demonstrates the physics of the
green flash at the level of the brief explanation in Sec. II A.
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
prism angle is smaller than in Fig. 3, the dispersion angle is
smaller. The green segment can still be seen in frames (b)
and (c) but it is smaller than in Fig. 3; its angular size is
now slightly closer to the low sun’s green segment that has
not been enhanced by a mirage—so small that it requires
binoculars or other optical instruments to be resolvable
(see Sec. II E). In frame (d), so much milk powder has been
added to the water that almost all colors other than red have
been scattered out of the transmitted light. The image of the
light source now looks uniformly orange and the green
segment is no longer visible, a fact that is consistent with the
rule of thumb that a red sunset is not a good candidate for
producing a green flash.2,18
Figure 5 shows an image of the aquarium taken from a distance of a few meters. The aquarium is orientated such that
light from the source travels along path 2 to reach the camera. This image shows a number of things.
(1) The colors of the light source, the scattered light, and the
unscattered light are clearly different: the light source,
visible to the right of the aquarium, is white; the scattered light, visible in the right part of the aquarium, is
blue (although not very bright in the image); and the
unscattered light, visible in the left part of the aquarium,
is mainly orange.
(2) The curvature of the aquarium sides is now important.
The effect of this curvature can be approximated as the
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Am. J. Phys., Vol. 80, No. 11, November 2012
Fig. 5. (Color online) Green segment, enhanced by an artificial mirage (left
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
side of the tank); and light source, seen directly to the right of the tank.
addition of a cylindrical lens (with a vertical axis) to the
prism formed by the water in the aquarium. Moving the
camera away from the aquarium results in the image
being stretched sideways.38 This stretching is significant
enough that only a small part of the image can be seen in
the left part of the aquarium in Fig. 5. It is to minimize
such distortion that the images in Figs. 3 and 4 were taken
with the camera as close as possible to the aquarium.
(3) The distortion of the image, in combination with reflection off the flat side of the aquarium (the top side in
Fig. 2), is a crude simulation of a mirage that is seen to
magnify the green(ish) part of the image.
IV. POSSIBLE EXERCISES
The theoretical and practical details of the demonstration
experiment outlined above provide numerous opportunities
for students to explore related topics. I outline a few possibilities below.
A. Observations in nature
First and foremost, students should keep an eye out for the
real thing—the green flash occurring naturally. I would go so
far as to say that the demonstration experiment has succeeded if students look for the green flash the next time they
see a setting or rising sun (or better yet whenever they see a
setting or rising sun for the rest of their lives). Of course,
instructors should encourage their students to do so. In this
context it is worth reiterating that looking at a very low sun
is considered safe.4
Another effect that is readily observable in nature, and
which students should be able to explain from what they
know about atmospheric refraction, is the apparent flattening
of the low sun (or moon) due to a higher deflection of the
sun’s (moon’s) lower part compared to its upper part.26
I hope that the experiment described here raises students’
awareness of atmospheric optical phenomena, and more generally of optical phenomena in the outdoors and in nature.
Numerous amateurs and professionals have a particular fascination with this area of optics, and many wonderful books
are devoted to it.39,40
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959
B. Atmospheric refraction
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
at sea level, as was done in Sec. II B, simplifies the discussion of many related effects. As an introduction to these
related effects, students could be asked to work out, from the
deflection angle of rays and the refractive index of air at sea
level, the geometry of this equivalent prism and hopefully
arrive at the results listed in Sec. II B.
By comparing the deflection angle of light from the low sun
to the sun’s angular size, students should be able to work out
that the low sun (or moon) is actually completely below the
horizon even when its visible bottom edge is still above the
horizon. In this context, it might also be worth discussing
the so-called moon illusion, which makes the moon appear
unusually large when it is close to the horizon.41
Finally, mirages42 are an interesting atmosphericrefraction topic of special relevance to the green flash. Some
interesting theory, for example, about the formation and orientation of multiple images produced by mirages, can be
worked out and even illustrated by producing an artificial mirage using sugar solutions.30,43,44 If the demonstrator is willing to compromise the (relative) simplicity of the experiment
described here, and if a suitable container can be
found such
#
that the water prism can be turned through 90 without the
water spilling out, then perhaps the green-flash and artificialmirage demonstrations could even be combined.
C. Atmospheric scattering
Almost everybody has seen the blue color of the clear daylight sky and the red(ish) color of the low sun. Here, there is
an opportunity to experiment with the relevant parameters.
Specifically, it is possible to vary the concentration of scatterers, and to vary the length of liquid intersected by the line
of sight.
There are a number of alternative ways of simulating the
scattering properties of the atmosphere. One such experiment, sometimes called a “chemical sunset,” is particularly
memorable; it simulates not just a static situation, but also
the typical time evolution of the color of the setting sun. The
colors produced in this experiment can be very vivid and realistic—I still remember seeing this demonstration when I
was an undergraduate student (many setting suns ago). The
experiment involves a chemical reaction that creates the
scattering particles, and increases their concentration on a
timescale that allows a reddening of the artificial sun to be
observed on the timescale of a natural sunset.12–14 It uses sodium thiosulfate (Na2 S2 O3 , also known as “hypo”) and either
hydrochloric or sulfuric acid (HCl or H2 SO4 ). In the case of
the mixture involving HCl, the ingredients combine to form
colloidal sulphur according to the reaction
Na2 S2 O3 þ 2HCl ! 2NaCl þ SO2 " þH2 O þ S # :
A simpler alternative that uses Dettol45,46 instead of specialised chemicals is also available.47 A recent, spectrometerenhanced experiment that explores Rayleigh scattering is
described in Ref. 48.
The mechanism for the color change of light scattered by,
or transmitted through, the atmosphere is mostly Rayleigh
scattering. This can be the topic for a separate experiment
with water waves, normally in a ripple tank, which
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Am. J. Phys., Vol. 80, No. 11, November 2012
demonstrates that small objects scatter waves with smaller
wavelengths more strongly.49
D. Other exercises
The green-flash demonstration experiment described here
can be used as the starting point for more in-depth explorations of other topics. Students could, for example, be asked
to observe and explain what happens if the knife edge that
simulates the horizon is placed not between the aquarium
and the observer, but between the light source and the
aquarium.
The demonstration, especially if it is performed using a
camera, also provides an opportunity to learn about a camera’s white balance. It is worth mentioning how remarkable
it is that our visual system does this automatically so that we
do not normally notice that artificial light has a completely
different color from natural light.
V. CONCLUSIONS
The experiment described here demonstrates—and allows
experimentation with—the basic physics of the green flash.
It uses everyday, non-toxic ingredients and it touches upon
the important mirage aspect of the green flash.
The special appeal of this demonstration lies in the overlap
of a number of interesting areas (green flash, blue sky, red
sunset, mirages, etc.) and the fact that the experiment can be
performed using simple everyday pieces of equipment and
ingredients.
ACKNOWLEDGMENTS
Thanks to Richard Bowman and Nong Chen for useful discussions related to optics. Many thanks to Beth Paschke and
Adrian Lapthorn for help and advice on chemistry.
1
D. K. Lynch and W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge U.P., Cambridge, United Kingdom, 2001), Chap. 4.2, p. 103ff.
2
D. K. Lynch and W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge U.P., Cambridge, UK, 2001), Chap. 2.20, p. 48ff.
3
G. Johnson, “Experiments with flasks, prism and lamp explain rainbows
and sun’s green flash,” Pop. Sci. Monthly, 118, 52–53 October (1934).
4
A. T. Young, “Green flashes and mirages,” Opt. Photonics News 10, 31–
37 (1999).
5
J. Verne, The Green Ray (Sampson Low, Marston, Searle and Riving,
London, 1883).
6
B. E. Schaefer, “The green flash,” Sky Telesc. 83, 200–203 (1992).
7
The green flash is normally observed from the coast, as the horizon is then
particularly low and the light path through the atmosphere particularly
long. But it can also be seen over land, best from places with a low horizon
such as airplanes, mountain tops, and tall buildings (see Ref. 4).
8
Looking in the right direction at the right time is more difficult during sunrise, which is why “sunrises” shown on TV are often sunsets played
backwards.
9
A. T. Young, “Sunset Science. III. Visual adaptation and green flashes,” J.
Opt. Soc. Am. A 17, 2129–2139 (2000).
10
T. S. Jacobsen, “On the spectrum of the green flash at sunset,” J. R.
Astron. Soc. Canada 46, 93–102 (1952).
11
C. J. P. Cave, “The ‘green flash’,” Nature 120, 876 (1927).
12
R. M. Sutton, Demonstration Experiments in Physics (McGraw-Hill, New
York, 1938), pp. 387–388.
13
M. H. Moore, “Apparatus for teaching physics: Blue sky and red sunsets,”
Phys. Teach. 11, 436–437 (1973).
14
E. Zhu and S. Mak, “Demonstrating colors of sky and sunset,” Phys.
Teach. 32, 420–421 (1994).
15
H. Kruglak, “Apparatus for teaching physics: A simplified sunset demonstration,” Phys. Teach. 11, 559 (1973).
Johannes Courtial
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960
16
D. Pye, Polarised Light in Science and Nature (IOP Publishing Ltd.,
Bristol, 2001), Chap. 6.
17
R. J. Strutt (Lord Rayleigh), “Normal atmospheric dispersion as the cause
of the ‘green flash’ at sunset, with illustrative experiments,” Proc. R. Soc.
London Ser. A 126, 311–318 (1930).
18
R. J. Strutt (Lord Rayleigh), “Further experiments in illustration of the
green flash at sunset,” Proc. Phys. Soc. 46, 487–498 (1934).
19
“Coast” is a documentary series describing different aspects of Britain’s
coastline. Its scope ranges from science to fiction, occasionally in combination, like in the piece on the green flash (part of Series 7, Episode 1),
which contained a scientific explanation and told Jules Verne’s mythical
story.
20
More specifically its mass density decreases approximately exponentially
with altitude.
21
Wikipedia, “K!arm!an line,” <http://en.wikipedia.org/wiki/Karman_line>
(2011), last accessed 10/8/11.
22
Wikipedia, “Atmosphere of Earth,” <http://en.wikipedia.org/wiki/
Atmosphere_of_Earth> (2011), last accessed 10/8/11.
23
L. H. Auer and E. M. Standish, “Astronomical refraction: Computational
method for all zenith angles,” Astron. J. 119, 2472–2474 (2000).
24
D. K. Lynch and W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge U.P., Cambridge, UK, 2001), Chap. 2.17, p. 44f.
25
An arc minute is 1/60 of a degree.
26
D. K. Lynch and W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge U.P., Cambridge, UK, 2001), Chap. 2.19, p. 47.
27
G. S. Smith, “Human color vision and the unsaturated blue color of the
daytime sky,” Am. J. Phys. 73, 590–597 (2005).
28
Lord Kelvin (W. Thomson), for example, observed a Blue Flash from his
hotel room in the Alps as the sun was rising over Mont Blanc (Ref. 50).
29
G. Dietze, “Die Sichtbarkeit des ‘gr€
unen Strahls’,” Z. f. Meteorol. 9, 169–
178 (1955).
30
Wikipedia, “Mirage,” <http://en.wikipedia.org/wiki/Mirage> (2011), last
accessed 5/9/11.
31
J. Evershed, “The green flash at sunset,” Nature 111, 13 (1923).
32
An arc second is 1/60 of an arc minute, and therefore 1/3,600 of a degree.
33
D. J. K. O’Connell and C. Treusch, The Green Flash and other Low-sun
Phenomena (North-Holland, Amsterdam, 1958).
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34
D. K. Lynch and W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge U.P., Cambridge, UK, 2001), Chap. 1.9, p. 15ff.
35
See <http://www.lamptech.co.uk/Spec%20Sheets/WelchAllyn%20MR11%
2010W.htm> for details of the bulb.
36
Fluorescent-light illumination, color temperature approximately 4 000 K.
37
Note that inserting the artificial horizon on the other side of the aquarium—between the light source and aquarium—effectively makes the light
source smaller but does not change the fact that one of its sides appears
green and the other red.
38
Note that this is true only up to a distance that corresponds to the astigmatic image of the light source that has been produced by the cylindrical
lens.
39
M. G. J. Minnaert, Light and Color in the Outdoors (Springer-Verlag,
New York, 1992).
40
D. K. Lynch and W. Livingston, Color and Light in Nature, 2nd ed.
(Cambridge U.P., Cambridge, UK, 2001).
41
D. K. Lynch and W. Livingston, Color and Light in Nature, 2nd ed.
(Cambridge U.P., Cambridge, UK, 2001), Chap. 7.10, p. 226f.
42
D. K. Lynch and W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge U.P., Cambridge, UK, 2001), Chap. 2.23, p. 52ff.
43
S. Houde-Walter and G. Pierce, “Sugar water mirage,” Opt. Photonics
News 3, 50–51 (1992).
44
M. Vollmer, “Mirrors in the air: Mirages in nature and in the laboratory,”
Phys. Educ. 44, 165–174 (2009).
45
Dettol is the trade name of a liquid antiseptic that contains a number of
ingredients that are insoluble in water. When mixed with water, it produces an emulsion of oil droplets.
46
Wikipedia, “Dettol,” http://en.wikipedia.org/wiki/Dettol, last accessed
5/4/2012.
47
B. G. Eaton and J. B. Johnston, “More about light scattering demonstrations,” Am. J. Phys. 53, 184–185 (1985).
48
M. Liebl, “Blue Skies, Coffee Creamer, and Rayleigh Scattering,” Phys.
Teach. 48, 300 (2010).
49
T. A. Mitchell, “Teacher’s pet: Why is the sky blue and the sunset red?,”
Phys. Teach. 16, 282 (1978).
50
W. Thomson (Lord Kelvin), “Blue Ray of Sunrise over Mont Blanc,” Nature 60, 411 (1899).
Johannes Courtial
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961