What Causes the Green Flash at Sunset? The Numbers • The Science 360

Every clear sunset you have ever watched had a green edge on top of the Sun. It was there, in real light, and a pair of binoculars would have shown it. You did not see it because it was about 15 arcseconds thick, about the width of a 0.1 mm hair held 1.4 metres from your eye. The naked eye needs about 60. The green flash that people actually see, and photograph, happens on the evenings when the air near the horizon acts as a magnifying lens for that rim.

Most pages on the green flash get the first half of this right: refraction bends green light more than red, and blue gets scattered away. Few of them put numbers on it, and almost none explain why that textbook mechanism is far too small to see on its own. A minority still describe the flash as an afterimage, which it is not. Below we trace sunlight through a standard atmosphere and work out how thick the green rim is, how long it lasts and why a mirage is usually needed.

Quick answerAir refracts green light slightly more than red, so at the horizon the Sun's green image sits about 15 arcseconds above its red image. Blue is lifted more but scattered away. That green rim is too thin for the naked eye, so most visible flashes happen when a mirage near the horizon stretches it vertically for a second or two.

Infographic: What causes the green flash? A setting Sun sits half below a sea horizon with a thin green rim on top, and a magnifier shows the rim is 15 arcseconds thick. Air bends green light more than red, but the eye needs about 60 arcseconds, so a mirage must stretch the rim 4 to 8 times. A line chart shows how long the rim takes to sink: 1.2 seconds at the equator, 1.6 seconds at 40 degrees latitude, longer toward the poles. Tiles: refraction lifts the whole Sun 33.0 arcminutes, about 60 times more green than blue survives the horizon path, and violet is lifted 42.2 arcseconds but scattered away. Myth: the flash is not an afterimage. — Tap the image to view it full size. View the accessible, editable SVG.

How much does the atmosphere bend the setting Sun?

Light from the Sun enters the atmosphere at a shallow angle and passes into denser and denser air, which bends it downward along a curved path. You see the Sun along the direction the light arrives from, so it appears higher than it really is. At the zenith this effect is zero. At the horizon it is huge.

We traced rays through the US Standard Atmosphere (15 °C at sea level, temperature falling 6.5 °C per kilometre), using the Ciddor (1996) formula for the refractive index of air and integrating the bending layer by layer over a curved Earth.

Refraction at the horizon, 550 nm light

Refractive index of standard air: $n - 1 = 2.778\times10^{-4}$ .

Ray trace, US Standard Atmosphere, Sun's apparent centre on the horizon: 33.0′.

Bennett's (1982) formula, standardised to 10 °C and 101.0 kPa:

R = \cot\!\left(0^\circ + \frac{7.31}{4.4}\right) = \mathbf{34.5'}

The Sun's angular diameter is about 32′, so when the bottom of the Sun appears to touch a sea horizon, the whole Sun is geometrically below it.

Plot of atmospheric refraction in arcminutes against the Sun's apparent altitude from 0 to 10 degrees. The ray-traced curve starts at 33.0 arcminutes at the horizon, falls to about 18 at 2 degrees and 5 at 10 degrees. Bennett's formula runs just above it, starting at 34.5. A dotted line marks the Sun's 32 arcminute diameter. — Figure 1. Refraction versus apparent altitude, from our ray trace through the US Standard Atmosphere and from Bennett's empirical formula. The two differ by about 1.5′ at the horizon because they assume different temperatures and lapse rates; real sunsets vary by several arcminutes either way.

Refraction also falls steeply with altitude near the horizon, by about 11′ per degree. The bottom of the setting Sun is lifted more than the top, which squashes the disk into the familiar flattened oval. It also slows the apparent sunset, which matters for timing the flash.

Why does green light get bent more than red?

Air, like glass, has a refractive index that rises toward short wavelengths. The effect is tiny, but at the horizon it multiplies a 33′ total.

Dispersion of air (Ciddor 1996, standard air)

\begin{aligned}(n-1)_{650\ \mathrm{nm}} &= 2.7632\times10^{-4} \\ (n-1)_{530\ \mathrm{nm}} &= 2.7825\times10^{-4} \\ \text{difference} &= \frac{2.7825 - 2.7632}{2.778} \\ &= \mathbf{0.70\%}\end{aligned}

Refraction scales almost exactly with $n - 1$ , so green is lifted more than red by

0.70\% \times 33.0' \approx 0.23' = \mathbf{14''}

Full ray trace: 14.9″ for 530 nm, 32.6″ for 450 nm, 42.2″ for 420 nm.

So the setting Sun is really a stack of slightly offset images, one per colour, with the violet image highest. Through the body of the disk they overlap and add up to orange. Only at the top edge does the short-wavelength image stick out on its own, and at the bottom edge the red one does. That is the green upper rim and the red lower rim, and astronomers have recorded them since Pierre Bouguer described the blue upper limb in 1748.

Plot of how far each wavelength's image of the Sun is lifted above the 650 nm red image, in arcseconds, against wavelength from 420 to 700 nm. With the Sun on the horizon the curve falls from 42 arcseconds at 420 nm through 15 at 530 nm to zero at 650 nm. Curves for the Sun 2 and 5 degrees up are about half and a quarter as large. A dashed line at 60 arcseconds marks naked-eye resolution, well above all curves. — Figure 2. Extra lift of each colour's image relative to 650 nm red, from the ray trace. Even at the horizon, the whole spread from red to violet is smaller than the roughly 60″ the unaided eye can resolve.

Why is the flash green and not blue or violet?

If dispersion were the whole story, the last light to vanish would be violet. It is not, because the sunlight skimming the horizon has crossed a huge amount of air. Our ray trace gives an air mass of 38.2 at the horizon (that is, 38 times the air you look through straight up), and Rayleigh scattering removes short wavelengths fast over that path. This is the same scattering that makes the daytime sky blue, which we worked through in why the sky is blue and not violet.

Rayleigh transmission through 38.2 air masses (Bodhaine et al. optical depths)

\begin{aligned}650\ \mathrm{nm}:\ \tau &= 0.0492 \times 38.2 = 1.88 \\ T &= e^{-1.88} = \mathbf{15\%} \\ 530\ \mathrm{nm}:\ \tau &= 0.113 \times 38.2 = 4.31 \\ T &= \mathbf{1.3\%} \\ 450\ \mathrm{nm}:\ \tau &= 0.221 \times 38.2 = 8.45 \\ T &= \mathbf{0.021\%}\end{aligned}

Green arrives about 60 times stronger than blue, relative to the light each started with.

Log-scale plot of the fraction of light transmitted through 38 air masses against wavelength from 420 to 700 nm, coloured by wavelength. The curve rises from about 0.00001 at 420 nm through 0.021 percent at 450 nm and 1.3 percent at 530 nm to 15 percent at 650 nm. — Figure 3. Fraction of sunlight surviving Rayleigh scattering along the horizon path. Haze removes more at all wavelengths, and ozone's Chappuis band removes orange, which helps green stand out from yellow.

Two more filters act on the colour. Ozone absorbs in a weak band centred on orange, which Andrew Young (San Diego State University), who has studied green flashes for decades, credits with most of the orange removal. And haze or pollution can remove the green too, leaving a yellow flash. In exceptionally clean air enough blue survives for a rare blue flash.

Combine dispersion and scattering and you get the colour order on the top of the Sun: red, orange and yellow merged into the disk, then a green strip, then a faint cyan and blue fringe that has mostly been scattered away.

Magnified diagram of the top edge of the setting Sun drawn as overlapping arcs. Red, orange and yellow images merge into the disk. A green band sits 7 to 15 arcseconds above, labelled green rim. Faint light-blue bands extend to 33 arcseconds, labelled mostly scattered away. A vertical scale bar shows 60 arcseconds, the smallest detail the naked eye can resolve, much larger than the green band. — Figure 4. The top of the setting Sun as separate colour images, offset by the computed dispersion at the horizon. The vertical direction is stretched about 3 times relative to horizontal. The green rim is far thinner than the 60″ scale bar.

The misconception: the textbook green flash is too small to see

Here is where page 1 goes quiet. The usual explanation stops at "refraction separates the colours, the green is the last to set". That mechanism is real, but on its own it makes a rim 7 to 15″ thick, against a naked-eye resolution of about 60″ (the definition of 20/20 vision is resolving detail 1 arcminute across). That is 4 to 8 times too thin. Young's history of the subject credits Gerhard Dietze with showing in 1955 that the standard-atmosphere flash is "ten times smaller than the naked eye can see"; Dietze's factor includes contrast and brightness, not just geometry, but the conclusion is the same. Dietze published in an East German journal and the result was overlooked for about 40 years.

Young's own simulations of the standard-atmosphere sunset describe that textbook flash as "so puny it can only be seen through binoculars". In binoculars or a telephoto viewfinder, you can see the green rim on most clear evenings, and his advice is to look 5 to 10 minutes before sunset when the Sun is 3 or 4 diameters up. Do that with care: never point binoculars at the Sun while it is still bright and high.

So how does anyone see one?

Most naked-eye flashes need a mirage. The air just above the sea is rarely at the temperature the standard atmosphere assumes. When the water is warmer than the air, the bottom few metres of air are warmer and less dense, and rays are bent upward near the surface: an inferior mirage, the same effect as a "wet" road on a hot day. The setting Sun then shows an inverted image below its erect image, and the two join in an Ω shape.

Young's description of his inferior-mirage simulation, computed for an observer 4 m above sea level, is that the flash "appears where the erect and inverted images join", in "a narrow zone of sky parallel to the horizon that has very great vertical magnification". When the green rim reaches that zone it is stretched enough to be seen. From our numbers, the stretch has to be at least 4 to 8 times for a 7 to 15″ rim to reach 60″, which is our own estimate of the threshold.

When the water is colder than the air above it, you get the opposite: a temperature inversion. Rays bending around the inversion make a mock mirage, which slices thin strips off the top of the Sun and can tint a detached strip green. Under a strong inversion, a duct can trap light and produce the rarer sub-duct flash, which Wikipedia's summary of the literature puts at up to 15 seconds. All of these are refraction by layers below your eye level, not in the upper atmosphere.

Mirages and refraction this close to the horizon are also why the distance to the sea horizon is not quite what simple geometry predicts, which we calculate in how far is the horizon. And the same thin, layered air near the ground is what makes stars twinkle while planets don't.

Is the green flash an afterimage?

No, but there is a grain of truth in the idea. The afterimage claim falls apart at sunrise: flashes appear as the first sliver of the Sun breaks the horizon, before your eyes have been exposed to anything bright, and observers have reported sunrise flashes since the earliest records. Flashes are also photographed routinely, and a camera has no afterimage. Young points out that a real solar afterimage is much dimmer and bluer, and so inconspicuous that he knew of only two or three published observations of it.

The grain of truth is bleaching. If you stare at the low orange-red Sun for a few seconds, the red-sensitive pigment in your retina is partly used up. Young notes that this is enough to make most flashes look green at a stage where they photograph as yellow. So at sunset the colour you perceive is part physics, part physiology. At sunrise it is almost pure physics. The light is real either way.

Practical tips: watch a sharp, distant horizon (sea or a large lake is best). Do not stare at the Sun while it is still bright, both for your eyes and to avoid bleaching. Look only for the last few seconds. Try binoculars or a phone camera's zoom only once the Sun is reduced to a thin, dim sliver on the horizon. A sunrise flash is harder to catch, because you don't know exactly where the first sliver will appear, but its colour is the honest one.

How long does a green flash last?

The Sun moves across the sky at 15.04″ per second of time (360° in one sidereal day). Near the equator it sets almost vertically. At latitude φ, with the Sun on the celestial equator, its altitude falls at 15.04″ × cos φ per second. Refraction slows the apparent motion further: because refraction drops by about 0.19′ for every 1′ of altitude near the horizon, the apparent Sun sinks about 19% slower than the true one (a factor 1 / 1.19 = 0.84).

Time for a 15″ green rim to sink below a sharp horizon

The Sun moves 15.04″ per second; at latitude $\varphi$ it sinks at that rate times $\cos\varphi \times 0.84$ at the equinox.

\begin{aligned}t_{0^\circ} &= \frac{15}{15.04 \times \cos 0^\circ \times 0.84} \\ &= \mathbf{1.2\ s} \\ t_{40^\circ} &= \frac{15}{15.04 \times 0.766 \times 0.84} \\ &= \mathbf{1.6\ s} \\ t_{60^\circ} &= \frac{15}{15.04 \times 0.500 \times 0.84} \\ &= \mathbf{2.4\ s}\end{aligned}

Latitude 40° covers the Mediterranean and mid-USA; 60° is Oslo or Anchorage. Away from the equinoxes the Sun sets at an even shallower angle, so these are lower limits at a given latitude.

Plot of seconds for the setting Sun to sink by the green rim thickness against observer latitude from 0 to 70 degrees. For a 15 arcsecond rim the time rises from 1.2 seconds at the equator to 1.6 at 40 degrees, 2.4 at 60 degrees and 3.5 at 70 degrees. A 10 arcsecond rim gives two thirds of those values. — Figure 5. How long the green rim survives as the Sun sinks, for rim thicknesses of 10″ and 15″, Sun on the equator. A mirage changes the timing, since it stretches the rim, but the same latitude trend holds.

That matches the observing record: Young puts the green colour at "a second or two at moderate latitudes", and Wikipedia's summary notes that at the equator a flash rarely lasts longer than a second. At high latitudes in summer, where the Sun slides along the horizon, it can come and go repeatedly. The best-known case is the Byrd Antarctic expedition, which reported green seen on and off for 35 minutes as the Sun skimmed an uneven ice horizon. Young's account, drawing on the expedition meteorologist W. C. Haines, is that the individual flashes lasted from a fraction of a second to several seconds, spread over more than half an hour, not one continuous 35-minute flash.

Source note The Byrd expedition details (35 minutes, Haines's description) come from Young's fallacies page; we did not see the original 1929 report. The 15-second figure for sub-duct flashes is from Wikipedia's summary, not a primary source we opened.

Where did the idea of a green ray come from?

Jules Verne's 1882 novel Le Rayon vert (The Green Ray) popularised the phenomenon. The genuine "green ray", a green beam extending a few degrees up from the horizon after sunset, does exist, but it is much rarer than the "green dot" or flattened green segment most people see, and it needs hazy air to light up the beam.

FAQ

What causes the green flash at sunset?

The atmosphere refracts green light slightly more than red, so the green image of the Sun sits about 15 arcseconds higher than the red one at the horizon. Blue and violet are lifted even more but are scattered away along the long horizon path. A mirage near the horizon usually stretches that thin green rim enough for the naked eye to see it for a second or two.

Is the green flash an afterimage?

No. Green flashes are seen at sunrise, before the eye has been exposed to the Sun, and they are routinely photographed. Staring at the red setting Sun does bleach the red-sensitive pigment in your eye, which can make a yellowish flash look greener, but the flash itself is real light.

How long does a green flash last?

Usually a second or two. Without a mirage the green rim takes about 1.2 seconds to sink at the equator and about 2 seconds at 55 degrees latitude, because the Sun sets at a shallower angle further from the equator. Rare duct displays last longer, up to about 15 seconds.

Do you need an ocean horizon to see a green flash?

No. Flashes are seen over land and from mountains too. A sea or large lake horizon helps because water's temperature differs from the air above it, which creates the mirages that magnify the green rim, and because the horizon is sharp and distant.

Why is the flash green and not blue?

Blue and violet are refracted even more than green, but at the horizon sunlight passes through about 38 times more air than overhead. Rayleigh scattering alone then lets through about 1.3% of 530 nm green but only about 0.02% of 450 nm blue. In exceptionally clear air a blue flash is occasionally seen.

Sources

A. T. Young, San Diego State University, "An Introduction to Green Flashes": aty.sdsu.edu
A. T. Young, "Simulation of the Textbook Green Flash" (binocular visibility, timing advice, Bouguer 1748): aty.sdsu.edu
A. T. Young, "Simulation of the Inferior-Mirage Green Flash at Sunset" (4 m observer, magnification zone): aty.sdsu.edu
A. T. Young, "Green-flash Fallacies and Misconceptions" (afterimages, bleaching, Dietze 1955, Byrd expedition, ozone): aty.sdsu.edu
P. E. Ciddor, "Refractive index of air: new equations for the visible and near infrared", Applied Optics 35, 1566 (1996), via refractiveindex.info: refractiveindex.info
B. A. Bodhaine et al., "On Rayleigh optical depth calculations", J. Atmos. Oceanic Technol. 16, 1854 (1999): PDF via Colorado State University
Wikipedia, "Atmospheric refraction" (Bennett and Sæmundsson formulas): en.wikipedia.org/wiki/Atmospheric_refraction
Wikipedia, "Green flash" (types, durations, Verne 1882): en.wikipedia.org/wiki/Green_flash

Method note: refraction, dispersion and air mass are computed by integrating rays through a spherically layered US Standard Atmosphere 1976 (sea-level observer, dry air) with the Ciddor refractive index. Transmission includes Rayleigh scattering only. Real sunsets have non-standard temperature profiles near the surface, which change horizon refraction by several arcminutes and create the mirages discussed above; those are not modelled here.

Header image: NASA (image STS067-709-007), regraded for this article.

How much does the atmosphere bend the setting Sun?

Why does green light get bent more than red?

Why is the flash green and not blue or violet?

The misconception: the textbook green flash is too small to see

So how does anyone see one?

Is the green flash an afterimage?

How long does a green flash last?

Where did the idea of a green ray come from?

FAQ

What causes the green flash at sunset?

Is the green flash an afterimage?

How long does a green flash last?

Do you need an ocean horizon to see a green flash?

Why is the flash green and not blue?

Related on The Science 360

Sources