Twenty metres down, a diver can still see the sunlit surface. To almost every other kind of light, the same water is as dark as a wall.
Chapter 8 · Beyond the visible
The Window
Water, and the light it lets through. Why is it clear, and why does that answer the question chapter 7 ended on?
Look first
How far each colour goes
Shine light into a long column of the purest water, and it fades as it goes. The distance over which it dims to about a third (more exactly, to 1/e, 37%) is a fair measure of how clear the water is to that light.
For the colours you can see, that distance is long. Blue light travels more than a hundred metres, and blue-green about fifty. Red fades much sooner, in a few metres, which is why underwater photographs turn blue, and why a deep pool of clean water, or the inside of a glacier, is blue even with no sky above it.
Distance in pure water before light dims to 1/e. Pure water is very slightly blue.
Commit to a prediction
Six times the wavelength
Now take infrared light at a wavelength of 3 micrometres. That is about six times the wavelength of the blue-green light that goes fifty metres, and about four times that of red.
How far does it go into the same water?
Both axes are logarithmic: each step is ten times the last. The curve spans more than ten factors of ten.
Why the first guesses made sense
Clear is a word made by eyes
If you chose tens of metres, you trusted the most familiar fact about water: you can see through it. But you can see through it because your eyes use only light that water lets through. Every judgement of “clear” you have ever made was made in that band. To an eye that saw at 3 micrometres, a glass of water would be as black as ink.
If you chose centimetres or a millimetre, you followed the trend from blue to red, and you were right that it keeps going. What no trend could tell you is how fast: past the red the distance does not shrink by a few times. It falls by a factor of ten every few hundred nanometres, and by 3 micrometres it has fallen by tens of millions from its value in the blue-green.
The bench
What water does with light
A water molecule can take energy from light in three ways, and each one closes the window somewhere. Far into the ultraviolet, light has enough energy to lift an electron, and is stopped within nanometres. In the infrared, light at the right frequency shakes the molecule: the hydrogens stretching against the oxygen near 3 micrometres, and bending near 6. Further out, at microwave wavelengths, it sets the molecules turning, which is how a microwave oven heats food at 12 centimetres.
Between the electrons and the shaking there is a gap. Light in it has too much energy to rock the molecule gently and too little to lift an electron, so water has almost nothing to do with it. That gap is the window. Its faint red edge comes from overtones of the shaking, which reach weakly into the visible and give water its blue.
Move through the spectrum, and then go down into the water.
The window
What you can now say
Water is clear only in a narrow window, from the near ultraviolet to the deep red, and our eyes see inside it. Everywhere else, light is stopped within millimetres or less.
The first eyes evolved in the sea, more than half a billion years ago. Whatever they used had to be light that water lets through. The band you see is, very likely, the shape of that window.
For the determined reader: the numbers, the data, and the limits
The quantity
Light of intensity I0 entering water keeps I = I0 e−αz after a path z. The absorption coefficient α is related to the imaginary part k of water’s refractive index by α = 4πk/λ. The distance 1/α is the 1/e depth used throughout this chapter.
| Wavelength | What water does | 1/e depth |
|---|---|---|
| 150 nm | lifts electrons | |
| 250 nm | near ultraviolet: clear | |
| 418 nm | the clearest point | |
| 650 nm | overtones begin: red fades | |
| 2950 nm | O–H stretch | |
| 6100 nm | H–O–H bend | |
| 12 cm | molecules turning (a microwave oven) |
The data
From 380 to 727.5 nm: R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Applied Optics 36 (1997), the most careful measurements of water in the visible, which found it far clearer in the blue than earlier work. Elsewhere, from 90 nm to 12 cm: D. J. Segelstein, “The complex refractive index of water,” MSc thesis, University of Missouri–Kansas City (1981), a compilation of many measurements. Both are tabulated by S. Prahl at the Oregon Medical Laser Center. The older compilation put the clearest point near 485 nm and about 54 m; Pope and Fry moved it to 418 nm and more than 220 m. The shape of the window is unchanged.
Where this stops
This is pure water. Sea water adds salt, which conducts electricity and makes long radio waves stop within metres, and plankton and dissolved matter, which absorb blue and turn coastal water green. Pure water becomes clear again for radio waves many metres long, a second window that salt closes. And the window’s edges are not where vision stops for every animal: bees, many birds and many fish see into the near ultraviolet, which water also passes. Human lenses absorb it.
A case you have not seen
A snake’s sense, under water
Pit vipers hunt in the dark with a sense we lack: a pair of pits on the face, lined with a membrane that warms when infrared light falls on it. A mouse at body temperature glows most strongly near 9 micrometres, and a snake can strike it from tens of centimetres away, through air.
Could a fish evolve the same sense, to find warm prey under water?
The snake’s sense is a use of air’s own windows, and only works on land. Under water, warm bodies still glow, but their glow is absorbed before it has crossed the thickness of a hair. A fish that wants to find warm prey has to use something else: smell, pressure, electric fields. Several kinds of fish do exactly that.
Why is the sea blue?
For much of the nineteenth century the favourite answer was that the sea is blue because it reflects the sky. Lord Rayleigh, who had explained the blue of the sky itself, said as much.
In 1921 the young Indian physicist C. V. Raman sailed to Europe, and spent the voyage looking at the Mediterranean through a polarising prism, which cut out the reflected skylight. The water stayed a deep blue. He wrote to Nature that the colour came from the water itself, from light scattered by its molecules, and the question set him on the work that led to the Raman effect and a Nobel Prize.
Raman was right that the blue belongs to the water, and the full answer turned out to involve the window in this chapter. Scattering plays its part, but in deep, clean water the greater part of the colour comes from absorption: the overtones of the molecule’s shaking reach just far enough into the visible to take a little red out of every metre. That makes water unusual. Almost every other colour in nature comes from electrons; water’s comes from the vibrations of its molecules.
Where this explanation stops
Other windows
Air has windows too, and they are not the same as water’s. It passes the visible, a few bands of infrared, and radio waves from about a centimetre to tens of metres, which is why radio astronomy can work from the ground and X-ray astronomy cannot. Every instrument in this exhibition, the pinhole, the lens, the polariser, the detector, the eye, and Herschel’s thermometer, works inside some window, and sees only what that window lets through.
If our eyes are the shape of a window in water, what else in how we see the world is the shape of where we came from?
End of chapter 8
Added to your notebook
Water is clear only in a narrow window, and our eyes see inside it. Everywhere else, light is stopped within millimetres or less.
Water has a window. Does the air?
Chapter 9 · Windows in the Sky