Water is blue ... because water is blue

Pacific Ocean near Santa Barbara, California

One of the most appealing aspects of the ocean is the colour of the water, ranging from a greyish green to deep blue.

But wait a minute: When I pour water in a glass, it is a clear, transparent liquid. So, what is the cause of the blue colour of the sea? Is it the reflection of the blue sky, perhaps?

The answer is simple, and perhaps surprising: Water is blue, because water is blue.

Blue Oceans,

Actually, water is quite a transparent liquid, but not perfectly transparent. All substances to a certain degree absorb light, and as a consequence, the intensity of a beam of light spreading through matter drops exponentially with distance, as described by the so-called Beer-Lambert law. Pure water appears transparent because it takes a distance of the order of metres to reduce by half the intensity of light passing through it. And, what is most important for the apparent colour of water, the absorption depends on the wavelength of light, hence colour.

The blue curve in the following figure shows the so-called absorption spectrum of pure water (data via Optical Absorption of Water by by Scott Prahl).



The absorption spectrum gives, on the vertical axis, the so-called absorption coefficient as a function of the wavelength of light (as measured outside of the medium). The area marked in yellow corresponds to the range of visible light, reaching from deep blue (at a wavelength of about 380 nanometer) to red (at a wavelength of about 760 nanometer). At the left of the visible spectrum lies the ultraviolet, and at the right, where the absorption curve is climbing and going through several bumps, the infrared.

The absorption coefficient is the inverse of the distance along which the intensity of light drops by a factor of e = 2.718..., and is measured in "inverse centimetre". Hence, an absorption coefficient of a = 10⁻² cm⁻¹ means that it takes a distance of d = 1/a = 10² cm = 1 m for the intensity of light to drop by one e-folding.

Now, as we can see, the absorption coefficient is very different at the red end of the visible spectrum than at the blue end. The absorption coefficient is plotted in the figure on a logarithmic scale, and indeed, absorption is about one hundred times stronger at the red end of the visible spectrum than at the minimum of the curve, which at a wavelength just below 500 nanometer still lies in the range of blue.

But this, of course, explains the intrinsic colour of water: when light passes through large amounts of water, its red component is absorbed the strongest, and the blue component the least - and hence, pure water appears to be blue.

... Vibrations,

Actually, the strong increase of the absorption coefficient of water towards the infrared not only causes the blue colour of the ocean. It is also intimately linked to the molecular structure of water.

Molecules of water consist of two hydrogen atoms bonded to one oxygen atom in a kinked shape. Water molecules are not completely rigid, but they can vibrate in different ways. The most important ways of shaking, or "vibrational modes", are a symmetric stretching, called ν₁, a symmetric bending, called ν₂, and an asymmetric stretching, called ν₃:



As with any oscillatory system, vibrations are possible not just for these three modes, but also for higher harmonics - that is, overtones - and for combinations of different modes of oscillation. Indeed, bumps in the absorption curve of water can be identified with a combination of all three modes ("ν₁+ ν₂+ν₃"), with a combination of the first overtone of mode 1 and mode 3 ("2ν₁+ν₃"), and with a combination of the second overtone of mode 1 and mode 3 ("3ν₁+ν₃"). For the higher harmonics 2ν₁ and 3ν₁, the frequency of oscillation is higher, and hence, absorption occurs at shorter wavelengths.

... Heavy Water,

There is, interestingly, a very clever way to check experimentally this explanation of the blue colour of water by the vibration of its molecules: Just look at heavy water instead of normal water!

In heavy water, D₂O, the hydrogen atoms contain deuterons instead of protons, and hence have double the mass of "normal" hydrogen atoms. The electromagnetic forces bonding the hydrogen to the oxygen, however, are the same for heavy water and normal water. But this means that the frequencies of the different vibration modes of the molecule shift to lower values. It's the same phenomenon as when different masses are fixed to a spring: the higher the mass, the lower the frequency of oscillation.

As a consequence, one could expect the excitation of vibrations for the molecules of heavy water happens at lower frequencies than for normal water, hence at longer wavelengths. The increase of the absorption coefficient towards longer wavelengths could be expected to set in further in the infrared, barely touching the visible spectrum. And this is exactly what happens!

The following figure shows a measurement of the absorption spectra of normal and of heavy water, taken from WHY IS WATER BLUE? by Charles L. Braun and Sergei N. Smirnov, reproduced from J. Chem. Edu. 70(8) (1993) 612. The scale of the figures is linear, and the curves to the left are just scaled-up for a better visibility of the shape of the spectrum.



One can see that the bump corresponding to the mode 2ν₁+ν₃ is shifted form a wavelength of about 1,000 nm in normal water to about 1,300 nm in heavy water. There is an analogous shift towards longer wavelengths in all other features, and as result, the absorption spectrum of heavy water in the visible spectrum is nearly flat.

But this means that there are no marked differences in the absorption of light of different colours by heavy water. Thus, heavy water, different from normal water, should be colourless. And indeed, as shown in this photo by Braun and Smirnov, this is really the case!

While a long tube filled with normal water (left) looks blue due to the absorption of the red component of the visible spectrum, the tube filled with heavy water is colourless (from WHY IS WATER BLUE? by Charles L. Braun and Sergei N. Smirnov).

... and Real Oceans

Beautiful physics is hidden below the blue surface of the ocean. But when I tried to inform me a bit about all this, I've also learned that whole books have been written on the topic, and that "the complexity of sea water as a substance means that its optical properties are essentially different from those of pure water. Sea water contains numerous dissolved mineral salts and organic substances, suspensions of solid organic and inorganic particles, including various live microorganisms, and also gas bubbles and oil droplets. Many of these components [..] absorb or scatter photons." (Light Absorption in Sea Water by Bogdan Woźniak and Jerzy Dera, page 5).

Here is a comparison of the absorption spectra of samples of water taken from different places around the globe (Light Absorption in Sea Water, page 6).



Curve 5, which resembles most the absorption spectrum of water we have seen above, has been measured in a sample taken from the Tonga Trench in the Pacific Ocean, at a depth of 10,000 m. And curve 8, the uppermost flat one, has been measured in surface water from the Gulf of Riga in the Baltic Sea.

From the shape of this spectrum, I would guess the sea near Riga looks more grey than blue.

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Edit: The first version of the post falsely claimed that a microwave oven heats up food by setting into vibration the molecules of water. That's not correct: Microwaves, with frequencies in the range between 0.3 GHz and 300 GHz, corresponding to wavelengths from 1 mm to 1 m, have not enough energy to excite the vibrational modes of the water molecule. What the electromagnetic field of microwave frequencies does is to shake the water molecules by grappling them by their electrical dipole moments, and to set them in rotation. A detailed explanation can be found on Martin Chaplins unique site, Water Structure and Science", under Water and Microwaves.

Actually, the wavelength of microwaves is about a factor of 1000 longer than in the infrared and far infrared region where the vibrational absorption bands can be found. The vibrational bands in the infrared, though, make water vapour a strong greenhouse gas.

Thanks to all our readers who have pointed out the mistake to me, especially CIP and Jay!

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Tags: Physics, Colour, Blue