## The nature of light

Electromagnetic energy occurs in indivisible units referred to as quanta or photons. Thus a beam of sunlight in air consists of a continual stream of photons travelling at 3 x 108ms_1. The actual numbers of quanta Fig. 1.1 The relationship between hydrologic optics and other branches of optics (after Preisendorfer, 1976).

involved are very large. In full summer sunlight. for example, 1m2 of horizontal surface receives about 1021 quanta of visible light per second. Despite its particulate nature, electromagnetic radiation behaves in some circumstances as though it has a wave nature. Every photon has a wavelength, 1, and a frequency, n. These are related in accordance with

where c is the speed of light. Since c is constant in a given medium, the greater the wavelength the lower the frequency. If c is expressed in ms_1 and n in cycles s_1, then the wavelength, 1, is expressed in metres. For convenience, however, wavelength is more commonly expressed in nanometres, a nanometre (nm) being equal to 10 9m. The energy, e, in a photon varies with the frequency, and therefore inversely with the wavelength, the relation being e = hv = hc/1 (1.2)

where h is Planck's constant and has the value of 6.63 x 10 34 J s. Thus, a photon of wavelength 700 nm from the red end of the photosynthetic spectrum contains only 57% as much energy as a photon of wavelength 400 nm from the blue end of the spectrum. The actual energy in a photon of wavelength 1 nm is given by the relation e = (1988/1) x 10"19 J (1.3)

A monochromatic radiation flux expressed in quanta s"1 can thus readily be converted to Js"1, i.e. to watts (W). Conversely, a radiation flux, F, expressed in W, can be converted to quantas"1 using the relation quanta s"1 = 5.03 F1 x 1015 (1.4)

In the case of radiation covering a broad spectral band, such as for example the photosynthetic waveband, a simple conversion from quantas"1 to W, or vice versa, cannot be carried out accurately since the value of l varies across the spectral band. If the distribution of quanta or energy across the spectrum is known, then conversion can be carried out for a series of relatively narrow wavebands covering the spectral region of interest and the results summed for the whole waveband. Alternatively, an approximate conversion factor, which takes into account the spectral distribution of energy that is likely to occur, may be used. For solar radiation in the 400 to 700 nm band above the water surface, Morel and Smith (1974) found that the factor (Q/W) required to convert W to quantas"1 was 2.77 x 1018 quanta s^W"1 to an accuracy of plus or minus a few per cent, regardless of the meteorological conditions.

As we shall discuss at length in a later section (§6.2) the spectral distribution of solar radiation under water changes markedly with depth. Nevertheless, Morel and Smith found that for a wide range of marine waters the value of Q:W varied by no more than ±10% from a mean of 2.5 x 1018 quanta s"1W"1. As expected from eqn 1.4, the greater the proportion of long-wavelength (red) light present, the greater the value of Q:W. For yellow inland waters with more of the underwater light in the 550 to 700 nm region (see §6.2), by extrapolating the data of Morel and Smith we arrive at a value of approximately 2.9 x 1018 quanta s"1 W"1 for the value of Q:W.

In any medium, light travels more slowly than it does in a vacuum. The velocity of light in a medium is equal to the velocity of light in a vacuum, divided by the refractive index of the medium. The refractive index of air is 1.00028, which for our purposes is not significantly different from that of a vacuum (exactly 1.0, by definition), and so we may take the velocity of light in air to be equal to that in a vacuum. The refractive index of water, although it varies somewhat with temperature, salt concentration and wavelength of light, may with sufficient accuracy he regarded as equal to 1.33 for all natural waters. Assuming that the velocity of light in a vacuum is 3 x 108ms-1, the velocity in water is therefore about 2.25 x 108ms-1 The frequency of the radiation remains the same in water but the wavelength diminishes in proportion to the decrease in velocity. When referring to monochromatic radiation, the wavelength we shall attribute to it is that which it has in a vacuum. Because c and l change in parallel, eqns 1.2, 1.3 and 1.4 are as true in water as they are in a vacuum: furthermore, when using eqns 1.3 and 1.4. it is the value of the wavelength in a vacuum which is applicable, even when the calculation is carried out for underwater light.