3) Energy:

As mentioned earlier, light is a form of energy. According to the quantum theory, all energy is transmitted and absorbed in discrete particles called quanta or photons. Thus, the smallest amount of radiation energy that can exist is one photon.

If one thinks of the photon as a small packet or ball of energy, it is most useful in understanding light, especially for our purpose of reefkeeping. For our purposes, let us take a simplified, unified description that says that light travels as discrete photons along a wave. Visible light is a mixture of many photons with different wavelengths. The photons are reflected and absorbed by various surfaces, and when they reach the eyes, they create the sensation of sight and resultant perceptions of color and brightness. These photons are also directly responsible for photosynthesis in plants and corals. The energy from the photons is used during photosynthesis to convert CO2 into sugar, which is a primary energy source for the photosynthetic endosymbiotic zooxanthellae living within corals.

As discussed earlier, the energy carried by electromagnetic radiation is contained in the photons that travel as a wave. According to quantum theory, the energy in a photon varies with its frequency, according to the equation:

Energy = Plank's constant × FrequencyE = hν = hc/λ

Where h = Plank's constant is 6.626 × 10-34 joules per second

Energy is measured in units called joules.

As the frequency of the radiation increases (wavelength gets shorter), the amount of energy in each photon increases. Now we can begin to understand why the red light gets absorbed quickly in water as a function of depth.

Example: What is the energy in a single photon of light at 500nm?

E = 6.626 × 10-34 × 3.0 × 108/(500 × 10-9)E = 0.039756 × 10-17 J

Example: How many photons per joule exist for light at wavelength λ = 500nm?

E = Energy/photon, so to create 1 J of energy we will need N photons.N × E = 1 joule, hence N = 1/EN = λ/hc = 25.15 × 1017 photons

As seen above, to produce 1 Joule of energy by light at a wavelength of 500nm requires a very large number of photons. To avoid having to deal with such large numbers, we can measure the number of photons in "moles" where 1 mole = Avagadro's number = 6.02 × 10 23. So 25.15 × 1017 photons would correspond to .000004177 moles. Now, this number is too small, so instead we will measure in "micromoles," where 1 micromole (denoted as µmol) is 10-6 mole, giving us 4.177 micromoles of photons.

What about watts? Energy is measured in joules, and the "watt" is the unit used as a measure of power. Power is defined as the rate of flow of energy. By definition, 1 watt = 1 joule/second. So, one watt of power from light at 500nm would need to provide 25.15 × 10 17

photons per second or 4.1769 micromoles/sec. The figure below shows the relationship between watts and micromoles of photons to generate 1 watt of power.

Summary:

This column has focused on providing the basic terminology required to understand light. Light is a form of energy, and can be simply described as a stream of photons traveling along a wave. Photons are discrete particles of energy. The characteristics of light and the photons are specified by three terms: wavelength, frequency and energy, which are mathematically related. Photons with wavelengths of 400 nm carry more energy than those with larger wavelengths and will appear violet to the human eye, and photons with wavelengths of 700nm carry less energy and will appear red. White light is a mixture of photons in the wavelength range 400-700nm. This range is what the eye can see and is also useful for photosynthesis. The photons carry the energy and the number of photons is measured in units of "micromoles."

Irradiance is the power of electromagnetic radiation per unit area (radiative flux) incident on a surface. Radiant emittance or radiant exitance is the power per unit area radiated by a surface. The SI units for all of these quantities are watts per square meter (W/m2), while the cgs units are ergs per square centimeter per second (erg·cm−2·s−1, often used in astronomy).

These quantities are sometimes called intensity, but this usage leads to confusion with radiant intensity, which has different units.

All of these quantities characterize the total amount of radiation present, at all frequencies. It is also common to consider each frequency in the spectrum separately. When this is done for radiation incident on a surface, it is called spectral irradiance, and has SI units W/m3, or commonly W·m−2·nm−1.

If a point source radiates light uniformly in all directions through a non-absorptive medium, then the irradiance decreases in proportion to the square of the distance from the object.

The irradiance of a monochromatic light wave in matter is given in terms of its electric field by [1]

where E is the complex amplitude of the wave's electric field, n is the refractive index of the medium, is the speed of light in vacuum, and ϵ0 is the vacuum permittivity. (This formula assumes that the magnetic susceptibility is negligible, i.e. where is the magnetic permeability of the light transmitting media. This assumption is typically valid in transparent media in the optical frequency range.)

Irradiance is also the time average of the component of the Poynting vector perpendicular to the surface.

Solar energy

The global irradiance on a horizontal surface on Earth consists of the direct irradiance Edir and diffuse irradiance Edif. On a tilted plane, there is another irradiance component: Eref, which is the component that is reflected from the ground. The average ground reflection is about 20% of the global irradiance. Hence, the irradiance Etilt on a tilted plane consists of three components: Etilt = Edir + Edif + Eref.[2]

The integral of solar irradiance over a time period is solar irradiation or insolation. Irradiation is generally measured in J/m2 and is represented by the symbol H.[2]

SI radiometry units

QuantitySymbol[nb

1] SI unit Symbol Dimension Notes

Radiant energy

Qe[nb 2] joule J M⋅L2⋅T−2 energy

Radiant flux Φe[nb 2] watt W M⋅L2⋅T−3

radiant energy per unit time, also called radiant power.

Spectral power

Φeλ[nb 2][nb 3] watt per metre W⋅m−1 M⋅L⋅T−3 radiant power per

wavelength.

Radiant intensity

Iewatt per steradian W⋅sr−1 M⋅L2⋅T−3 power per unit

solid   angle .

Spectral intensity

Ieλ[nb 3]

watt per steradian per metre

W⋅sr−1⋅m−1 M⋅L⋅T−3 radiant intensity per wavelength.

Radiance Le

watt per steradian per square   metre

W⋅sr−1⋅m −2 M⋅T−3

power per unit solid angle per unit projected source area.

confusingly called "intensity" in some other fields of study.

Spectral radiance

Leλ[nb 3]

orLeν

[nb 4]

watt per steradian per metre3

or

watt per steradian per squaremetre per hertz

W⋅sr−1⋅m−3

orW⋅sr−1⋅m−2⋅Hz−1

M⋅L−1⋅T−3

orM⋅T−2

commonly measured in W⋅sr−1⋅m−2⋅nm−1 with surface area and either wavelength or frequency.

Irradiance Ee[nb 2] watt per

square metre W⋅m−2 M⋅T−3

power incident on a surface, also called radiant flux density.

sometimes confusingly called "intensity" as well.

Spectral irradiance

Eeλ[nb 3]

orEeν

[nb 4]

watt per metre3

orwatt per square metre per hertz

W⋅m−3

orW⋅m−2⋅Hz−1

M⋅L−1⋅T−3

orM⋅T−2

commonly measured in W⋅m−2⋅nm−1

or 10−22W⋅m−2⋅Hz−1, known as solar flux unit.[nb 5]

Radiant exitance /

Me[nb 2] watt per

square metreW⋅m−2 M⋅T−3 power emitted from a

surface.

Radiant emittanceSpectral radiant exitance /Spectral radiant emittance

Meλ[nb 3]

orMeν

[nb 4]

watt per metre3

or

watt per squaremetre per hertz

W⋅m−3

orW⋅m−2⋅Hz−1

M⋅L−1⋅T−3

orM⋅T−2

power emitted from a surface per wavelength or frequency.

RadiosityJe or Jeλ

[nb

3]watt per square metre W⋅m−2 M⋅T−3 emitted plus reflected

power leaving a surface.Radiant exposure

Hejoule per square metre J⋅m−2 M⋅T−2

Radiant energy density

ωejoule per metre3 J⋅m−3 M⋅L−1⋅T−2