## Light and its characterstics

Light

Light is a form of energy which travels as electromagnetic waves (a wave of self sustaining electric and magnetic fields). The variation of electric and magnetic fields in a electromagnetic wave along the direction of propagation is shown in the figure.

Variation of electric and magnetic fields in a electromagnetic wave

It is of dual nature which behaves as both particles and waves. It behaves as a particle while interacting with matter but behaves as a wave while travelling from one place to another. Light is a transverse wave with the electric and magnetic fields oscillating perpendicular to the direction og propagation of light. A wave is defined uniquely in terms of wavelength and frequency. A Wave consists of crests and troughs which are maxima and minima of electric or magnetic field in an electromagnetic wave.

Wavelength is defined as the distance between two successive crests or troughs. Wave number is defined as the number of waves that exist per 2*π units of distance. It has units on m-1.The relation between Wavelength and Wave number is given as

β = 2*π

Frequency is defined as the number of crests or troughs that crosses a fixed point per unit time. Angular frequency is given as

ω = 2*π

The wave velocity is the rate at which wave travels.

Wave velocity = ν*λ = ω/ β

Light being a wave exhibits interference (superposition of two or more waves) and diffraction (bending of light around edges). The speed of light in vacuum is a constant and is equal to 3*108 m/s.  The relation between the wavelength and frequency of light is

C = ν*λ

where ν is frequency of light,

λ is the wavelength of light.

Light consists of mass less particles called photons which is a quantum (smallest possible piece) of electromagnetic energy. The Planck’s hypothesis gives the relation between the photon energy and wavelength of light. It is given as

E = h*ν = (h*C/λ)

Where E is energy of photon,

h is Planck’s constant which is given as 6.625*10-34 J.s.

The energy of photon is generally expressed in terms of electron volts. The conversion of energy from joules to electron volts is given as

E (in eV) = 1242.2/λ (in nm)

Visible light occupies the light spectrum from 400 nm to 700 nm.

Note: 1 nm= 1*10-9 m.

Spectral power density or spectral irradiance

The spectral power density or spectral irradiance denoted by P is a quantity which has spectral information, in contrast to irradiance. The spectral power density is the incident power per unit area and per unit wavelength. . It is usually expressed in terms of per square meter per nano meter (W/m^2/nm) or w/m^3. It is denoted by P (λ).The spectral power density of light incident on a differential area dA normal to the direction of light rays falling on it for wavelengths ranging from λ+Δλ and λ with power equal to dP is given as

P(λ) =dP /(dAnormal*dλ)

The irradiance is the power per unit area and is usually expressed in Watts per square meter. The irradiance does not provide us any information about the spectral shape of the light source. The total area under graph plotted between spectral irradiance and wavelength give the irradiance of  the light source. The spectral irradiance of light from sun reaching the earth’s surface is shown in the figure. The total area in the shaded region gives the total irradiance of the sun.

I = $\int_{o}^{\lambda&space;_{max}_{_{}}}P(\lambda&space;)*d\lambda$

Where P (λ) is spectral power density or spectral irradiance. The limits of integration extend from the zero wavelengths to the maximum wavelength of light the source can emit.

Spectral photon flux

Spectral photon flux is defined as the number of photons per unit area per unit wavelength. It is specified in units of m-2*s-1*nm-1. It is denoted by Ф (λ). At any wavelength λ spectral irradiance gives the power The spectral photon flux in terms of spectral irradiance is given as

Ф (λ) = P (λ)/E = p(λ)* λ/(h*C)

It gives the information about the spectrum of light.

photon flux

The photon flux is defined as the number of photons per second per unit area. It is denoted by  and is specified in units of m-2*s-1. As the photon flux does not give information about the energy (or wavelength) of the photons, the energy or wavelength of the photons in the light source must also be specified. The photon flux in terms of Spectral photon flux is given as

At a given wavelength, the combination of the photon wavelength or energy and the photon flux at that wavelength can be used to calculate the power density for photons at the particular wavelength. The power density is calculated by multiplying the photon flux by the energy of a single photon. Since the photon flux gives the number of photons striking a surface in a given time, multiplying by the energy of the photons comprising the photon flux gives the energy striking a surface per unit time, which is equivalent to a power density. To determine the power density in units of W/m², the energy of the photons must be in Joules. The equation is:

H (W/m2) =  Φ×h×c/λ using SI units

H (W/m2) =  Φ× q×1.24×λ(μm) for wavelength in μm

H (W/m2) =  Φ× q×E for energy in eV

Where Φ is the photon flux and q is the value of the electronic charge 1.6 ×10-19 Coulombs.