Light is a form of energy.

Light is a form of energy.

Light is just one portion of the various

electromagnetic waves flying through space.

(is light is a special kind of electromagnetic energy)

Electromagnetic (EM) waves are created when electric charge is accelerated.

To create regular sinusoidal EM wave one have

to move, vibrate, electric charge accordingly.

„light treated as a wave”

Waves are easy to imagine.

Time evolution, (one place) T is distance in time = period

Snapshot (one moment) λ Is distance in space = wavelength.

A typical human eye responds to wavelengths from about 350 to 750 nm.

Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of

electric and magnetic fields. Note that the electric

and magnetic fields in such a wave are in-phase

with each other, reaching minima and maxima

together.

From Maxwell's equations

One can get electromagnetic wave equations

The equations introduce the electric field E, a vector field, and the magnetic field B, a pseudovector field, where each generally have time-dependence. The sources of these fields are electric

charges and electric currents, which can be expressed as local densities, namely charge density ρ and current density i.

In general wave equation has following form:

where v is the speed of the wave.

Typical example of wave function F = F(x – vt) is:

F = Asin(kx – ω t) = Asin[k(x – vt)], v = ω /k

For the node Asin0 = 0 -> x - vt = 0 -> v = x/t is the speed of node and the whole of the wave,

c is speed of light (about 3x10⁸ m/s)

The speed of light, although quite fast, is not infinite.

Consider the EM wave described as: E = E

_o

sin[k(x – ct)], c = 3x10

⁸

m/s

and calculate period T, the duration of one cycle of the electric charge

oscillation, that generate EM wave with the wave length λ = 500nm (visible)

. T = λ /c = 5x10

^-7

m/3x10

⁸

≈ 1.66x10

^-15

s!

So the frequency f = 1/T = 6x10

¹⁴

Hz

The frequency of the visible region lies from 4 x 10¹⁴ - 7.5 x 10¹⁴ Hz.

(Frequency impossible for motors, but natural in atoms and molecules)

Photons are the components of a light beam, whilst waves are a mathematical description of a beam of light.

Description of light in terms of photons is mandatory when dealing with events at an

A typical human eye responds to wavelengths from about 350 to 750 nm.

The watt (W), the fundamental unit of any power (and of optical power), is defined as a rate of energy of one joule (J) per second.

Optical power is a function of both the number of photons and the wavelength.

Each photon carries an energy that is described by Planck’s equation:

where Q is the photon energy (joules), ν is frequency of the radiation, h is

Planck’s constant (6.623 x 10^-34 J s), c is the speed of light (2.998 x 10⁸ m s^-1), and λ is the wavelength of the radiation.

All light measurement units are spectral, spatial, or temporal distributions of optical energy.

Spectra of Light Sources

Usually sources are divided into two categories, natural (stars, meteors, lightning, volcanic eruption….) and

artificial, man-made (incandescent lamps,

electroluminescent (EL) lamps, Lasers, combustion…).

The emission and the absorption spectra are of importance.

Every atom and molecule has its own characteristic set of spectral lines.

Energy-level diagram for a hydrogen atom

All materials with temperatures above absolute

zero emit electromagnetic radiation.

Blackbody (ideal thermal radiator) radiation

Most sources are emitting over a broad band of the spectrum.

Incandescent lamps are a good

example. By measuring the red

to blue ratio of a lamp, one can

monitor and adjust its spectral

output.

Interactions of Light with Matter

When light travels through a medium, it interacts with the medium.

The most important interactions are absorption and scattering.

Absorption

is a transfer of energy from the EM wave to the atoms or molecules of the medium. Energy transferred to an atoms or molecules can excite electrons to higher energy states or can excite vibrations or rotations of molecules. The wavelengths of light that can excite these energy states depend on the types of atoms and molecules contained in the medium.

The spectrum of the light after passing through a medium appears to have

certain wavelengths removed because they have been absorbed. This is called an absorption spectrum. Selective absorption is also the basis for objects

having color. A red object is red because it absorbs the other colors of the visible spectrum and reflects red light.

When light is incident on an interface between two transparent optical media such as between air and glass or between water and glass at least

four things can happen.

• It can be partly or totally reflected at the interface.

• It can be scattered in random directions at the interface.

• It can be partly transmitted via refraction at the interface and enter the second medium.

• It can be partly absorbed in either medium.

If dN – loss of N per unit of distance is proportional to the amount of N still present and absorption coefficient α then N decreases exponentially:

Diffuse reflection is typical of particulate substances like powders.

The powder (e.g. flour) will appear uniformly bright from every direction.

Many reflections are a combination of both diffuse and specular components.

The Gaussian reflection is reflection in which intensity of reflected light based on angle at the surface of the reflector and an angle between a normal line and the reflected light vary according to values of a Gaussian function.

The Lambertian reflection is reflection in which intensity of

reflected light based on angle at the surface of the reflector and

an angle between a normal line and the reflected light vary

Scattering is the redirection of light caused by it’s interaction with matter. The scattered EM radiation may have the same or longer wavelength as the incident one. It may have a different polarization.

If the dimensions of the scatterer are much smaller than the

wavelength of light, the scatterer can absorb the incident light and reemit the light in a different direction. If the reemitted light has the same wavelength as the incident light, the process is

called Rayleigh scattering (If the reemitted light has a longer wavelength, the molecule is left in an excited state, and the process is called Raman scattering).If the dimensions of the

scatterer are larger than the wavelength of light, the scatterer can

reemit the light in a different direction wit different intensity, and

the process is called Mie scattering).

When light passes between dissimilar materials, the rays change velocity and bend.

The index of refraction itself is also dependent on wavelength. This dispersion

Perception of light

Rods, and cones in retina are photoreceptor of the human eye.

Rods can function in less intense light than cones. Rod cells are almost entirely responsible for night vision (scotopic vision).

A rod cell is sensitive enough to respond to a single photon of light and is about 100 times more sensitive to a single photon than

cones. Rods are most sensitive to wavelengths of light around 498 nm (green-blue), and insensitive to wavelengths longer than about 640 nm (red).

Cone cells require tens to hundreds of photons to become

activated.

Rods – for night vision (not for colors)

Cones, - cones that absorb long-wavelength light (red)

- cones that absorb middle-wavelength light (green) - cones that absorb short-wavelength light (blue)

Normalised

responsiveness of rods compared

to that of three types of cones.

The dashed gray curve is for rods.

Relative sensitivity.

The units used in the measurement of light are confusing because absolute measurements of energy, radiometric units, do not

correspond to visual perception, measured in photometric units.

Radiometry is the measurement of energy or electromagnetic radiation. It is the measurement of the physical properties of light and may include radiation like ultraviolet, infrared or radiation of more specific wavelengths.

Photometry involves the physical measurement of visible light energy and attempts to compensate for the psychophysical attributes of the human response and physical units of power.

Photometry is just like radiometry except that everything is weighted by the

spectral response ( luminosity function) of the human eye as defined by the CIE (INTERNATIONAL COMMISSION ON ILLUMINATION).

lumen (lm) the unit of Flux

Photometric equivalent of the watt, weighted to match the eye response of the “standard observer”.

Yellowish-green light receives the greatest weight because it stimulates the eye more than blue or

red light of equal radiometric power:

1 watt at 555 nm = 683.0 lumens

The human eye can detect a flux of about 10 photons per second at a wavelength of 555 nm;

this corresponds to a radiant power of 3.58 x 10

^-18

W. The eye can

Lumens are related to lux

in that one lux is one lumen per square meter 1 lux = 1 lm/m

²

The lumen is defined in relation to the candela (luminous intensity unit) as

1 cd = 1 lm/sr

A full sphere has a solid angle of 4·π sr so a light source that uniformly radiates one candela in all directions has a total luminous flux of

1 cd·4π sr = 4π cd·sr ≈ 12.57 lumens.

From Wikipedia

The Inverse Square Law

The inverse square law defines the relationship between their radiance from a point

source and distance. It states that the intensity per unit area varies in inverse proportion to the square of the distance. The same energy fall on growing area of the sphere

surface (4πr²).

Lambert’s Cosine Law

The irradiance or illuminance falling on any surface varies as the cosine of the incident angle Θ.

luminous intensity

The candela (cd is the SI base unit of luminous intensity) has its origin in the

brightness of a "standard candle", but has received a more precise definition in SI (the International System of Units) and the unit was also renamed from "candle" to "candela".

The luminous intensity is described in terms of an angle, therefore the distance at which you measure this intensity is irrelevant. It is power emitted by a light source in a particular direction, weighted by the luminosity function (also known as the luminous efficiency function). A common candle emits light with a

luminous intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the emission would still be approximately one candela in the directions that are not obscured. In 1979, the candela has been defined as the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5,4×10¹⁴ hertz and that has a radian intensity in that direction of 1⁄683 watt per steradian.

In the picture, screen A₁ would catch exactly the same amount of light rays (emitted from the light source) as screen A₂ or A₃. This is because screen A₂ as well as A₃ covers the same angle

as screen A₁ .

Kandela (cd) Jednostka światłości źródła światła, jednostka podstawowa w układzie SI, oznaczana jako: cd.

(dawno temu jednostką była „świeca”)

Jest to światłość, z jaką świeci w określonym kierunku źródło emitujące

promieniowanie monochromatyczne o częstotliwości 5,4·10¹⁴ Hz i wydajności energetycznej w tym kierunku równej 1/683 W/sr.

Starsza definicja określała kandelę jako światłość 1/600 000 m² powierzchni ciał doskonale czarnego w temperaturze krzepnięcia platyny pod ciśnieniem 1 atmosfery fizycznej. Jednak z powodu trudności w wykonywaniu układu

pomiarowego i małej dokładności pomiaru (rzędu 0,1–0,2%), definicja ta została zarzucona w 1979 r.

lumen (lm) - jednostka miary strumienia świetlnego w układzie SI (jednostka pochodna układu SI). 1 lm = 1 cd·sr

Illuminance

In photometry, illuminance is the total luminous flux incident on a surface, per unit area.

It says how much the incident light illuminates the surface (weighted by the luminosity function).

In SI derived units these are measured in lux (lx) or lumens per

square meter (cd·sr·m

^-2

).

luminous emittance

luminous emittance is the luminous flux per unit area emitted from a surface.

Luminous emittance is also known as luminous exitance in units:

lumens per unit area

[lm/m

²

]

Luminous efficacy refers to the ratio of lumen output from the source to the power input, and has the units of lumens per Watt (lm/W).

Conventional incandescent and fluorescent lights have typical luminous efficacies of about 15 lm/W and 70 lm/W, respectively.

Currently available LED-based replacements have luminous

efficacies as high as 80 lm/W up to 150 lm/w depending on

manufacturer.

Luminance (and radiance in radiometry)

It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle.

Luminance is often used to characterize emission or reflection from flat, diffuse surfaces. The luminance indicates how much luminous power will be detected by an eye looking at the surface from a particular angle of view. Luminance is thus an indicator of how bright the surface will appear. In this case, the solid angle of interest is the solid angle subtended by the eye's pupil. A typical

computer display emits between 50 and 300 cd/m². The sun has luminance of about 1.6×10⁹ cd/m² at noon.

RGB color model

Colours can be specified by

coordinates in the plane of the colour triangle.

The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of comparable hue to that of the light source.

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