# Light

Light is a form of electromagnetic radiation. In a narrower sense, only those parts of the entire electromagnetic spectrum are meant which are visible to the human eye. In a broader sense, electromagnetic waves of shorter wavelength (ultraviolet) and longer wavelength (infrared) are also counted among them.

The physical properties of light are described by various models: In ray optics, the straight-line propagation of light is illustrated by "light rays"; in wave optics, the wave nature of light is emphasized, which can also explain diffraction and interference phenomena. In quantum physics, light is described as a stream of quantum objects, the photons. A complete description of light is provided by quantum electrodynamics. In a vacuum, light propagates at the constant speed of light of 299792458 m/s. When light strikes matter, it can be scattered, reflected, refracted and slowed down or absorbed.

Light is the sensory stimulus adequate for the human eye. The intensity of light is perceived as brightness, the spectral composition as color.

## History

Until well into modern times, it was largely unclear what light actually is. It was partially believed that brightness fills space without time delay, and that "rays" emanate from the eyes and scan the environment during the visual process. However, there were already since the antiquity conceptions, according to which the light is emitted by the light source with finite speed.

Galileo Galilei was one of the first to attempt to seriously measure the speed of propagation of light, but without success. The means available to him were much too coarse for this purpose. This succeeded first Ole Romer on the basis of observation data of the Jupiter moons 1676/78. Although the deviation of his measured value from the actual value (ca. 3 – 10 8 m/s) about 30 %. However, the real achievement of Romer was to prove that light propagates with finite speed. Romer’s measurement was more and more precise in the course of the following 200 years by more and more sophisticated methods (especially by Hippolyte Fizeau and Leon Foucault).

The nature of light, however, remained unexplained. In the 17. In the nineteenth century, Isaac Newton’s corpuscle theory attempted to explain the propagation of light by the motion of small particles. With this, one could understand the reflection, but not some other optical phenomena, like the diffraction, which is clearly a wave phenomenon. At the same time, Christiaan Huygens and others founded the wave theory of light, which, however, did not become established until the beginning of the 19th century. The magnetization of light became more and more common after the double-slit experiments of Thomas Young in the middle of the nineteenth century.

In 1846, Michael Faraday was the first to prove that light and magnetism are two physical phenomena linked to each other. He published the magneto-optical effect he had found, which today is called the Faraday effect [1], under the title About the magnetization of light and the exposure of the lines of magnetic force. [2]

James Clerk Maxwell formulated the basic equations of electrodynamics in 1864, which are still valid today, and realized that it predicted the existence of free electromagnetic waves. Since their predicted velocity of propagation agreed with the known velocity of light, he concluded that light was probably an electromagnetic wave. He assumed (like nearly all physicists at that time) that this wave could not exist in empty space, but needed a propagation medium. This medium, which should fill the whole universe, was called ether.

With the on this basis based electromagnetic theory of light In the late 19th century. century almost all questions about light had been solved. However, on the one hand the postulated aether could not be proved (see Michelson-Morley experiment), which finally opened the door to the special theory of relativity. On the other hand, the photoelectric effect seemed to contradict the wave nature of light. This gave rise to a radically new view of light, which was founded by the quantum hypothesis of Max Planck and Albert Einstein. The key point of this hypothesis is the wave-particle duality, which now describes light not exclusively as a wave or exclusively as a particle, but as a quantum object. As such, it combines properties of wave and of particle, without being one or the other, and thus escapes our concrete contemplation. From this arose at the beginning of the 20. Century quantum physics and later quantum electrodynamics, which until today represents our understanding of the nature of light.

## Science

### Physics

In the following the most important models for the description of light are presented. Like all models in physics, the ones listed here are limited in scope. Only quantum electrodynamics can provide a complete description of the phenomenon "light" according to our present knowledge.

#### Light as an electromagnetic wave

In classical electrodynamics, light is considered to be a high frequency electromagnetic wave. In a narrower sense, "light" is only the part of the electromagnetic spectrum visible to the human eye, i.e. wavelengths between ca. 380 and 780 nm. It is a transverse wave, where the amplitude is given by the vector of the electric field or magnetic field. The direction of propagation is perpendicular to it. The direction of the $\vec$ field vector or $\vec$ -field vector is called polarization direction. For unpolarized light, the radiation field is composed of waves of all polarization directions. Like all electromagnetic waves, visible light propagates in vacuum at the speed of light $c \,=\, 299\,792\,458\ \frac>>$ from.

The wave equation of this electromagnetic wave can be derived from Maxwell’s equations. This results in a simple relationship between the speed of light, the magnetic field constant $\mu_0$ and the electric field constant $\varepsilon_0$ :

Obviously, the velocity of light – more precisely: the phase velocity of light – in media depends on their material properties. These can be summarized in the refractive index $n$. In general, it is frequency dependent, which is called dispersion. This is one of the reasons for the ability of a prism to split light into its spectral components. Short wavelength blue light is refracted more strongly than long wavelength red light under normal dispersion conditions.

#### Ray optics

ray optics (also geometrical optics) makes use of the approximation that the propagation of light can be illustrated by straight "rays". This approximation is especially justified when the dimensions of the experimental setup are large compared to the wavelength of the light. Then all diffraction phenomena can be neglected. The link between wave optics and ray optics is the wave vector, whose direction coincides with the direction of the light beam. Ray optics is particularly well suited for describing phenomena such as light and shadow, reflection or refraction. Therefore, it can be used to explain the function of many optical devices (pinhole camera, magnifying glass, telescope, microscope). In particular, the imaging laws are also the basis for the understanding of the refractive apparatus in the human eye.

Principles of rays

• Light rays always propagate in a straight line and change direction only when they strike a body (by reflection, refraction, or scattering), disregarding the deflection of light by heavy masses observed in astronomy (gravitational lensing effect).
• light rays can penetrate each other without influencing each other in the process.
• The light path is reversible. This means that any ray path would satisfy all optical laws even if the propagation direction of the light were reversed.
##### reflection

On reflecting surfaces (like on bare metals) light is reflected according to the law of reflection. The incident and the outgoing beam as well as the perpendicular on the reflecting surface lie in one plane. angle of incidence and angle of reflection are equal to each other. The ratio of the reflected light intensity to the incident light intensity is called the reflectance and is material and wavelength dependent.

##### Refraction

Light is refracted at the interface between two media of different optical density, d. h., a ray changes its direction at this interface. (For the sake of completeness, it should be mentioned that reflection always occurs to a greater or lesser extent at such an interface).) The law of refraction of Snellius states:

The incident and the refracted beam as well as the perpendicular on the interface lie in one plane. The angle between the perpendicular and the light beam is smaller in the medium which has the higher refractive index.

The exact angles $\delta_i$ can be calculated by the refractive indices $n_i$ of the media involved:

If the incident beam from the optically denser medium hits the interface at a flat angle, there is no real angle for the refracted beam that satisfies this condition. In this case, total reflection occurs instead of refraction.

#### Wave optics

Wave optics is based on the principle of Huygens and Fresnel.

Each point of a wave front is the starting point of an elementary wave. A wave front results as superposition of these elementary waves.

Using elementary wave in this context means a spherical wave emanating from a certain point. Wave fronts the surfaces are of the same phase. The distance between two successive wavefronts is therefore the wavelength. The wave fronts of a plane wave are planes, the wave fronts of elementary waves are concentric spherical surfaces. The direction of propagation (i.e. the direction of the wave vector) always forms a normal to the wave front. With wave optics all phenomena of diffraction and interference can be understood. But it is also suitable to derive the law of reflection and the law of refraction. The wave optics does not contradict the ray optics, but extends and deepens it.

Historically, the wave optics of Huygens and Fresnel already anticipates essential findings of electrodynamics: the light waves are electromagnetic waves.

#### Photons

In quantum physics, light is no longer considered as a classical wave, but as a quantum object. According to this, the light is composed of single discrete energy quanta, the so-called photons. A photon is an elementary particle, more precisely: a boson with a rest mass of 0, which always moves with the velocity of light $c$.

It carries an energy of

Here $\nu$ is the frequency of light and $h$ is Planck’s quantum of action with $h = 6626\,069\,57(29) \cdot 10^\,\text$ .

The photon has a momentum of

where $\lambda$ is the wavelength of light.

The spin of the photon is related to the polarization: The wave function of a single photon is circularly polarized. Depending on the direction of rotation of the $\vec E$ -field vector, the spin of the photon is $+1$ or $-1$ .

A photon is either absorbed and emitted as a whole or not at all. It is therefore "countable" like a particle. Nevertheless, everything that has been said here so far about the wave properties of light remains valid. The wave is quantum mechanically correctly described by a special case of the Klein-Gordon equation for massless particles (which corresponds to Maxwell’s wave equation). This strange behavior of photons, which, however, is also exhibited by all other quantum objects, has been called by the catchword "wave-particle duality": Quantum objects are to be understood neither like classical particles nor like classical waves. Depending on the point of view, they show properties of one or the other.

In today’s most common interpretation of quantum mechanics (Copenhagen interpretation), the exact location of a photon cannot be determined a priori predict. One can only make statements about the probability with which a photon will strike a certain spot. This probability density is given by the magnitude square of the amplitude of the light wave.

Historically, the quantum mechanical description of light became necessary because some phenomena could not be explained by purely classical electrodynamics.