Reflection (physics)

Reflection (Latin reflectere, dt back bend, twist ) called in physics, throwing waves at an interface at which changes the characteristic impedance or the refractive index of the propagation medium.

With smooth (ie small compared to the wavelength Rauigkeitsstrukturen ) surfaces, the law of reflection applies, this is called a specular reflection. On rough surfaces waves or radiation are scattered diffusely and then obeys approximately the Lambertian radiation law.

Typically, only a portion of the energy of the incident wave is reflected at the reflection, one speaks in this context of partial reflection ( partial reflection). The remaining portion of the wave propagates in the second medium further out ( = transmission), as amended by the characteristic impedance, the wave experiences a directional (see refraction ) and velocity change. The angle of refraction can be with the snelliusschem law of refraction and the amplitudes of reflection and transmission calculated with the Fresnel formulas - depending on impedance and polarization.

A special case of reflection, the total internal reflection, in which the shaft is completely reflected when incident on a medium with a lower impedance at the interface. Strictly speaking, this occurs only in ideal transparent media. For example, the second medium in a certain frequency range absorbent, there is the so-called attenuated total reflection, in which changes in the reflection characteristics in this area. Is applied, the total reflection for example in the retro-reflection (reflection of a wave in the direction of the source).

• 4.1 application

• 5.1 Reflection of voltage jumps 5.1.1 Infinitely long cable
• 5.1.2 Finite cable length

• 6.1 Types of Reflections
• 6.2 Room Acoustic Design
• 6.3 context, reflection, absorption, transmission

• 8.1 optics
• 8.2 acoustics

Reflection in the wave model

An incident wave front generated circular wavelets to the respective impingement ( huygens cal principle), the radius r is proportional to the time t increases:

Wherein the propagation speed of the wave in the respective medium.

In the pictures below you can see how the radii of the circles grow first incurred during the current impact point moves to the right. The tangent to the circles represents a new wave front, which leaves the reflecting plane to the right above. The angle between the wavefront and plane are equal ( law of reflection ).

Note: on the underside of the mirror arise elementary waves. If they are there - usually at a different speed c - can spread, it is called refraction.

Reflection of individual pulses

A pulse waveform is a waveform of any packet that can be split in accordance with the rules of Fourier analysis into a sum of sine waves of different wavelengths λ. Between two reflectors at a distance A, only those allowed, in which:

Wherein n is a natural number. Under certain conditions, the waveform of the resulting composite pulse remains the same and this soliton can undamped commute between the two reflectors, as can be seen in the picture. By comparing these pendulum period with the exact time marks an atomic clock can be extremely high frequencies determine ( frequency comb ).

Law of reflection

The law of reflection states that the angle of reflection (including reflection angle) is exactly the same as the angle of incidence, and both with the solder in a plane, the plane of incidence lie. In the case of waves while the wavelength should be substantially greater than the distance between the scattering centers (e.g., atoms). Otherwise, it may come to the formation of several "Reflection Rays", such as X-rays, which are reflected on a crystal ( see X-ray diffraction ).

Specular reflection

Directed The wave field on a reflective surface can be described by " mirror sources ". For each original source this source is a mirror behind the reflective surface of " attached " to the same distance from the reflective surface as the original source. The wave field is obtained by superposition of the wave fields of original and mirror sources.

Applications is the specular reflection in planar and non-planar mirrors, for example, concave curved concave mirror as a shaving mirror or mirror telescopes. Convex curved mirrors are used as mirrors on motor vehicles.

Diffuse reflection

Interfaces with a large roughness relatively diffusely reflect to the wavelength. If the material contains many scatterers, the reflection follows the Lambertian law. The main backscatter is then perpendicular to the material, regardless of the direction of irradiation. Examples are milk, wall paint or paper. In milk have the fat droplets in the water, the magnitude of the wavelength of visible light and make the scattering centers for light waves, and the same applies to the air pockets between the fibers in paper.

Applications of diffuse reflection, ie the uniform distribution of light are, for example

• Integrating sphere,
• A projection screen,
• Avoid specular reflections on screens and photographic prints.

The sum of specular and diffuse reflection is also called remission, based on the amount of incident light reflectance. For not perfectly diffuse scattering, curved surfaces, and possibly color shifts, there are different ways of definition. In the field of meteorology and astronomy see albedo, the industry uses different definitions of whiteness.

Reflection of electromagnetic waves in the optical system

In the following, the reflection will be explained using the example of electromagnetic waves. For easier understanding, while the beam model of geometrical optics is utilized.

In the diagram (see law of reflection ) hits a beam from the left on top of the surface of a medium with other radiation propagation characteristics. A part of the radiation is refracted towards the perpendicular ( transmitted partial ), another reflected. In this case, the law of reflection applies: The angle of incidence equals the angle of reflection. Under appropriate conditions, however, the incident radiation will be totally reflected, the total reflection see.

The reflection of electromagnetic radiation at an interface is only partially in control and the other part is transmitted. The reflectance is defined as the ratio of the reflected to the incident light intensity

The reflectance can be calculated by the reflection coefficient from the Fresnel formulas. It depends on the angle of incidence and polarization of the light as well as the properties of the materials involved. For circularly polarized waves varies at each reflection the helicity.

The refractive index is wavelength dependent in general. This means that waves of different wavelengths can be different highly reflective. For example, have metals due to absorption by the electron gas has a high extinction coefficient for electromagnetic radiation in the infrared range, they are so opaque and have a very high degree of reflection of generally more than 90 percent. However, the reflectivity of metals in the visible or ultraviolet region is lowered sometimes within a small frequency range, very fast ( see figure to the example silver). In the reflectance spectroscopy is closed from the measured reflectance spectrum to the material effective mechanisms and their parameters, such as the density of electrons in the conduction band, or polarizability.

Due to the different degree of reflection depending on the polarization of the light, these changes at each reflection. That is, non-polarized light falls on a boundary surface, the reflected and diffracted light ( and at ) is partially polarized. In the special case of parallel polarized to the incident plane of the light is not reflected but totally broken ( Brewster's angle). The reflected portion is then completely polarized perpendicular and the transmitted contains both polarization directions. This effect makes it possible for example to allow laser light to pass through without reflection loss through a window.

Further effect on the reflection is dependent on the crystal orientation of the index ellipsoid of the birefringent materials. Here, the reflectivity is different also dependent on the crystal orientation of the crystal surface. And a magnetic field can influence the reflection, which is used for magneto- optical storage technology.

A reduction in the total reflection by several coordinated layers is possible to see anti-reflection layer.

Application

An important application of the reflection of electromagnetic waves or rays is their targeted guidance. This will Exploited in everyday objects such as mirrors in which the one person " emitted " light is reflected, so that the person, for example, can see her face itself. Technically, this beam deflection is applied to plane mirrors or prisms in more or less complex optics, for example, in simple periscopes or deflecting prism or mirrors of SLRs. In this way, reflection can also be used to non-contact detection or measurement of reflective surfaces ( deflectometry ), or by time of flight measurements to measure the distance of a radiation source to a reflecting surface ( Time Domain Reflectometry ).

Furthermore, exploited the reflection at specially shaped surfaces in order to concentrate electromagnetic radiation targeted. For example, when antennas, the transmission power is converged by the parabolic mirror and achieves a directivity. The same principle is also used in almost all frequency ranges, a typical example of this are reflecting telescopes.

Far away from the technical necessity is the way how a body reflects light because of its material, shape and surface characteristics and thus affects the people, also used in many creative areas such as product design or architecture. For example, surfaces are polished specifically to witness a shiny, mirror-like impression. Similar effect can also with the use of different paints (eg gloss, semi- gloss, matte) are generated. However, the type of reflection can also have an influence on the technical parameters, in case of matte screens the disturbing influence of stray light reflections by means of diffuse reflection on a rough surface is reduced. However, the rough surface decreased as compared to reflective displays also the blackness and the brilliance of the light transmitted through the protective glass light.

Since the reflection intensity of a characteristic of a material portion is reflected, can also properties of materials, such as refractive index, thickness, impurities, etc., are determined in this way. Here, both measurements at a single wavelength are therefore also used spectral distributions ( thin film reflectometry measurement, ellipsometry, and much more. ). The latter form the basis for the spectroscopy, in which, in addition to the transmission, the reflection of the polarized and unpolarized electromagnetic waves is a frequently used examination technique, see reflectance spectroscopy.

Reflection at electrical wires

When an electric wave with an amplitude A0 is passed through a line that is terminated with its characteristic impedance, there will completely absorbed without reflection and independent of their frequency. The degree may be a load resistor, an antenna, the input impedance of an analog or digital circuitry, or one or more other lines. When mismatch occurs - assuming linearity - a reflected wave of the same frequency and (usually) a modified amplitude AR. The ratio AR/A0 is called reflection coefficient:

This includes the impedance of the termination and the impedance of the line.

In general is frequency dependent and complex, typically amount to less than 1; his argument is a phase change. In practice, a real value is always aimed at.

Special cases:

• Means that the wave is not reflected, there is no echo. (Case: custom line ).
• Means that the wave is reflected 100% (case: = open end voltage doubling by superimposing the leading and reflected wave ).
• Means that the shaft 100 % reflected, but is inverted (case: short circuit, voltage = 0 at the end of the line by superimposing the leading and reflected wave ).

The experimental verification is described in the article Time Domain Reflectometry. The current on the line leading and reflected waves can overlap and lead to a position-dependent distribution of current and voltage.

Reflection of voltage jumps

Should a flash in a high-voltage line, passes a high voltage pulse to the cable end and may cause damage there. A similar phenomenon is observed when a first uncharged, lossless coaxial cable ( line impedance Z) a DC voltage ( a voltage step ) is applied. The DC voltage is supplied from a power supply to the internal resistance R, where R is chosen = Z.

Infinitely long cable

If the DC voltage U set at time zero to an infinitely long coaxial cable, a constant current I would forever flowing:

At the entry point, a constant voltage U / 2 can be measured, it does not matter whether the cable end but quite far away is open or shorted - the corresponding information would arrive only after infinite time at the feed point. If you limit yourself by measurement of the feed-in point, one can not distinguish whether the direct current flowing in an infinitely long cable or whether an ohmic resistor with the value Z the supplied electrical energy into heat. The cable stores the electrical energy, and after an infinitely long time, the cable is "loaded". It has different properties than a capacitor.

One can predict the timing of the " arrival" of the voltage jump at a remote measuring point, because the speed of propagation is cmedium. The insulation material with relative permittivity between the inner and outer conductor of the coaxial cable determines the pulse velocity in the cable

Finite cable length

If the cable in the above thought experiment, the finite length L, the voltage jump comes after the time

To the cable end. The local degree decides how to proceed:

• Are the inner and outer conductor of the coaxial cable via a resistor R = Z connected, the electrical energy flows freely in these reflection terminating resistor that heats up accordingly. At the entry point ( cable beginning ) can not be distinguished from an infinitely long cable that case.

• Are the inner and outer conductors are not connected, the voltage jump is reflected in phase. This leads to a doubling of the voltage and the superposed voltage jump cmedium runs back to the cable beginning. The top image shows the stress distribution shortly after the reflection. As soon as the voltage jump arrives at the entry point, it is not reflected because of the internal resistance of the power supply to the line impedance. From this moment, the equilibrium state is reached, it flows no further power, and at any point of the cable is measured between the inner and outer conductors of the voltage U. With an oscilloscope can this " voltage staircase " on first U / 2, and then - from time 2T - prove to U.

• Are inner and outer conductors short-circuited, the voltage jump is reflected in phase opposition. The superposition of the forward and reverse current "wave" is available in the area of ​​overlap zero. Which is measured at the cable beginning, but only when the reflected voltage jump after the time of 2 · T arrives. With an oscilloscope can this rectangular pulse on first U / 2, and then - from the time 2T - prove to zero. A short-circuited at the end of cable acts like a "delayed short-circuit".

Reflection in acoustics

Types of reflections

In acoustics, the sound reflection is meant, that the discarding of sound. Level, sound- hard, non-absorbent surfaces reflect well the sound waves. In recognizing this sound reflections which echo perception threshold plays an important role. Depending on the arrangement and number of reflective surfaces and type of PA results in a different listening experience:

• Echo ( rock wall at a greater distance )
• Flutter echo ( two parallel reflective walls )
• Reverberation (large rooms with hard walls, such as in churches )
• High dimensionality (acoustic space perception in concert halls )
• Dry sound ( in rooms with low reflectivity surfaces )

Important for the acoustic are:

• Proportion of direct sound in the overall sound level
• Time delay and direction of early reflections, as well as their share of the total sound
• Use delay and spatial distribution of reverberation, as well as its share of the overall sound levels and the temporal profile ( reverberation time )

Room Acoustic Design

For rooms other room acoustic properties and thus each has different reflective properties of the walls are useful depending on usage:

• Up to a certain limit anechoic rooms in recording studios (so no anechoic rooms), so that the acoustic character of the receiving space gets little influence as possible on the recording.
• Rooms with moderately reflective walls for classrooms. On one hand, the teacher's voice to be supported by early reflections to 15 ms, on the other hand, the intelligibility of speech must not be diminished by excessive late reflections and excessive reverberation time though. The favorable reverberation time for normal hearing in accordance with DIN 18041 " Acoustical quality in small to medium-sized rooms " is dependent on the volume between 0.3 and 0.8 seconds. In the classroom with a volume of 125 up to 250 m3 a reverberation time of 0.4 to 0.6 s is optimal. For the hearing impaired reverberation times should be sought by 0.3 seconds.
• Spaces with highly reflective walls and a balanced ratio of direct sound, early reflections and reverb for concert halls. Here, the goal is, through early wall reflections laterally incident on the ears to achieve a possible " spatial " music experience. Also, a high diffusivity, ie scattering of sound is important. Cheap reverberation time is 1.5 to 2 seconds.

A very special importance in the spatial space detection is the initial time gap ( ITDG ).

Related reflection, absorption, transmission

The following variables play a role in sound reflections:

• The acoustic reflectance and is a measure of the reflected sound intensity.
• The degree of sound absorption, or is a measure of the absorbed sound intensity.
• The sound transmittance and is a measure of the transmitted sound intensity.
• The Schalldissipationsgrad or is a measure of the " lost" sound intensity.

On impact on limiting faces the incoming sound intensity is either reflected or absorbed at the boundary surface of the boundary surface. It is thus

The absorbed fraction of the sound intensity is transmitted here either from the boundary surface ( transmitted ) or converted into the materials of the boundary surface into heat ( dissipated ). It is thus

Thus, a total applies

In acoustics, the following words are disturbed propagation of sound:

• Sound absorption
• Sound reflection
• Sound transmission
• Schalldissipation.

Reflection of water waves

Wave reflection means for progressive water waves, throwing a portion of their energy on a structure ( breakwater, embankment ) or in places where the configuration changes of the natural seabed (strong). At the same time, another portion of the wave energy is propagated, and the remainder through the processes of wave breaking, the dissipated fluid and bottom friction and absorbs compare to wave transformation, wave absorption.

Accordingly, the law is the conservation of energy:

In it mean

• = Energy of the incoming waves
• = The energy ( through the building ) continues forwarded ( transmitted ) waves
• = Energy of the reflected waves on the structure
• = Energy loss due to wave absorption.

If the above energy components, each set in proportion to the energy of the incoming waves, such values ​​can be specified as a transmission coefficient, reflection coefficient and absorption coefficient. Generally, the reflection coefficient. Only in the theoretical case of perfect reflection ( in the presence of perfect Clapotis ) is. Only this is true, the statement that with the reflection on an ideal smooth vertical wall a phase shift does not occur. Particularly in the case of partial reflection at steep, flat river banks, the phase shift amount to about 180 °, cf accompanying picture.

Since wave energy is the square of wave height proportional to the reflection coefficient can be easily written as a quotient of the height of the reflected wave and the level of the oncoming wave.