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80-462: The paint system (and competing versions made by other companies) are known by a wide variety of proprietary names, including ChromaLusion , ChromaPremier , ColourShift , Exclusive Line , Extreme Colors , Harlequin Color , IllusionColor , Maziora , MultiTones , MystiChrome , Ch(K)ameleon , Interference Fireglow and Paradis Spectrashine . The ChromaFlair effect is achieved by interfering with

160-414: A 2000 MCM (1000 square millimeter) copper conductor has 23% more resistance than it does at DC. The same size conductor in aluminum has only 10% more resistance with 60 Hz AC than it does with DC. Skin depth also varies as the inverse square root of the permeability of the conductor. In the case of iron, its conductivity is about 1/7 that of copper. However being ferromagnetic its permeability

240-592: A cable or a coil, the AC resistance is also affected by proximity effect , which can cause an additional increase in the AC resistance. The internal impedance per unit length of a segment of round wire is given by: Z int = k ρ 2 π R J 0 ( k R ) J 1 ( k R ) . {\displaystyle \mathbf {Z} _{\text{int}}={\frac {k\rho }{2\pi R}}{\frac {J_{0}(kR)}{J_{1}(kR)}}.} This impedance

320-431: A conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the conductor. It is caused by opposing eddy currents induced by the changing magnetic field resulting from the alternating current. The electric current flows mainly at the skin of the conductor, between the outer surface and a level called the skin depth . Skin depth depends on

400-437: A mirror ) the angle at which the wave is incident on the surface equals the angle at which it is reflected. In acoustics , reflection causes echoes and is used in sonar . In geology, it is important in the study of seismic waves . Reflection is observed with surface waves in bodies of water. Reflection is observed with many types of electromagnetic wave , besides visible light . Reflection of VHF and higher frequencies

480-471: A torus . Note that these are theoretical ideals, requiring perfect alignment of perfectly smooth, perfectly flat perfect reflectors that absorb none of the light. In practice, these situations can only be approached but not achieved because the effects of any surface imperfections in the reflectors propagate and magnify, absorption gradually extinguishes the image, and any observing equipment (biological or technological) will interfere. In this process (which

560-478: A coating, for example, on synthetic polyurethane leather , or dispersed in a resin for injection molding . Reflection (physics) Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light , sound and water waves . The law of reflection says that for specular reflection (for example at

640-405: A complex conjugating mirror, it would be black because only the photons which left the pupil would reach the pupil. Materials that reflect neutrons , for example beryllium , are used in nuclear reactors and nuclear weapons . In the physical and biological sciences, the reflection of neutrons off of atoms within a material is commonly used to determine the material's internal structure. When

720-402: A flat surface forms a mirror image , which appears to be reversed from left to right because we compare the image we see to what we would see if we were rotated into the position of the image. Specular reflection at a curved surface forms an image which may be magnified or demagnified; curved mirrors have optical power . Such mirrors may have surfaces that are spherical or parabolic . If

800-407: A good conductor, skin depth is proportional to square root of the resistivity. This means that better conductors have a reduced skin depth. The overall resistance of the better conductor remains lower even with the reduced skin depth. However the better conductor will show a higher ratio between its AC and DC resistance, when compared with a conductor of higher resistivity. For example, at 60 Hz,

880-414: A large imaginary part) and at frequencies that are much below both the material's plasma frequency (dependent on the density of free electrons in the material) and the reciprocal of the mean time between collisions involving the conduction electrons. In good conductors such as metals all of those conditions are ensured at least up to microwave frequencies, justifying this formula's validity. For example, in

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960-488: A larger cross-section corresponding to the larger skin depth at mains frequencies. Conductive threads composed of carbon nanotubes have been demonstrated as conductors for antennas from medium wave to microwave frequencies. Unlike standard antenna conductors, the nanotubes are much smaller than the skin depth, allowing full use of the thread's cross-section resulting in an extremely light antenna. High-voltage, high-current overhead power lines often use aluminum cable with

1040-400: A longitudinal sound wave strikes a flat surface, sound is reflected in a coherent manner provided that the dimension of the reflective surface is large compared to the wavelength of the sound. Note that audible sound has a very wide frequency range (from 20 to about 17000 Hz), and thus a very wide range of wavelengths (from about 20 mm to 17 m). As a result, the overall nature of

1120-924: A phase velocity of only about 500 m/s. As a consequence of Snell's law and this very tiny phase velocity in a conductor, any wave entering a conductor, even at grazing incidence, refracts essentially in the direction perpendicular to the conductor's surface. The general formula for skin depth when there is no dielectric or magnetic loss is: δ = 2 ρ ω μ ( 1 + ( ρ ω ε ) 2 + ρ ω ε ) {\displaystyle \delta ={\sqrt {{\frac {\,2\rho \,}{\omega \mu }}\left({\sqrt {1+\left({\rho \omega \varepsilon }\right)^{2}\,}}+\rho \omega \varepsilon \right)\,}}} where At frequencies much below 1 / ( ρ ε ) {\displaystyle 1/(\rho \varepsilon )}

1200-438: A single wire, this reduction becomes of diminishing significance as the wire becomes longer in comparison to its diameter, and is usually neglected. However, the presence of a second conductor in the case of a transmission line reduces the extent of the external magnetic field (and of the total self-inductance) regardless of the wire's length, so that the inductance decrease due to skin effect can still be important. For instance, in

1280-472: A specialized multistrand wire called litz wire . Because the interior of a large conductor carries little of the current, tubular conductors can be used to save weight and cost. Skin effect has practical consequences in the analysis and design of radio-frequency and microwave circuits, transmission lines (or waveguides), and antennas . It is also important at mains frequencies (50–60 Hz) in AC electric power transmission and distribution systems. It

1360-431: A steel reinforcing core ; the higher resistance of the steel core is of no consequence since it is located far below the skin depth where essentially no AC current flows. In applications where high currents (up to thousands of amperes) flow, solid conductors are usually replaced by tubes, eliminating the inner portion of the conductor where little current flows. This hardly affects the AC resistance, but considerably reduces

1440-432: Is a complex quantity corresponding to a resistance (real) in series with the reactance (imaginary) due to the wire's internal self- inductance , per unit length. A portion of a wire's inductance can be attributed to the magnetic field inside the wire itself which is termed the internal inductance ; this accounts for the inductive reactance (imaginary part of the impedance) given by the above formula. In most cases this

1520-729: Is a constant phasor. To satisfy the boundary condition for the current density at the surface of the conductor, J ( R ) , {\displaystyle \mathbf {J} (R),} C {\displaystyle \mathbf {C} } must be J ( R ) J 0 ( k R ) . {\displaystyle {\frac {\mathbf {J} (R)}{J_{0}(kR)}}.} Thus, J ( r ) = J ( R ) J 0 ( k r ) J 0 ( k R ) . {\displaystyle \mathbf {J} (r)=\mathbf {J} (R){\frac {J_{0}(kr)}{J_{0}(kR)}}.} The most important effect of skin effect on

1600-440: Is a measure of the depth at which the current density falls to 1/e of its value near the surface. Over 98% of the current will flow within a layer 4 times the skin depth from the surface. This behavior is distinct from that of direct current which usually will be distributed evenly over the cross-section of the wire. An alternating current may also be induced in a conductor due to an alternating magnetic field according to

1680-570: Is a small portion of a wire's inductance which includes the effect of induction from magnetic fields outside of the wire produced by the current in the wire. Unlike that external inductance, the internal inductance is reduced by skin effect, that is, at frequencies where skin depth is no longer large compared to the conductor's size. This small component of inductance approaches a value of μ 8 π {\displaystyle {\frac {\mu }{8\pi }}} (50 nH/m for non-magnetic wire) at low frequencies, regardless of

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1760-543: Is about 0.25 m. A type of cable called litz wire (from the German Litzendraht , braided wire) is used to mitigate skin effect for frequencies of a few kilohertz to about one megahertz. It consists of a number of insulated wire strands woven together in a carefully designed pattern, so that the overall magnetic field acts equally on all the wires and causes the total current to be distributed equally among them. With skin effect having little effect on each of

1840-466: Is about 10,000 times greater. This reduces the skin depth for iron to about 1/38 that of copper, about 220 micrometers at 60 Hz. Iron wire is impractical for AC power lines (except to add mechanical strength by serving as a core to a non-ferromagnetic conductor like aluminum). Skin effect also reduces the effective thickness of laminations in power transformers, increasing their losses. Iron rods work well for direct-current (DC) welding but it

1920-423: Is also known as phase conjugation), light bounces exactly back in the direction from which it came due to a nonlinear optical process. Not only the direction of the light is reversed, but the actual wavefronts are reversed as well. A conjugate reflector can be used to remove aberrations from a beam by reflecting it and then passing the reflection through the aberrating optics a second time. If one were to look into

2000-431: Is attenuated to e (1.87×10 , or −54.6 dB) of its surface value. The wavelength in the conductor is much shorter than the wavelength in vacuum , or equivalently, the phase velocity in a conductor is very much slower than the speed of light in vacuum. For example, a 1 MHz radio wave has a wavelength in vacuum λ o of about 300 m, whereas in copper, the wavelength is reduced to only about 0.5 mm with

2080-413: Is called the skin depth which is defined as the depth below the surface of the conductor at which the current density has fallen to 1/ e (about 0.37) of J S . The imaginary part of the exponent indicates that the phase of the current density is delayed 1 radian for each skin depth of penetration. One full wavelength in the conductor requires 2 π skin depths, at which point the current density

2160-868: Is complex, the Bessel functions are also complex. The amplitude and phase of the current density varies with depth. Combining the electromagnetic wave equation and Ohm's law produces ∇ 2 J ( r ) + k 2 J ( r ) = ∂ 2 ∂ r 2 J ( r ) + 1 r ∂ ∂ r J ( r ) + k 2 J ( r ) = 0. {\displaystyle \nabla ^{2}\mathbf {J} (r)+k^{2}\mathbf {J} (r)={\frac {\partial ^{2}}{\partial r^{2}}}\mathbf {J} (r)+{\frac {1}{r}}{\frac {\partial }{\partial r}}\mathbf {J} (r)+k^{2}\mathbf {J} (r)=0.} The solution to this equation is, for finite current in

2240-425: Is difficult to use them at frequencies much higher than 60 Hz. At a few kilohertz, an iron welding rod would glow red hot as current flows through the greatly increased AC resistance resulting from skin effect, with relatively little power remaining for the arc itself. Only non-magnetic rods are used for high-frequency welding. At 1 megahertz skin effect depth in wet soil is about 5.0 m; in seawater it

2320-406: Is ignored. Let the dimensions a , b , and c be the inner conductor radius, the shield (outer conductor) inside radius and the shield outer radius respectively, as seen in the crossection of figure  A below. For a given current, the total energy stored in the magnetic fields must be the same as the calculated electrical energy attributed to that current flowing through the inductance of

2400-403: Is important for radio transmission and for radar . Even hard X-rays and gamma rays can be reflected at shallow angles with special "grazing" mirrors. Reflection of light is either specular (mirror-like) or diffuse (retaining the energy , but losing the image) depending on the nature of the interface. In specular reflection the phase of the reflected waves depends on the choice of

2480-404: Is located at the imaginary intersection of the mirrors. A square of four mirrors placed face to face give the appearance of an infinite number of images arranged in a plane. The multiple images seen between four mirrors assembling a pyramid, in which each pair of mirrors sits an angle to each other, lie over a sphere. If the base of the pyramid is rectangle shaped, the images spread over a section of

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2560-661: Is not changed by the skin effect and is given by the frequently cited formula for inductance L per length D of a coaxial cable: L / D = μ 0 2 π ln ⁡ ( b a ) {\displaystyle L/D={\frac {\mu _{0}}{2\pi }}\ln \left({\frac {b}{a}}\right)\,} At low frequencies, all three inductances are fully present so that L DC = L cen + L shd + L ext {\displaystyle L_{\text{DC}}=L_{\text{cen}}+L_{\text{shd}}+L_{\text{ext}}\,} . At high frequencies, only

2640-430: Is not desired, since the light would then be directed back into the headlights of an oncoming car rather than to the driver's eyes. When light reflects off a mirror , one image appears. Two mirrors placed exactly face to face give the appearance of an infinite number of images along a straight line. The multiple images seen between two mirrors that sit at an angle to each other lie over a circle. The center of that circle

2720-557: Is one of the reasons for preferring high-voltage direct current for long-distance power transmission. The effect was first described in a paper by Horace Lamb in 1883 for the case of spherical conductors, and was generalized to conductors of any shape by Oliver Heaviside in 1885. Conductors, typically in the form of wires, may be used to transfer electrical energy or signals using an alternating current flowing through that conductor. The charge carriers constituting that current, usually electrons , are driven by an electric field due to

2800-498: Is returned in the direction from which it came. When flying over clouds illuminated by sunlight the region seen around the aircraft's shadow will appear brighter, and a similar effect may be seen from dew on grass. This partial retro-reflection is created by the refractive properties of the curved droplet's surface and reflective properties at the backside of the droplet. Some animals' retinas act as retroreflectors (see tapetum lucidum for more detail), as this effectively improves

2880-407: Is strongest / most concentrated at the center of the conductor, allowing current only near the outside skin of the conductor, as shown in the diagram on the right. Regardless of the driving force, the current density is found to be greatest at the conductor's surface, with a reduced magnitude deeper in the conductor. That decline in current density is known as the skin effect and the skin depth

2960-468: Is the inverse of one produced by a single mirror. A surface can be made partially retroreflective by depositing a layer of tiny refractive spheres on it or by creating small pyramid like structures. In both cases internal reflection causes the light to be reflected back to where it originated. This is used to make traffic signs and automobile license plates reflect light mostly back in the direction from which it came. In this application perfect retroreflection

3040-441: Is used as a means of focusing waves that cannot effectively be reflected by common means. X-ray telescopes are constructed by creating a converging "tunnel" for the waves. As the waves interact at low angle with the surface of this tunnel they are reflected toward the focus point (or toward another interaction with the tunnel surface, eventually being directed to the detector at the focus). A conventional reflector would be useless as

3120-449: The frequency of the alternating current; as frequency increases, current flow becomes more concentrated near the surface, resulting in less skin depth. Skin effect reduces the effective cross-section of the conductor and thus increases its effective resistance . At 60 Hz in copper, skin depth is about 8.5 mm. At high frequencies, skin depth becomes much smaller. Increased AC resistance caused by skin effect can be mitigated by using

3200-413: The reflection and refraction of light from the painted object's surface. The paint contains tiny synthetic flakes about one micrometer thick. The flakes are constructed of aluminium coated with glass -like magnesium fluoride embedded in semi-translucent chromium . The aluminium and chrome give the paint a vibrant metallic sparkle, while the glass-like coating acts like a refracting prism , changing

3280-517: The X-rays would simply pass through the intended reflector. When light reflects off of a material with higher refractive index than the medium in which is traveling, it undergoes a 180° phase shift . In contrast, when light reflects off of a material with lower refractive index the reflected light is in phase with the incident light. This is an important principle in the field of thin-film optics . Specular reflection forms images . Reflection from

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3360-411: The angle of incidence equals the angle of reflection. In fact, reflection of light may occur whenever light travels from a medium of a given refractive index into a medium with a different refractive index. In the most general case, a certain fraction of the light is reflected from the interface, and the remainder is refracted . Solving Maxwell's equations for a light ray striking a boundary allows

3440-404: The animals' night vision. Since the lenses of their eyes modify reciprocally the paths of the incoming and outgoing light the effect is that the eyes act as a strong retroreflector, sometimes seen at night when walking in wildlands with a flashlight. A simple retroreflector can be made by placing three ordinary mirrors mutually perpendicular to one another (a corner reflector ). The image produced

3520-411: The apparent color of the surface as the observer moves. ChromaFlair paints contain no conventional absorbing pigments ; rather, the pigment is a light interference pigment . The color observed is created entirely by the refractive properties of the flakes, analogous to the perception of rainbow colors in oil slicks . ChromaFlair paint has also been used as a substitute for optically variable ink in

3600-484: The asymptotic value of 11 meters. The conclusion is that in poor solid conductors, such as undoped silicon, skin effect does not need to be taken into account in most practical situations: Any current is equally distributed throughout the material's cross-section, regardless of its frequency. When skin depth is not small with respect to the radius of the wire, current density may be described in terms of Bessel functions . The current density inside round wire away from

3680-457: The auditory feel of a space. In the theory of exterior noise mitigation , reflective surface size mildly detracts from the concept of a noise barrier by reflecting some of the sound into the opposite direction. Sound reflection can affect the acoustic space . Seismic waves produced by earthquakes or other sources (such as explosions ) may be reflected by layers within the Earth . Study of

3760-400: The case of a telephone twisted pair, below, the inductance of the conductors substantially decreases at higher frequencies where skin effect becomes important. On the other hand, when the external component of the inductance is magnified due to the geometry of a coil (due to the mutual inductance between the turns), the significance of the internal inductance component is even further dwarfed and

3840-685: The case of copper, this would be true for frequencies much below 10  Hz . However, in very poor conductors, at sufficiently high frequencies, the factor under the large radical increases. At frequencies much higher than 1 / ( ρ ε ) {\displaystyle 1/(\rho \varepsilon )} it can be shown that skin depth, rather than continuing to decrease, approaches an asymptotic value: δ ≈ 2 ρ ε μ   . {\displaystyle \delta \approx {2\rho }{\sqrt {{\frac {\,\varepsilon \,}{\mu }}\,}}~.} This departure from

3920-408: The center of the conductor, J ( r ) = C J 0 ( k r ) , {\displaystyle \mathbf {J} (r)=\mathbf {C} J_{0}(kr),} where J 0 {\displaystyle J_{0}} is a Bessel function of the first kind of order 0 {\displaystyle 0} and C {\displaystyle \mathbf {C} }

4000-589: The coax; that energy is proportional to the cable's measured inductance. The magnetic field inside a coaxial cable can be divided into three regions, each of which will therefore contribute to the electrical inductance seen by a length of cable. The net electrical inductance is due to all three contributions: L total = L cen + L shd + L ext {\displaystyle L_{\text{total}}=L_{\text{cen}}+L_{\text{shd}}+L_{\text{ext}}\,} L ext {\displaystyle L_{\text{ext}}\,}

4080-879: The conductor's circumference. Thus a long cylindrical conductor such as a wire, having a diameter D large compared to δ , has a resistance approximately that of a hollow tube with wall thickness δ carrying direct current. The AC resistance of a wire of length ℓ and resistivity ρ {\displaystyle \rho } is: R ≈ ℓ ρ π ( D − δ ) δ ≈ ℓ ρ π D δ {\displaystyle R\approx {{\ell \rho } \over {\pi (D-\delta )\delta }}\approx {{\ell \rho } \over {\pi D\delta }}} The final approximation above assumes D ≫ δ {\displaystyle D\gg \delta } . A convenient formula (attributed to F.E. Terman ) for

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4160-504: The deep reflections of waves generated by earthquakes has allowed seismologists to determine the layered structure of the Earth . Shallower reflections are used in reflection seismology to study the Earth's crust generally, and in particular to prospect for petroleum and natural gas deposits. Skin depth In electromagnetism , skin effect is the tendency of an alternating electric current (AC) to become distributed within

4240-533: The density of induced currents, inside a bulk material when a plane wave impinges on it at normal incidence . The AC current density J in a conductor decreases exponentially from its value at the surface J S according to the depth d from the surface, as follows: J = J S e − ( 1 + j ) d / δ {\displaystyle J=J_{\mathrm {S} }\,e^{-{(1+j)d/\delta }}} where δ {\displaystyle \delta }

4320-470: The derivation of the Fresnel equations , which can be used to predict how much of the light is reflected, and how much is refracted in a given situation. This is analogous to the way impedance mismatch in an electric circuit causes reflection of signals. Total internal reflection of light from a denser medium occurs if the angle of incidence is greater than the critical angle . Total internal reflection

4400-441: The diameter D W of a wire of circular cross-section whose resistance will increase by 10% at frequency f is: D W = 200   m m f / H z {\displaystyle D_{\mathrm {W} }={\frac {200~\mathrm {mm} }{\sqrt {f/\mathrm {Hz} }}}} This formula for the increase in AC resistance is accurate only for an isolated wire. For nearby wires, e.g. in

4480-408: The dielectric region has magnetic flux, so that L ∞ = L ext {\displaystyle L_{\infty }=L_{\text{ext}}\,} . Most discussions of coaxial transmission lines assume they will be used for radio frequencies, so equations are supplied corresponding only to the latter case. As skin effect increases, the currents are concentrated near the outside

4560-516: The electrical inductance at these higher frequencies. Although the geometry is different, a twisted pair used in telephone lines is similarly affected: at higher frequencies, the inductance decreases by more than 20% as can be seen in the following table. Representative parameter data for 24 gauge PIC telephone cable at 21 °C (70 °F). More extensive tables and tables for other gauges, temperatures and types are available in Reeve. Chen gives

4640-432: The forward radiation cancels the incident light, and backward radiation is just the reflected light. Light–matter interaction in terms of photons is a topic of quantum electrodynamics , and is described in detail by Richard Feynman in his popular book QED: The Strange Theory of Light and Matter . When light strikes the surface of a (non-metallic) material it bounces off in all directions due to multiple reflections by

4720-403: The glass is the combination of the forward radiation of the electrons and the incident light. The reflected light is the combination of the backward radiation of all of the electrons. In metals, electrons with no binding energy are called free electrons. When these electrons oscillate with the incident light, the phase difference between their radiation field and the incident field is π (180°), so

4800-457: The impedance of a single wire is the increase of the wire's resistance, and consequent losses . The effective resistance due to a current confined near the surface of a large conductor (much thicker than δ ) can be solved as if the current flowed uniformly through a layer of thickness δ based on the DC resistivity of that material. The effective cross-sectional area is approximately equal to δ times

4880-537: The individual atoms (or oscillation of electrons, in metals), causing each particle to radiate a small secondary wave in all directions, like a dipole antenna . All these waves add up to give specular reflection and refraction, according to the Huygens–Fresnel principle . In the case of dielectrics such as glass, the electric field of the light acts on the electrons in the material, and the moving electrons generate fields and become new radiators. The refracted light in

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4960-408: The inductance of a coil used as a circuit element. The inductance of a coil is dominated by the mutual inductance between the turns of the coil which increases its inductance according to the square of the number of turns. However, when only a single wire is involved, then in addition to the external inductance involving magnetic fields outside the wire (due to the total current in the wire) as seen in

5040-598: The influences of other fields, as function of distance from the axis is given by: J ( r ) = k I 2 π R J 0 ( k r ) J 1 ( k R ) = J ( R ) J 0 ( k r ) J 0 ( k R ) {\displaystyle \mathbf {J} (r)={\frac {k\mathbf {I} }{2\pi R}}{\frac {J_{0}(kr)}{J_{1}(kR)}}=\mathbf {J} (R){\frac {J_{0}(kr)}{J_{0}(kR)}}} where Since k {\displaystyle k}

5120-611: The inner conductor ( r  =  a ) and the inside of the shield ( r  =  b ). Since there is essentially no current deeper in the inner conductor, there is no magnetic field beneath the surface of the inner conductor. Since the current in the inner conductor is balanced by the opposite current flowing on the inside of the outer conductor, there is no remaining magnetic field in the outer conductor itself where b < r < c {\displaystyle b<r<c\,} . Only L ext {\displaystyle L_{\text{ext}}} contributes to

5200-405: The law of induction . An electromagnetic wave impinging on a conductor will therefore generally produce such a current; this explains the attenuation of electromagnetic waves in metals. Although the term skin effect is most often associated with applications involving transmission of electric currents, skin depth also describes the exponential decay of the electric and magnetic fields, as well as

5280-414: The light is reflected with equal luminance (in photometry) or radiance (in radiometry) in all directions, as defined by Lambert's cosine law . The light sent to our eyes by most of the objects we see is due to diffuse reflection from their surface, so that this is our primary mechanism of physical observation. Some surfaces exhibit retroreflection . The structure of these surfaces is such that light

5360-434: The microscopic irregularities inside the material (e.g. the grain boundaries of a polycrystalline material, or the cell or fiber boundaries of an organic material) and by its surface, if it is rough. Thus, an 'image' is not formed. This is called diffuse reflection . The exact form of the reflection depends on the structure of the material. One common model for diffuse reflection is Lambertian reflectance , in which

5440-468: The origin of coordinates, but the relative phase between s and p (TE and TM) polarizations is fixed by the properties of the media and of the interface between them. A mirror provides the most common model for specular light reflection, and typically consists of a glass sheet with a metallic coating where the significant reflection occurs. Reflection is enhanced in metals by suppression of wave propagation beyond their skin depths . Reflection also occurs at

5520-468: The quantity inside the large radical is close to unity and the formula is more usually given as: δ = 2 ρ ω μ   . {\displaystyle \delta ={\sqrt {{\frac {\,2\rho \,}{\omega \mu }}\,}}~.} This formula is valid at frequencies away from strong atomic or molecular resonances (where ε {\displaystyle \varepsilon } would have

5600-432: The reflecting surface is very smooth, the reflection of light that occurs is called specular or regular reflection. The laws of reflection are as follows: These three laws can all be derived from the Fresnel equations . In classical electrodynamics , light is considered as an electromagnetic wave, which is described by Maxwell's equations . Light waves incident on a material induce small oscillations of polarisation in

5680-402: The reflection varies according to the texture and structure of the surface. For example, porous materials will absorb some energy, and rough materials (where rough is relative to the wavelength) tend to reflect in many directions—to scatter the energy, rather than to reflect it coherently. This leads into the field of architectural acoustics , because the nature of these reflections is critical to

5760-542: The same data in a parameterized form that he states is usable up to 50 MHz. Chen gives an equation of this form for telephone twisted pair: L ( f ) = ℓ 0 + ℓ ∞ ( f f m ) b 1 + ( f f m ) b {\displaystyle L(f)={\frac {\ell _{0}+\ell _{\infty }\left({\frac {f}{f_{m}}}\right)^{b}}{1+\left({\frac {f}{f_{m}}}\right)^{b}}}\,} In

5840-408: The source of electrical energy. A current in a conductor produces a magnetic field in and around the conductor. When the intensity of current in a conductor changes, the magnetic field also changes. The change in the magnetic field, in turn, creates an electric field that opposes the change in current intensity. This opposing electric field is called counter-electromotive force (back EMF). The back EMF

5920-439: The surface of transparent media, such as water or glass . In the diagram, a light ray PO strikes a vertical mirror at point O , and the reflected ray is OQ . By projecting an imaginary line through point O perpendicular to the mirror, known as the normal , we can measure the angle of incidence , θ i and the angle of reflection , θ r . The law of reflection states that θ i = θ r , or in other words,

6000-411: The surface of a conductor, it can be seen that this will reduce the magnetic field inside the wire, that is, beneath the depth at which the bulk of the current flows. It can be shown that this will have a minor effect on the self-inductance of the wire itself; see Skilling or Hayt for a mathematical treatment of this phenomenon. The inductance considered in this context refers to a bare conductor, not

6080-431: The thin strands, the bundle does not suffer the same increase in AC resistance that a solid conductor of the same cross-sectional area would due to skin effect. Litz wire is often used in the windings of high-frequency transformers to increase their efficiency by mitigating both skin effect and proximity effect. Large power transformers are wound with stranded conductors of similar construction to litz wire, but employing

6160-540: The use of counterfeiting the currency of the United States. Counterfeiter Art Williams stamped green-silver ChromaFlair paint onto counterfeit bills to replicate the color-shifting ink on the 1996-issued $ 100 bill . The ChromaFlair pigment is available in thousands of color variations. It is usually applied to items where visual appeal is important — such as motor vehicles , electric guitars and computer case mods . In addition to paint, it can be applied as

6240-405: The usual formula only applies for materials of rather low conductivity and at frequencies where the vacuum wavelength is not much larger than the skin depth itself. For instance, bulk silicon (undoped) is a poor conductor and has a skin depth of about 40 meters at 100 kHz ( λ = 3 km). However, as the frequency is increased well into the megahertz range, its skin depth never falls below

6320-434: The white region of the figure below, there is also a much smaller component of internal inductance due to the portion of the magnetic field inside the wire itself, the green region in figure B. That small component of the inductance is reduced when the current is concentrated toward the skin of the conductor, that is, when skin depth is not much larger than the wire's radius, as will become the case at higher frequencies. For

6400-440: The wire's radius. Its reduction with increasing frequency, as the ratio of skin depth to the wire's radius falls below about 1, is plotted in the accompanying graph, and accounts for the reduction in the telephone cable inductance with increasing frequency in the table below . Refer to the diagram below showing the inner and outer conductors of a coaxial cable. Since skin effect causes a current at high frequencies to flow mainly at

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