Degrees Brix (symbol °Bx) is a measure of the dissolved solids in a liquid, and is commonly used to measure dissolved sugar content of a solution. One degree Brix is 1 gram of sucrose in 100 grams of solution and represents the strength of the solution as percentage by mass . If the solution contains dissolved solids other than pure sucrose, then the °Bx only approximates the dissolved solid content. For example, when one adds equal amounts of salt and sugar to equal amounts of water, the degrees of refraction (BRIX) of the salt solution rises faster than the sugar solution. The °Bx is traditionally used in the wine , sugar , carbonated beverage , fruit juice , fresh produce , maple syrup , and honey industries. The °Bx is also used for measuring the concentration of a cutting fluid mixed in water for metalworking processes.
80-706: Comparable scales for indicating sucrose content are: the Plato scale (°P), which is widely used by the brewing industry ; the Oechsle scale used in German and Swiss wine making industries, amongst others; and the Balling scale, which is the oldest of the three systems and therefore mostly found in older textbooks, but is still in use in some parts of the world. A sucrose solution with an apparent specific gravity (20°/20 °C) of 1.040 would be 9.99325 °Bx or 9.99359 °P while
160-563: A lens is determined by its refractive index n and the radii of curvature R 1 and R 2 of its surfaces. The power of a thin lens in air is given by the simplified version of the Lensmaker's formula : 1 f = ( n − 1 ) [ 1 R 1 − 1 R 2 ] , {\displaystyle {\frac {1}{f}}=(n-1)\left[{\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}\right]\ ,} where f
240-529: A consequence, a refractometer measurement made on a sugar solution once fermentation has begun results in a reading substantially higher than the actual solids content. Thus, an operator must be certain that the sample they are testing has not begun to ferment. (If fermentation has indeed started, a correction can be made by estimating alcohol concentration from the original, pre-fermentation reading, termed "OG" by homebrewers.) Brix or Plato measurements based on specific gravity are also affected by fermentation, but in
320-649: A function of photon energy, E , applicable to amorphous materials. Forouhi and Bloomer then applied the Kramers–Kronig relation to derive the corresponding equation for n as a function of E . The same formalism was applied to crystalline materials by Forouhi and Bloomer in 1988. The refractive index and extinction coefficient, n and κ , are typically measured from quantities that depend on them, such as reflectance, R , or transmittance, T , or ellipsometric parameters, ψ and δ . The determination of n and κ from such measured quantities will involve developing
400-606: A green spectral line of mercury ( 546.07 nm ), called d and e lines respectively. Abbe number is defined for both and denoted V d and V e . The spectral data provided by glass manufacturers is also often more precise for these two wavelengths. Both, d and e spectral lines are singlets and thus are suitable to perform a very precise measurements, such as spectral goniometric method. In practical applications, measurements of refractive index are performed on various refractometers, such as Abbe refractometer . Measurement accuracy of such typical commercial devices
480-412: A material with higher refractive index, the angle of refraction will be smaller than the angle of incidence and the light will be refracted towards the normal of the surface. The higher the refractive index, the closer to the normal direction the light will travel. When passing into a medium with lower refractive index, the light will instead be refracted away from the normal, towards the surface. If there
560-702: A more accurate description of the wavelength dependence of the refractive index, the Sellmeier equation can be used. It is an empirical formula that works well in describing dispersion. Sellmeier coefficients are often quoted instead of the refractive index in tables. Because of dispersion, it is usually important to specify the vacuum wavelength of light for which a refractive index is measured. Typically, measurements are done at various well-defined spectral emission lines . Manufacturers of optical glass in general define principal index of refraction at yellow spectral line of helium ( 587.56 nm ) and alternatively at
640-462: A plasma with an index of refraction less than unity is Earth's ionosphere . Since the refractive index of the ionosphere (a plasma ), is less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" (see Geometric optics ) allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications. See also Radio Propagation and Skywave . Recent research has also demonstrated
720-468: A ratio with a fixed numerator, like "10000 to 7451.9" (for urine). Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1 (water). Young did not use a symbol for the index of refraction, in 1807. In the later years, others started using different symbols: n , m , and µ . The symbol n gradually prevailed. Refractive index also varies with wavelength of the light as given by Cauchy's equation . The most general form of this equation
800-503: A refractive index below 1. This can occur close to resonance frequencies , for absorbing media, in plasmas , and for X-rays . In the X-ray regime the refractive indices are lower than but very close to 1 (exceptions close to some resonance frequencies). As an example, water has a refractive index of 0.999 999 74 = 1 − 2.6 × 10 for X-ray radiation at a photon energy of 30 keV ( 0.04 nm wavelength). An example of
880-546: A refractometer is used, the Brix value can be obtained from the polynomial fit to the ICUMSA table: where n D {\displaystyle n_{D}} is the refractive index measured at the wavelength of the sodium D line (589.3 nm) at 20 °C. Temperature is important as refractive index changes dramatically with temperature. Many refractometers have built in "Automatic Temperature Compensation" (ATC), which
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#1732779712416960-402: A sugar solution is measured by refractometer or density meter, the °Bx or °P value obtained by entry into the appropriate table only represents the amount of dry solids dissolved in the sample if the dry solids are exclusively sucrose. This is seldom the case. Grape juice ( must ), for example, contains little sucrose but does contain glucose, fructose, acids, and other substances. In such cases,
1040-488: A theoretical expression for R or T , or ψ and δ in terms of a valid physical model for n and κ . By fitting the theoretical model to the measured R or T , or ψ and δ using regression analysis, n and κ can be deduced. For X-ray and extreme ultraviolet radiation the complex refractive index deviates only slightly from unity and usually has a real part smaller than 1. It is therefore normally written as n = 1 − δ + iβ (or n = 1 − δ − iβ with
1120-416: Is n ( λ ) = A + B λ 2 + C λ 4 + ⋯ , {\displaystyle n(\lambda )=A+{\frac {B}{\lambda ^{2}}}+{\frac {C}{\lambda ^{4}}}+\cdots ,} where n is the refractive index, λ is the wavelength, and A , B , C , etc., are coefficients that can be determined for a material by fitting
1200-399: Is α = 4π κ / λ 0 , and the penetration depth (the distance after which the intensity is reduced by a factor of 1/ e ) is δ p = 1/ α = λ 0 /4π κ . Both n and κ are dependent on the frequency. In most circumstances κ > 0 (light is absorbed) or κ = 0 (light travels forever without loss). In special situations, especially in the gain medium of lasers , it
1280-468: Is a function of the refractive index and the operator detects this critical angle by noting where a dark-bright boundary falls on an engraved scale. The scale can be calibrated in Brix or refractive index. Often the prism mount contains a thermometer that can be used to correct to 20 °C in situations where measurement cannot be made at exactly that temperature. These instruments are available in bench and handheld versions. Digital refractometers also find
1360-629: Is also possible that κ < 0 , corresponding to an amplification of the light. An alternative convention uses n = n + iκ instead of n = n − iκ , but where κ > 0 still corresponds to loss. Therefore, these two conventions are inconsistent and should not be confused. The difference is related to defining sinusoidal time dependence as Re[exp(− iωt )] versus Re[exp(+ iωt )] . See Mathematical descriptions of opacity . Dielectric loss and non-zero DC conductivity in materials cause absorption. Good dielectric materials such as glass have extremely low DC conductivity, and at low frequencies
1440-418: Is based on knowledge of the way the refractive index of sucrose changes. For example, the refractive index of a sucrose solution of strength less than 10 °Bx is such that a 1 °C change in temperature would cause the Brix reading to shift by about 0.06 °Bx. Beer, conversely, exhibits a change with temperature about three times this much. It is important, therefore, that users of refractometers either make sure
1520-703: Is called "normal dispersion", in contrast to "anomalous dispersion", where the refractive index increases with wavelength. For visible light normal dispersion means that the refractive index is higher for blue light than for red. For optics in the visual range, the amount of dispersion of a lens material is often quantified by the Abbe number : V = n y e l l o w − 1 n b l u e − n r e d . {\displaystyle V={\frac {n_{\mathrm {yellow} }-1}{n_{\mathrm {blue} }-n_{\mathrm {red} }}}.} For
1600-545: Is called the absolute refractive index of medium 2. The absolute refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299 792 458 m/s , and the phase velocity v of light in the medium, n = c v . {\displaystyle n={\frac {\mathrm {c} }{v}}.} Since c is constant, n is inversely proportional to v : n ∝ 1 v . {\displaystyle n\propto {\frac {1}{v}}.} The phase velocity
1680-434: Is commonly used to obtain high resolution in microscopy. In this technique the objective is dipped into a drop of high refractive index immersion oil on the sample under study. The refractive index of electromagnetic radiation equals n = ε r μ r , {\displaystyle n={\sqrt {\varepsilon _{\mathrm {r} }\mu _{\mathrm {r} }}},} where ε r
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#17327797124161760-485: Is critical. All three typical principle refractive indices definitions can be found depending on application and region, so a proper subscript should be used to avoid ambiguity. When light passes through a medium, some part of it will always be absorbed . This can be conveniently taken into account by defining a complex refractive index, n _ = n + i κ . {\displaystyle {\underline {n}}=n+i\kappa .} Here,
1840-409: Is desirable to know the actual dry solids content, empirical correction formulas can be developed based on calibrations with solutions similar to those being tested. For example, in sugar refining, dissolved solids can be accurately estimated from refractive index measurement corrected by an optical rotation (polarization) measurement. Alcohol has a higher refractive index (1.361) than water (1.333). As
1920-406: Is given by the ratio of speed of light in medium 1 to that in medium 2. This can be expressed as follows: n 21 = v 1 v 2 . {\displaystyle n_{21}={\frac {v_{1}}{v_{2}}}.} If the reference medium 1 is vacuum , then the refractive index of medium 2 is considered with respect to vacuum. It is simply represented as n 2 and
2000-419: Is in the order of 0.0002. Refractometers usually measure refractive index n D , defined for sodium doublet D ( 589.29 nm ), which is actually a midpoint between two adjacent yellow spectral lines of sodium. Yellow spectral lines of helium ( d ) and sodium ( D ) are 1.73 nm apart, which can be considered negligible for typical refractometers, but can cause confusion and lead to errors if accuracy
2080-432: Is maintained by NIST and can be found on their website), they reports in °Bx. If using the ICUMSA tables, they would report in mass fraction (m.f.). It is not, typically, actually necessary to consult tables as the tabulated °Bx or °P value can be printed directly on the hydrometer scale next to the tabulated value of specific gravity or stored in the memory of the electronic U-tube meter or calculated from polynomial fits to
2160-467: Is no angle θ 2 fulfilling Snell's law, i.e., n 1 n 2 sin θ 1 > 1 , {\displaystyle {\frac {n_{1}}{n_{2}}}\sin \theta _{1}>1,} the light cannot be transmitted and will instead undergo total internal reflection . This occurs only when going to a less optically dense material, i.e., one with lower refractive index. To get total internal reflection
2240-464: Is not interchangeable with the traditional hydrometer Brix unless corrections are applied. The formal term for such a refractive value is "Refractometric Dry Substance" (RDS). See § Brix and actual dissolved solids content below. The four scales are often used interchangeably since the differences are minor. Brix is used in the food industry for measuring the approximate amount of sugars in fruits , vegetables , juices, wine , soft drinks and in
2320-410: Is not representative of the exact amount of sugar in a must or fruit juice, it can be used for comparison of relative sugar content. As specific gravity was the basis for the Balling, Brix and Plato tables, dissolved sugar content was originally estimated by measurement of specific gravity using a hydrometer or pycnometer . In modern times, hydrometers are still widely used, but where greater accuracy
2400-526: Is required, an electronic oscillating U-tube meter may be employed. Whichever means is used, the analyst enters the tables with specific gravity and takes out (using interpolation if necessary) the sugar content in percent by mass . If the analyst uses the Plato tables (maintained by the American Society of Brewing Chemists ) they reports in °P. If using the Brix table (the current version of which
2480-966: Is the electron density. One may assume the electron density is simply the number of electrons per atom Z multiplied by the atomic density, but more accurate calculation of the refractive index requires replacing Z with the complex atomic form factor f = Z + f ′ + i f ″ {\displaystyle f=Z+f'+if''} . It follows that δ = r 0 λ 2 2 π ( Z + f ′ ) n atom β = r 0 λ 2 2 π f ″ n atom {\displaystyle {\begin{aligned}\delta &={\frac {r_{0}\lambda ^{2}}{2\pi }}(Z+f')n_{\text{atom}}\\\beta &={\frac {r_{0}\lambda ^{2}}{2\pi }}f''n_{\text{atom}}\end{aligned}}} with δ and β typically of
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2560-579: Is the focal length of the lens. The resolution of a good optical microscope is mainly determined by the numerical aperture ( A Num ) of its objective lens . The numerical aperture in turn is determined by the refractive index n of the medium filling the space between the sample and the lens and the half collection angle of light θ according to Carlsson (2007): A N u m = n sin θ . {\displaystyle A_{\mathrm {Num} }=n\sin \theta ~.} For this reason oil immersion
2640-509: Is the material's relative permittivity , and μ r is its relative permeability . The refractive index is used for optics in Fresnel equations and Snell's law ; while the relative permittivity and permeability are used in Maxwell's equations and electronics. Most naturally occurring materials are non-magnetic at optical frequencies, that is μ r is very close to 1, therefore n
2720-417: Is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity , the speed at which the pulse of light or the envelope of the wave moves. Historically air at a standardized pressure and temperature has been common as a reference medium. Thomas Young was presumably the person who first used, and invented, the name "index of refraction", in 1807. At
2800-450: Is transparent in the wavelength region from 2 to 14 μm and has a refractive index of about 4. A type of new materials termed " topological insulators ", was recently found which have high refractive index of up to 6 in the near to mid infrared frequency range. Moreover, topological insulators are transparent when they have nanoscale thickness. These properties are potentially important for applications in infrared optics. According to
2880-470: The Beer–Lambert law . Since intensity is proportional to the square of the electric field, intensity will depend on the depth into the material as I ( x ) = I 0 e − 4 π κ x / λ 0 . {\displaystyle I(x)=I_{0}e^{-4\pi \kappa x/\lambda _{0}}.} and thus the absorption coefficient
2960-483: The angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices n 1 and n 2 . The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection , their intensity ( Fresnel equations ) and Brewster's angle . The refractive index, n {\displaystyle n} , can be seen as
3040-507: The attenuation , while the real part accounts for refraction. For most materials the refractive index changes with wavelength by several percent across the visible spectrum. Consequently, refractive indices for materials reported using a single value for n must specify the wavelength used in the measurement. The concept of refractive index applies across the full electromagnetic spectrum , from X-rays to radio waves . It can also be applied to wave phenomena such as sound . In this case,
3120-411: The refractive index (or refraction index ) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refracted , when entering a material. This is described by Snell's law of refraction, n 1 sin θ 1 = n 2 sin θ 2 , where θ 1 and θ 2 are
3200-405: The theory of relativity , no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be less than 1. The refractive index measures the phase velocity of light, which does not carry information . The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, and thereby give
3280-418: The "existence" of materials with a negative refractive index, which can occur if permittivity and permeability have simultaneous negative values. This can be achieved with periodically constructed metamaterials . The resulting negative refraction (i.e., a reversal of Snell's law ) offers the possibility of the superlens and other new phenomena to be actively developed by means of metamaterials . At
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3360-473: The ASBC tables) from the best-fit polynomial: The difference between the °Bx and °P as calculated from the respective polynomials is: The difference is generally less than ±0.0005 °Bx or °P with the exception being for weak solutions. As 0 °Bx is approached °P tend toward as much as 0.002 °P higher than the °Bx calculated for the same specific gravity. Disagreements of this order of magnitude can be expected as
3440-491: The Brix table to obtain the °Bx, which is the concentration of sucrose by percent mass. It is important to point out that neither wort nor must is a solution of pure sucrose in pure water. Many other compounds are dissolved as well but these are either sugars, which behave similar to sucrose with respect to specific gravity as a function of concentration, or compounds that are present in small amounts (minerals, hop acids in wort, tannins , acids in must). In any case, even if °Bx
3520-496: The NBS and the ASBC used slightly different values for the density of air and pure water in their calculations for converting to apparent specific gravity. It should be clear from these comments that Plato and Brix are, for all but the most exacting applications, the same. The ICUMSA polynomials are generally only published in the form where mass fraction is used to derive the density. As a result, they are omitted from this section. When
3600-418: The alternative convention mentioned above). Far above the atomic resonance frequency delta can be given by δ = r 0 λ 2 n e 2 π {\displaystyle \delta ={\frac {r_{0}\lambda ^{2}n_{\mathrm {e} }}{2\pi }}} where r 0 is the classical electron radius , λ is the X-ray wavelength, and n e
3680-596: The amount of light that is reflected is determined by the reflectivity of the surface. The reflectivity can be calculated from the refractive index and the incidence angle with the Fresnel equations , which for normal incidence reduces to R 0 = | n 1 − n 2 n 1 + n 2 | 2 . {\displaystyle R_{0}=\left|{\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}\right|^{2}\!.} For common glass in air, n 1 = 1 and n 2 = 1.5 , and thus about 4% of
3760-423: The angles of incidence θ 1 must be larger than the critical angle θ c = arcsin ( n 2 n 1 ) . {\displaystyle \theta _{\mathrm {c} }=\arcsin \!\left({\frac {n_{2}}{n_{1}}}\right)\!.} Apart from the transmitted light there is also a reflected part. The reflection angle is equal to the incidence angle, and
3840-406: The atomic scale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons ) proportional to the electric susceptibility of the medium. (Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility .) As the electromagnetic fields oscillate in the wave,
3920-428: The charges in the material will be "shaken" back and forth at the same frequency. The charges thus radiate their own electromagnetic wave that is at the same frequency, but usually with a phase delay , as the charges may move out of phase with the force driving them (see sinusoidally driven harmonic oscillator ). The light wave traveling in the medium is the macroscopic superposition (sum) of all such contributions in
4000-448: The clear exception. Aerogel is a very low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the other end of the range with a refractive index as high as 2.65. Most plastics have refractive indices in the range from 1.3 to 1.7, but some high-refractive-index polymers can have values as high as 1.76. For infrared light refractive indices can be considerably higher. Germanium
4080-453: The critical angle, but the light path is entirely internal to the prism. A drop of sample is placed on its surface, so the critical light beam never penetrates the sample. This makes it easier to read turbid samples. The light/dark boundary, whose position is proportional to the critical angle, is sensed by a CCD array. These meters are also available in bench top (laboratory) and portable (pocket) versions. This ability to easily measure Brix in
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#17327797124164160-463: The dairy industry to measure the quality of colostrum given to newborn calves, goats, and sheep. Modern optical Brix meters are divided into two categories. In the first are the Abbe-based instruments in which a drop of the sample solution is placed on a prism; the result is observed through an eyepiece. The critical angle (the angle beyond which light is totally reflected back into the sample)
4240-504: The dielectric loss is also negligible, resulting in almost no absorption. However, at higher frequencies (such as visible light), dielectric loss may increase absorption significantly, reducing the material's transparency to these frequencies. The real n , and imaginary κ , parts of the complex refractive index are related through the Kramers–Kronig relations . In 1986, A.R. Forouhi and I. Bloomer deduced an equation describing κ as
4320-468: The equation to measured refractive indices at known wavelengths. The coefficients are usually quoted for λ as the vacuum wavelength in micrometres . Usually, it is sufficient to use a two-term form of the equation: n ( λ ) = A + B λ 2 , {\displaystyle n(\lambda )=A+{\frac {B}{\lambda ^{2}}},} where the coefficients A and B are determined specifically for this form of
4400-464: The equation. For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the adjacent table. These values are measured at the yellow doublet D-line of sodium , with a wavelength of 589 nanometers , as is conventionally done. Gases at atmospheric pressure have refractive indices close to 1 because of their low density. Almost all solids and liquids have refractive indices above 1.3, with aerogel as
4480-1046: The extent to which it rotates the plane of linearly polarized light. The refractive index, n D , for sucrose solutions of various percentage by mass has been measured and tables of n D vs. °Bx published. As with the hydrometer, it is possible to use these tables to calibrate a refractometer so that it reads directly in °Bx. Calibration is usually based on the ICUMSA tables, but the user of an electronic refractometer should verify this. Sugars also have known infrared absorption spectra and this has made it possible to develop instruments for measuring sugar concentration using mid-infrared (MIR), non-dispersive infrared (NDIR), and Fourier transform infrared (FT-IR) techniques. In-line instruments are available that allow constant monitoring of sugar content in sugar refineries, beverage plants, wineries, etc. As with any other instruments, MIR and FT-IR instruments can be calibrated against pure sucrose solutions and thus report in °Bx, but there are other possibilities with these technologies, as they have
4560-402: The factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/ n , and similarly the wavelength in that medium is λ = λ 0 / n , where λ 0 is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and assumes that the frequency ( f = v / λ ) of
4640-469: The field makes it possible to determine ideal harvesting times of fruit and vegetables so that products arrive at the consumers in a perfect state or are ideal for subsequent processing steps such as vinification. Due to higher accuracy and the ability to couple it with other measuring techniques (%CO 2 and %alcohol), most soft drink companies and breweries use an oscillating U-tube density meter. Refractometers are still commonly used for fruit juice. When
4720-445: The frequency of the light used in the measurement. That κ corresponds to absorption can be seen by inserting this refractive index into the expression for electric field of a plane electromagnetic wave traveling in the x -direction. This can be done by relating the complex wave number k to the complex refractive index n through k = 2π n / λ 0 , with λ 0 being the vacuum wavelength; this can be inserted into
4800-495: The goal of the Commission being to correct errors in the 5th and 6th decimal place in the Brix table. Equipped with one of these tables, a brewer wishing to know how much sugar was in his wort could measure its specific gravity and enter that specific gravity into the Plato table to obtain °Plato, which is the concentration of sucrose by percentage mass. Similarly, a vintner could enter the specific gravity of his must into
4880-644: The incident power is reflected. At other incidence angles the reflectivity will also depend on the polarization of the incoming light. At a certain angle called Brewster's angle , p -polarized light (light with the electric field in the plane of incidence ) will be totally transmitted. Brewster's angle can be calculated from the two refractive indices of the interface as θ B = arctan ( n 2 n 1 ) . {\displaystyle \theta _{\mathsf {B}}=\arctan \left({\frac {n_{2}}{n_{1}}}\right)~.} The focal length of
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#17327797124164960-465: The material: the original wave plus the waves radiated by all the moving charges. This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity. Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions or even at other frequencies (see scattering ). Depending on
5040-587: The opposite direction; as ethanol is less dense than water, an ethanol/sugar/water solution gives a Brix or Plato reading that is artificially low. Plato scale Too Many Requests If you report this error to the Wikimedia System Administrators, please include the details below. Request from 172.68.168.133 via cp1102 cp1102, Varnish XID 569070117 Upstream caches: cp1102 int Error: 429, Too Many Requests at Thu, 28 Nov 2024 07:41:52 GMT Refractive index In optics ,
5120-596: The optical path length. When light moves from one medium to another, it changes direction, i.e. it is refracted . If it moves from a medium with refractive index n 1 to one with refractive index n 2 , with an incidence angle to the surface normal of θ 1 , the refraction angle θ 2 can be calculated from Snell's law : n 1 sin θ 1 = n 2 sin θ 2 . {\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}.} When light enters
5200-540: The order of 10 and 10 . Optical path length (OPL) is the product of the geometric length d of the path light follows through a system, and the index of refraction of the medium through which it propagates, OPL = n d . {\text{OPL}}=nd. This is an important concept in optics because it determines the phase of the light and governs interference and diffraction of light as it propagates. According to Fermat's principle , light rays can be characterized as those curves that optimize
5280-1189: The plane wave expression for a wave travelling in the x -direction as: E ( x , t ) = Re [ E 0 e i ( k _ x − ω t ) ] = Re [ E 0 e i ( 2 π ( n + i κ ) x / λ 0 − ω t ) ] = e − 2 π κ x / λ 0 Re [ E 0 e i ( k x − ω t ) ] . {\displaystyle {\begin{aligned}\mathbf {E} (x,t)&=\operatorname {Re} \!\left[\mathbf {E} _{0}e^{i({\underline {k}}x-\omega t)}\right]\\&=\operatorname {Re} \!\left[\mathbf {E} _{0}e^{i(2\pi (n+i\kappa )x/\lambda _{0}-\omega t)}\right]\\&=e^{-2\pi \kappa x/\lambda _{0}}\operatorname {Re} \!\left[\mathbf {E} _{0}e^{i(kx-\omega t)}\right].\end{aligned}}} Here we see that κ gives an exponential decay, as expected from
5360-443: The polynomial: RMS disagreement between the polynomial and the NBS table is 0.0009 °Bx. Another accurate (R=0.999 999 956) and simpler formula is: The above formulas should not be used outside the range 1.00000 to 1.17874 SG (0 to 40 °Bx). The Plato scale can be approximated with a mean average error of less than 0.02°P with the following equation: or with even higher accuracy (average error less than 0.00053°P with respect to
5440-445: The potential to distinguish between sugars and interfering substances. Newer MIR and NDIR instruments have up to five analyzing channels that allow corrections for interference between ingredients. Formulas derived from the NBS table above: Approximate (R=0.9986) values can be computed from: where SG is the apparent specific gravity of the solution at 20 °C/20 °C. More accurate (R=0.999 999 987) values are available from
5520-653: The real part n is the refractive index and indicates the phase velocity , while the imaginary part κ is called the extinction coefficient indicates the amount of attenuation when the electromagnetic wave propagates through the material. It is related to the absorption coefficient , α abs {\displaystyle \alpha _{\text{abs}}} , through: α abs ( ω ) = 2 ω κ ( ω ) c {\displaystyle \alpha _{\text{abs}}(\omega )={\frac {2\omega \kappa (\omega )}{c}}} These values depend upon
5600-482: The refractive index varies with wavelength, so will the refraction angle as light goes from one material to another. Dispersion also causes the focal length of lenses to be wavelength dependent. This is a type of chromatic aberration , which often needs to be corrected for in imaging systems. In regions of the spectrum where the material does not absorb light, the refractive index tends to decrease with increasing wavelength, and thus increase with frequency. This
5680-506: The relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities: For most materials at visible-light frequencies, the phase is somewhere between 90° and 180°, corresponding to a combination of both refraction and absorption. The refractive index of materials varies with the wavelength (and frequency ) of light. This is called dispersion and causes prisms and rainbows to divide white light into its constituent spectral colors . As
5760-556: The representative sugar body, the International Commission for Uniform Methods of Sugar Analysis (ICUMSA), which favours the use of mass fraction , would report the solution strength as 9.99249%. Because the differences between the systems are of little practical significance (the differences are less than the precision of most common instruments) and wide historical use of the Brix unit, modern instruments calculate mass fraction using ICUMSA official formulas but report
5840-560: The result as °Bx. In the early 1800s, Karl Balling, followed by Adolf Brix , and finally the Normal-Commissions under Fritz Plato , prepared pure sucrose solutions of known strength, measured their specific gravities and prepared tables of percent sucrose by mass vs. measured specific gravity. Balling measured specific gravity to 3 decimal places, Brix to 5, and the Normal-Eichungs Kommission to 6 with
5920-420: The same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers. The ratio had the disadvantage of different appearances. Newton , who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396" (or "nearly 4 to 3"; for water). Hauksbee , who called it the "ratio of refraction", wrote it as
6000-476: The sample and prism of the instrument are both close to 20 °C or, if that is difficult to ensure, readings should be taken at 2 temperatures separated by a few degrees, the change per degree noted and the final recorded value referenced to 20 °C using the Bx vs. Temp slope information. As solutes other than sucrose may affect the refractive index and the specific gravity differently, this refractive "Brix" value
6080-487: The speed of sound is used instead of that of light, and a reference medium other than vacuum must be chosen. For lenses (such as eye glasses ), a lens made from a high refractive index material will be thinner, and hence lighter, than a conventional lens with a lower refractive index. Such lenses are generally more expensive to manufacture than conventional ones. The relative refractive index of an optical medium 2 with respect to another reference medium 1 ( n 21 )
6160-532: The starch and sugar manufacturing industry. Different countries use the scales in different industries: In brewing, the UK uses specific gravity X 1000; Europe uses Plato degrees ; and the US use a mix of specific gravity, degrees Brix, degrees Baumé , and degrees Plato. For fruit juices, 1.0 degree Brix is denoted as 1.0% sugar by mass. This usually correlates well with perceived sweetness. Brix measurements are also used in
6240-809: The tabulated data, in fact, the ICUMSA tables are calculated from a best-fit polynomial. Also note that the tables in use today are not those published by Brix or Plato. Those workers measured true specific gravity reference to water at 4 °C using, respectively, 17.5 °C and 20 °C, as the temperature at which the density of a sucrose solution was measured. Both NBS and ASBC converted to apparent specific gravity at 20 °C/20 °C. The ICUMSA tables are based on more recent measurements on sucrose, fructose, glucose and invert sugar, and they tabulate true density and weight in air at 20 °C against mass fraction. Dissolution of sucrose and other sugars in water changes not only its specific gravity but its optical properties, in particular its refractive index and
6320-435: The wave is not affected by the refractive index. The refractive index may vary with wavelength. This causes white light to split into constituent colors when refracted. This is called dispersion . This effect can be observed in prisms and rainbows , and as chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex -valued refractive index. The imaginary part then handles
6400-482: The °Bx value clearly cannot be equated with the sucrose content, but it may represent a good approximation to the total sugar content. For example, an 11.0% by mass D-Glucose ("grape sugar") solution measured 10.9 °Bx using a hand held instrument. For these reasons, the sugar content of a solution obtained by use of refractometry with the ICUMSA table is often reported as "Refractometric Dry Substance" (RDS), which could be thought of as an equivalent sucrose content. Where it
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