What Is the Refractive Index?

Refractive index, the ratio of the speed of light in a vacuum to the speed of light in the medium. The higher the refractive index of a material, the stronger the ability to refract incident light. The higher the refractive index, the thinner the lens, that is, the same thickness at the center of the lens, the same degree of the same material, the higher the refractive index than the lower refractive index lens edge is thinner. The refractive index is closely related to the electromagnetic properties of the medium. According to classical electromagnetic theory, _r and _r are the relative permittivity and relative permeability of the medium, respectively. Refractive index is also related to frequency, which is called dispersion. Light is reflected from a relatively dense medium to a relatively sparse medium, and the incident angle is greater than the critical angle, and total reflection can occur.

Chinese name: Refractive index
Foreign name: index of refraction

Field: Optics
Nature: A characteristic of medium to light

Refractive index formula

Refractive index vs. wavelength

The same monochromatic light propagates in different media, with the same frequency and different wavelength. Let be the wavelength of light in a vacuum and n be the refractive index of the medium, then the wavelength 'of light in the medium is

'= / n

Absolute refractive index

n = sin / sin

Let the speed of light in a medium be v . Since the speed of light in vacuum is c , the formula for the absolute refractive index of this medium is :

n = c / v

In the visible range, the refractive index of other media is greater than 1 because the speed of light propagation in the vacuum is the largest.

The phase velocity of light in the plasma can be much greater than c , so the refractive index of the plasma is less than 1.

The same medium has different refractive indices for light of different frequencies; in a medium that is transparent to visible light, the refractive index often increases with decreasing wavelength, that is, the red light has the smallest refractive index and the purple light has the largest refractive index.

Generally speaking, what is the refractive index of an object (such as 1.33 for water, 1.55 for crystal, 2.42 for diamond, and 1.5 to 1.9 depending on the composition of the glass), it refers to sodium yellow light (wavelength 5893 × 10 ^-10 m) In terms of.

Relative refractive index

Angle of incidence when light is refracted from medium 1 into medium 2

With refraction angle

Sine ratio

It is called the refractive index of medium 2 relative to medium 1, which is the "relative refractive index". Therefore, the "absolute refractive index" can be regarded as the refractive index of the medium relative to the vacuum. It is a physical quantity representing the ratio of the speed of light in two (isotropic) media.

Relative refractive index formula: n = sin / sin '= n ' / n = v / v 'A basic parameter of optical media. That is, the ratio of the speed c of light in a vacuum to the phase speed v of a medium.

The refractive index of a vacuum is equal to 1. The ratio of the refractive indices of two media is called the relative refractive index. For example, the refractive index of the first medium is

, The refractive index of the second medium is

,then

It is called the relative refractive index of the second medium to the first medium. The refractive index of a medium is also the relative refractive index of the medium to vacuum. The law of refraction can then be written as:

Factors affecting refractive index

When the two media are compared, the larger refractive index is called the optical dense medium, and the smaller refractive index is called the optical sparse medium. The refractive index is closely related to the electromagnetic properties of the medium. According to classical electrodynamics,

with

The relative permittivity and relative permeability of the medium are respectively. Refractive index is also related to wavelength, which is called dispersion. The refractive index data provided in the manual is for a specific wavelength (usually for sodium yellow light at 5893Å). Gas refractive index is also related to temperature and pressure. The refractive index of air is very close to 1 for light of various frequencies. For example, the refractive index of air at 20 ° C and 760mmHg is 1.00027. The refractive index of air is often regarded as 1 in engineering optics, while the refractive index of other media is the relative refractive index to air. ^[2]

The factors affecting the refractive index of the medium are mainly the following aspects.

Refractive index ion radius

According to Maxwell's electromagnetic field theory, the speed of light propagation in a medium

Abbe refractometer Degree should be

,Therefore:

. Where c is the speed of light in a vacuum, is the permeability of the medium, and is the dielectric constant of the medium,

Is the permeability in vacuum,

Is the dielectric constant of the vacuum,

Is the relative permeability of the medium,

Is the relative permittivity of the medium. In dielectrics like inorganic materials

, So there is

. It shows that the refractive index of a medium increases with its dielectric constant. The dielectric constant is related to the dielectric polarization. The speed of light is slowed by the interaction of light (electromagnetic radiation) and the electronic system inside the atom.

As the ionic radius increases, its dielectric constant also increases, so n also increases. Therefore, a material with a high refractive index can be obtained with a large ion. For example, n = 3.912 for lead sulfide, use low ions to obtain low refractive index materials, such as n = 1.412 for silicon tetrachloride.

Refractive index material

The refractive index is also closely related to the arrangement of ions. For isotropic optical materials, such as amorphous (amorphous) and cubic crystals, there is only one refractive index.

. When light enters a heterogeneous medium, it is generally divided into two waves whose vibration directions are perpendicular to each other and their propagation speeds are different, and they each have two refracted rays, forming what is called birefringence. The refractive index of these two refracted rays, which are parallel to the incident surface, is called the constant refractive index

No matter how the incident angle of incident light changes, it is always a constant and obeys the law of refraction. The refractive index of another light perpendicular to the incident surface varies with the direction of the incident light, and is called the extraordinary light refractive index

, It does not follow the law of refraction. When light is incident along the optical axis of the crystal, only

Exists, when incident perpendicular to the direction of the optical axis,

Up to the maximum, this value is the property of the material.

In summary, along the direction where the crystals are densely packed

Larger.

Refractive index internal stress

Transparent materials with internal stresses have a large n perpendicular to the direction of the main tensile stress and a small n parallel to the direction of the main tensile stress (please think carefully, why?).

In general, the denser the particles in the material, the greater the refractive index.

Refractive index isomers

In homogeneous and heterogeneous materials, the crystal form refractive index is low at high temperature, and the crystal form refractive index existing at low temperature is high. For example, at normal temperature, n = 1.46 for quartz glass and n = 1.55 for quartz crystals; n = 1.47 for scaly quartz at high temperatures; n = 1.49 for cristobalite, as for n = 1.51 for ordinary soda lime silicate glass It has a lower refractive index than quartz. An effective measure to increase the refractive index of glass is to incorporate the oxides of lead and barium. For example, lead glass containing 90% (volume) lead oxide has n = 2.1. ^[3]

Experimental determination of refractive index

The refractive index of a medium is usually determined experimentally, and there are various measurement methods. For solid media, the minimum deflection angle method or autocollimation method is commonly used, or the Michelson interferometer is used to measure the principle of equal thickness interference; for liquid media, the critical angle method (Abbe refractometer) is commonly used; for gas media, the precision is more precise. High interference method (Rayleigh interferometer).

The measurement method is as follows:

Refractive index deflection angle method

For a prism with apex angle and refractive index n to be measured, place it in the air (

= 1). When the first surface of the prism is incident

(2) angle

The angle of deflection reaches the minimum value when the refractive index is measured on the second surface

, Then use a goniometer

And , n can be calculated. (see picture 1)

Using a large precision goniometer with an accuracy of not less than 1 arc second, and using the minimum deflection angle method to measure the refractive index of solid optical materials, a measurement accuracy of ± 5 × 10 ^-6 can be obtained, which is the higher accuracy of various measurement methods One.

Refractive index autocollimation

The refractive index of the material can also be measured on the goniometer using autocollimation. As shown in Figure 2

figure 2 It shows that the incident angle of the light on the front surface of the prism is i . If the refracted light OC is just perpendicular to the rear surface BD of the prism, the reflected optical path COS coincides with the incident optical path SOC , which is called a self-collimating optical path. It is known from the geometric relationship shown in FIG. 2 that the refraction angle f of the light on the front surface is equal to the angle of the prism, so according to the law of refraction

n = sin i / sin ,

By measuring i and , n can be obtained.

Observing and adjusting the goniometer to establish the minimum deflection angle light path or self-collimating light path is not only cumbersome but also subjective error. For many years, China has developed a fully automatic refractometer based on a digital goniometer On this instrument, the minimum deflection angle method or the autocollimation method can be used to automatically find the refractive index, and the measurement results can be automatically processed. The measurement wavelength range can be extended to ultraviolet and infrared (0.2 ~ 15m).

Refractive index critical angle method

The representative instrument is Abbe refractometer. Figure 3 shows the contact of a liquid sample to be measured with a refractive index n coated on two prisms of the instrument

image 3 Between faces (no need to enter the light prism when measuring solid samples). The refractive index of the standard prism itself is known as

,in

> n , the light is refracted into a standard prism. The incident angle of light will not exceed 90 °, and the refraction law knows that the refraction angle will not exceed

The law of refraction knows that the refraction angle will not exceed Over 90 °.

Therefore, in the field of view of the instrument,

The light-dark dividing line corresponding to the refractive index measurement can determine the value of n according to the change of the position of the light-dark dividing line. If the light is retrograde, then

The refractive index measurement is just the critical angle at which total reflection occurs, so it is called the critical angle method.

The optical system of Abbe refractometer is shown in Figure 4. A series of n values are marked on the dial according to the relevant formula. When the center of the fork wire of the reticle is aligned with the light and dark dividing line, the n value of the test sample can be read directly from the dial, which is convenient to use. The Amici prism is used to eliminate dispersion on the dividing line. Therefore, although white light is used instead of a monochromatic light source, a colorless and clear dividing line can be obtained. The Abbe refractometer has a refractive index measurement range of 1.3 to 1.7 with an accuracy n = ± 3 × 10 ^-4 .

Index list

(The original author parameters have not been edited, all parameters refer to RGB or HSB format, R, G, BorH, S, B;

For example: aluminum foil refraction -180,0,0 This parameter is in HSB format, if you have time to continue to typeset the format, you are grateful)

Material Color Index List Metal

Color / RGB diffuse specular reflection bump

Aluminum foil 180, 180, 180/32/90/65/8

Aluminum foil (pure) 180, 180, 180/50/45/35/15

Aluminum 220, 223, 227/35/25/40/15

Polished aluminum 220, 223, 227/35/65/50/12

Brass 191, 173, 111/40/40/40/20

Polished brass 194, 173, 111/40/65/50/10

Aluminum foil

Chrome-plated alloy 150, 150, 150/40/40/25/35

Chrome-plated alloy 2 220, 230, 240/25/30/50/20

Chrome-plated aluminum 220, 230, 240/15/60/70/10

Chrome-plated plastic 220, 230, 240/15/60/85/10

Chrome-plated steel 220, 230, 240/15/60/40/5

Pure chrome 220, 230, 240/15/60/65/5

Copper 186, 110, 64/45/40 / 65/10

18K Gold 234, 199, 135/45/40 / 45/10

24K gold 218, 178, 115/35/40/65/10

Unrefined gold 255, 180, 66/35/40/15/25

Gold 242, 192, 86/45/40 / 25/10

Graphite 87, 33, 77/42/90 / 15/10

Iron 118, 119, 120/35/50/25/20

Lead-tin-antimony alloy 250, 250, 250/30/40 / 15/10

Silver 233, 233, 216/15/90/45/15

Sodium 250, 250, 250/50/90 / 25/10

Waste tin cans 229, 223, 206/30/40/45/30

Stainless steel 128, 128, 126/40/50/35/20

Polished stainless steel 220, 220, 220/35/50/25/35

Tin 220, 223, 227/50/90/35/20

Material color / RGB diffuse specular reflection bump

Purification bottle 27,108,131 / 90/60/5/20

Foam rubber 54,53,53 / 95/30/3/90

20, 20, 20/80/30/5/20

Composite (rough) 25, 25, 25/60/40/5/20

Composite (Smooth) 38, 38, 38/60/30/10/10

Composite (pure) 25, 25, 25/92/40/15/30

Rubber 20, 20, 20/80/30/5/10

Plastic (60 & transparent) 63,108,86 / 90/90/35/10

Plastic (high gloss) 20, 20, 20/70/90/15/5

Plastic (hard and bright) 20, 20, 20/80/80/10/15

Plastic (Icing) 200, 10, 10/80/30/5/10

Plastic (chocolate) 67, 40, 18/90/30/5/15

Rubber 30, 30, 30/30/20/0/50

Rubber buttons 150, 150, 150/60/20/0/30

Vinyl resin 45, 45, 45/60/40/15/30

Light source K

Candle flame 1500

Household white woven lamp 2500-3000

60 watt inflatable tungsten filament lamp 2800

100 watt tungsten filament lamp 2950

1000 watt tungsten filament lamp 3000

500 watt translucent shadow light 2865

500 watt tungsten filament lamp 3175

Huber flashing light 3200

R32 reflector flood light 3200

Zirconium fox light 3200

1,2,4 flood light 3400

Reflector floodlight 3400

Warm white fluorescent lamp 3500

Cool white fluorescent lamp 4500

Daytime Flood Light 4800

White flame carbon arc lamp 5000

M2B flashing signal light 5100

Noon daylight 5400

Direct sunlight in summer 5800

Direct sunlight from 10:00 to 15:00

Daylight fluorescent lamp 6500

Noon Clear Sky Daylight 6500

Cloudy light 6800 7000

Light from the gray sky 7500 8400

Light from a clear blue sky 10000 20,000

Clear blue sky over water

Material refractive index

Vacuum 1.000

glass

Air 1.0003

Liquid carbon dioxide 1.2000

Ice 1.3090

Water 1.3333

Acetone 1.3600

Ethanol 1.3600

Sugar solution (30%) 1.3800

Alcohol 1.3900

Fluorite 1.4340

Melted Quartz 1.4600

Refractive index after light intake of gemstones

Calspar 2 1.4860

Sugar solution (80%) 1.4900

Glass 1.5000

Glass, zinc crown 1.5170

Glass, crown 1.5200

Sodium chloride 1.5300

Triangular prism

Polystyrene 1.5500

Quartz 2 1.5530

Sodium chloride

Emerald 1.5700

Light flint glass 1.5750

Lapis lazuli, lapis lazuli 1.6100

Topaz 1.6100

Carbon disulfide 1.6300

Quartz 1 1.6440

Sodium chloride (salt) 2 1.6440

Heavy Flint Glass 1.6500

diamond

Calspar2 1.6600

Diiodomethane 1.7400

Ruby 1.7700

Sapphire 1.7700

Overweight flint glass 1.8900

Crystal 1.544 1.553

Bismuth oxychloride 2.15

Diamond 2.4170

Chromium oxide

Amorphous selenium 2.2920

Iodine crystal 3.3400

Chocolate 15. 5. 0 88. 29. 0 255.223.220 70 40

Red plastic 48. 0. 0 255. 0. 0 255.255.255 100 68 ^[4]

Refractive index

The problem of negative refractive index (dielectric constant and magnetic permeability are both negative) is a very active research area in the world in recent years. When electromagnetic waves propagate in negative refractive index materials, the electric field E , magnetic field B, and wave vector k form a left-handed spiral relationship. Therefore, negative refractive index materials are also referred to as left-handed materials. Veselago first conceptualized left-handed materials in 1968. Pendry pointed out in 1996 and 1999 that thin metal wires and slotted resonant ring arrays can be used to construct artificial media with a dielectric constant and a permeability that are both negative. In 2001, Smith et al. Followed Pendry's method to construct an artificial medium with negative permittivity and permeability, and experimentally observed for the first time that electromagnetic waves in the microwave band pass through the interface between this artificial medium and air. Negative refraction phenomenon. Although there was much controversy in Smith and others' experiments in the early days, more careful experiments since 2003 have confirmed negative refraction.

There are two types of materials that produce negative refractive index phenomena. One type of material is the dielectric constant and the permeability are both negative due to the local resonance mechanism, which means that the material has an effective negative refractive index. This type of material is also called meta materials. Smith et al.'S slotted resonant ring array is a metamaterial. However, the slotted resonant ring array structure has a large loss and a narrow negative refraction bandwidth, which will be subject to many restrictions in applications. Another type of material is a photonic crystal, which does not have an effective negative refractive index, but in some special cases, the complex dispersion relationship of the photon energy band can lead to negative refractive phenomena. In photonic crystals, the Bragg scattering mechanism of electromagnetic waves in the periodic structure plays a major role. Although both the local resonance mechanism and the non-local Bragg scattering mechanism produce negative refraction, both mechanisms have their own characteristics. As for the Bragg mechanism, it is relatively clear that the required negative refraction passband can be obtained through proper photonic crystal structure selection and photon energy band design. However, the Bragg mechanism requires that the lattice constant of the periodic structure be compared with the electromagnetic wave wavelength of the energy gap. The microwave band will cause the structure to be too large, which limits the device application. In addition, due to the non-local nature of the Bragg mechanism, it is sensitive to the incompleteness of periodic structures (such as structural disorder and defects). In contrast to the Bragg mechanism, the local resonance mechanism does not require the lattice constant of the periodic structure to be comparable to the electromagnetic wave wavelength of the energy gap, and is not sensitive to disorder and defects. However, at present, people do not know enough about some key issues of designing negative refractive index materials using local resonance mechanism, such as how to increase the negative refraction passband bandwidth and reduce loss. This paper proposes another method for the preparation of metamaterials. This method utilizes the periodic loading of a lumped inductor-capacitor resonance unit in a microwave transmission line to achieve an effective negative refractive index. Compared with the slotted resonant ring array structure of Smith et al., The periodic lumped inductor-capacitor resonant structure not only has smaller losses and wider negative refraction bandwidth, but also facilitates external field regulation.

In negative refractive index materials, the phase velocity (wave vector direction) of the electromagnetic wave is opposite to the propagation direction of the group velocity (Poynting vector direction). Many optical phenomena, such as refraction, Doppler shift, Cherenkov radiation, Even light pressure and so on have to be reversed. Planar imaging that breaks through the diffraction limit of media is an important application of negative refractive index materials, and research in this area has drawn great interest. Because of the importance of negative refractive materials in basic research and applications, it was listed as one of the top ten major breakthroughs in 2003 by the United States "Science" magazine. The research on negative refractive index materials is currently being carried out rapidly from two different levels of depth and breadth, and many novel theoretical and experimental results continue to appear. The following lists only three new developments related to this application.

(1) Numerical simulation results of the singular propagation behavior of photons at the interface and surface of negative refractive index materials found that when photons propagate from positive refractive index materials to negative refractive index materials, reflected light and refracted light do not appear at the same time. Instead, the reflected light appears first, and the refracted light appears after a process called "capacitive charging." Similar "capacitance charging" also exists in the process of photon barrier tunneling, but it is unclear whether there is a connection between the two.

(2) The singular transport operation of photonic crystals with negative refractive index materials is found that there is a zero average refractive index ( n = 0) energy gap in one-dimensional photonic crystals composed of positive and negative refractive index materials. This energy gap is different from the usual Bragg energy gap, that is, the position of the energy gap has nothing to do with the lattice size and the effect of disorder is small. Research in this area is very active and will broaden people's understanding of the behavior of photon transport in complex artificial structures.

(3) Design a negative refractive index material using a local resonance mechanism. The existing negative refractive index materials are based on the local resonance caused by the dielectric constant and magnetic permeability to be negative at the same time (also known as double negative materials), and proposed a new mechanism to form negative refractive index materials, That is, the effective negative refractive index is realized by using a single alternating periodic structure of a single negative material having a positive dielectric constant and a negative magnetic permeability (or a negative dielectric constant and a positive magnetic permeability). Recent studies have shown that special periodic lumped inductor-capacitor resonance structures can achieve uni-negative materials. This research not only makes the implementation of negative refractive index materials more diverse, but also deepens people's understanding. ^[3]

Refractive index total reflection

Light is transmitted from the relatively dense medium to the relatively sparse medium, and the incident angle is greater than or equal to the critical angle C , and total reflection can occur.

Total reflection of glass bricks to light The critical angle is the incident angle even when the refraction angle is equal to 90 °.

According to the law of refraction,

Because the refractive index of air n = 1, the incidence from a certain medium into the air is simplified to n = 1 / sin C.

Refractive index light dispersion

For different wavelengths, the refractive index n ( ) of the medium is also different, which is called light dispersion. The relationship between refractive index and wavelength or frequency is called the dispersion relationship of light. Commonly used refractive indices are:

n (d) is the refractive index of the medium in the square and phenanthrene spectrum d (helium yellow line 587.56nm).

n (F) is the refractive index of the medium in the square and phenanthrene spectrum F (hydrogen blue line 486.1nm).

n (C) is the refractive index of the medium in the square and phenanthrene spectrum C (hydrogen red line 656.3nm).

n (e) is the refractive index of the medium in the square and phenanthrene spectrum e (mercury green line 546.07nm). ^[1]

Refractive index meaning

Refractive index is a physical property of matter. It is a commonly used process control indicator in food production. By measuring the refractive index of liquid food, it can identify the composition of food, determine the concentration of food, and judge the purity and quality of food. The refractive index of the sucrose solution increases with increasing concentration. By measuring the refractive index, the concentration of sugar solution and the sugar content of foods such as beverages and canned sugar can be determined. The content of soluble solids in foods such as fruit juices and honey containing sugar as the main component can also be measured.

Various oils and fats have a certain fatty acid composition, and each fatty acid has its specific refractive index. When the number of carbon atoms is the same, the refractive index of unsaturated fatty acids is much larger than the refractive index of saturated fatty acids; the larger the molecular weight of unsaturated fatty acids, the larger the refractive index; Therefore, measuring the refractive index can identify the composition and quality of grease.

Under normal circumstances, the refractive index of certain liquid foods has a certain range, such as the refractive index of normal cow's whey is between 1.34199 and 1.34275. When the quality of these liquid foods changes due to doping, concentration changes, or variety changes, the refractive index often changes. Therefore, the determination of the refractive index can preliminarily determine whether some foods are normal. If milk is mixed with water, the refractive index of whey decreases. Therefore, by measuring the refractive index of milk whey, we can know the content of lactose and determine whether the milk is mixed with water. ^[6]