The higher the refractive index. Absolute refractive index and its relation to relative refractive index
In the 8th grade physics course, you got acquainted with the phenomenon of light refraction. Now you know that light is electromagnetic waves of a certain frequency range. Based on knowledge about the nature of light, you will be able to understand the physical cause of refraction and explain many other light phenomena associated with it.
Rice. 141. Passing from one medium to another, the beam is refracted, i.e., changes the direction of propagation
According to the law of light refraction (Fig. 141):
- rays incident, refracted and perpendicular drawn to the interface between two media at the point of incidence of the beam lie in the same plane; the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for these two media
where n 21 is the relative refractive index of the second medium relative to the first.
If the beam passes into any medium from a vacuum, then
where n is the absolute refractive index (or simply refractive index) of the second medium. In this case, the first "environment" is vacuum, the absolute index of which is taken as one.
The law of light refraction was discovered empirically by the Dutch scientist Willebord Snellius in 1621. The law was formulated in a treatise on optics, which was found in the scientist's papers after his death.
After the discovery of Snell, several scientists put forward a hypothesis that the refraction of light is due to a change in its speed when it passes through the boundary of two media. The validity of this hypothesis was confirmed by theoretical proofs carried out independently by the French mathematician Pierre Fermat (in 1662) and the Dutch physicist Christian Huygens (in 1690). By different paths they arrived at the same result, proving that
- the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for these two media, equal to the ratio of the speeds of light in these media:
(3)
From equation (3) it follows that if the angle of refraction β is less than the angle of incidence a, then the light of a given frequency in the second medium propagates more slowly than in the first, i.e. V 2 The relationship of the quantities included in equation (3) served as a good reason for the appearance of another formulation of the definition of the relative refractive index: n 21 \u003d v 1 / v 2 (4) Let a beam of light pass from vacuum to some medium. Replacing v1 in equation (4) with the speed of light in vacuum c, and v 2 with the speed of light in a medium v, we obtain equation (5), which is the definition of the absolute refractive index: According to equations (4) and (5), n 21 shows how many times the speed of light changes when it passes from one medium to another, and n - when it passes from vacuum to a medium. This is the physical meaning of the refractive indices. The value of the absolute refractive index n of any substance is greater than unity (this is confirmed by the data contained in the tables of physical reference books). Then, according to equation (5), c/v > 1 and c > v, i.e., the speed of light in any substance is less than the speed of light in vacuum. Without giving rigorous justifications (they are complex and cumbersome), we note that the reason for the decrease in the speed of light during its transition from vacuum to matter is the interaction of a light wave with atoms and molecules of matter. The greater the optical density of the substance, the stronger this interaction, the lower the speed of light and the greater the refractive index. Thus, the speed of light in a medium and the absolute refractive index are determined by the properties of this medium. According to the numerical values of the refractive indices of substances, one can compare their optical densities. For example, the refractive index different varieties glasses lie in the range from 1.470 to 2.040, and the refractive index of water is 1.333. This means that glass is an optically denser medium than water. Let us turn to Figure 142, with the help of which we can explain why, at the boundary of two media, with a change in speed, the direction of propagation of a light wave also changes. Rice. 142. When light waves pass from air to water, the speed of light decreases, the front of the wave, and with it its speed, change direction The figure shows a light wave passing from air into water and incident on the interface between these media at an angle a. In air, light propagates at a speed v 1 , and in water at a slower speed v 2 . Point A of the wave reaches the boundary first. Over a period of time Δt, point B, moving in the air at the same speed v 1, will reach point B. "During the same time, point A, moving in water at a lower speed v 2, will cover a shorter distance, reaching only point A". In this case, the so-called wave front A "B" in the water will be rotated at a certain angle with respect to the front of the AB wave in the air. And the velocity vector (which is always perpendicular to the wave front and coincides with the direction of its propagation) rotates, approaching the straight line OO", perpendicular to the interface between the media. In this case, the angle of refraction β is less than the angle of incidence α. This is how the refraction of light occurs. It can also be seen from the figure that upon transition to another medium and rotation of the wave front, the wavelength also changes: upon transition to an optically denser medium, the velocity decreases, the wavelength also decreases (λ 2< λ 1). Это согласуется и с известной вам формулой λ = V/v, из которой следует, что при неизменной частоте v (которая не зависит от плотности среды и поэтому не меняется при переходе луча из одной среды в другую) уменьшение скорости распространения волны сопровождается пропорциональным уменьшением длины волны. The processes that are associated with light are an important component of physics and surround us everywhere in our everyday life. The most important in this situation are the laws of reflection and refraction of light, on which modern optics is based. The refraction of light is an important part of modern science. Distortion effect This article will tell you what the phenomenon of light refraction is, as well as what the law of refraction looks like and what follows from it. When a beam falls on a surface that is separated by two transparent substances having different optical densities (for example, different glasses or in water), some of the rays will be reflected, and some will penetrate into the second structure (for example, it will propagate in water or glass). When passing from one medium to another, the beam is characterized by a change in its direction. This is the phenomenon of light refraction. water distortion effect Looking at things in the water, they seem distorted. This is especially noticeable at the border between air and water. Visually it seems that underwater objects are slightly deflected. The described physical phenomenon is precisely the reason why all objects seem distorted in water. When the rays hit the glass, this effect is less noticeable. Beam passage The same indicator is typical for other environments. Determined that this indicator depends on the density of the substance. If the beam is incident from a less dense to a denser structure, then the angle of distortion created will be larger. And if vice versa, then less. To determine this physical phenomenon and the law of refraction was created. The law of refraction of light fluxes allows you to determine the characteristics of transparent substances. The law itself consists of two provisions: Description of the law In this case, at the moment the beam exits the second structure into the first one (for example, when passing luminous flux out of the air, through the glass and back into the air), there will also be a distortion effect. The main indicator in this situation is the ratio of the sine of the angle of incidence to a similar parameter, but for distortion. As follows from the law described above, this indicator is a constant value. Indicators for different objects Thanks to this parameter, you can quite effectively distinguish between types of glass, as well as a variety of precious stones. It is also important for determining the speed of light in various media. Note! Top speed light flux - in a vacuum. When moving from one substance to another, its speed will decrease. For example, diamond, which has the highest refractive index, will have a photon propagation speed 2.42 times faster than air. In water, they will spread 1.33 times slower. For different types glasses, this parameter ranges from 1.4 to 2.2. Note! Some glasses have a refractive index of 2.2, which is very close to diamond (2.4). Therefore, it is not always possible to distinguish a piece of glass from a real diamond. Light can penetrate through different substances, which are characterized by different optical density. As we said earlier, using this law, you can determine the characteristic of the density of the medium (structure). The denser it is, the slower the speed of light will propagate in it. For example, glass or water will be more optically dense than air. This indicator tells how the speed of propagation of photons changes when passing from one substance to another. When moving the light flux through transparent objects, its polarization is possible. It is observed during the passage of a light flux from dielectric isotropic media. Polarization occurs when photons pass through glass. polarization effect Partial polarization is observed when the angle of incidence of the light flux at the boundary of two dielectrics differs from zero. The degree of polarization depends on what the angles of incidence were (Brewster's law). Concluding our short digression, it is still necessary to consider such an effect as a full-fledged internal reflection. Full Display Phenomenon For this effect to appear, it is necessary to increase the angle of incidence of the light flux at the moment of its transition from a denser to a less dense medium at the interface between substances. In a situation where this parameter exceeds a certain limit value, then the photons incident on the boundary of this section will be completely reflected. Actually, this will be our desired phenomenon. Without it, it was impossible to make fiber optics. The practical application of the features of the behavior of the light flux gave a lot, creating a variety of technical devices to improve our lives. At the same time, light has not opened all its possibilities to mankind, and its practical potential has not yet been fully realized.
TO LECTURE №24 "INSTRUMENTAL METHODS OF ANALYSIS" REFRACTOMETRY. Literature: 1.
V.D. Ponomarev " Analytical chemistry» 1983 246-251 2.
A.A. Ishchenko "Analytical Chemistry" 2004 pp 181-184 REFRACTOMETRY. Refractometry is one of the simplest physical methods of analysis at a cost minimum quantity analyte and is carried out in a very short time. Refractometry- a method based on the phenomenon of refraction or refraction i.e. change in the direction of light propagation when passing from one medium to another. Refraction, as well as the absorption of light, is a consequence of its interaction with the medium. The word refractometry means dimension
refraction of light, which is estimated by the value of the refractive index. Refractive index value n depends 1) on the composition of substances and systems, 2) from at what concentration
and what molecules the light beam meets on its way, because under the influence of light molecules different substances polarized differently. It is on this dependence that the refractometric method is based. This method has a number of advantages, as a result of which it has found wide application both in chemical research and in the control of technological processes. 1) The measurement of refractive indices is a very simple process that is carried out accurately and with a minimum investment of time and amount of substance. 2) Typically, refractometers provide up to 10% accuracy in determining the refractive index of light and the content of the analyte The refractometry method is used to control authenticity and purity, to identify individual substances, to determine the structure of organic and inorganic compounds in the study of solutions. Refractometry is used to determine the composition of two-component solutions and for ternary systems. Physical foundations method REFRACTIVE INDICATOR. The deviation of a light beam from its original direction when it passes from one medium to another is greater than more difference in the speeds of light propagation in two these environments. Consider the refraction of a light beam at the boundary of any two transparent media I and II (See Fig.). Let us agree that medium II has a greater refractive power and, therefore, n 1 And n 2- shows the refraction of the corresponding media. If medium I is not a vacuum or air, then the ratio sin of the angle of incidence of the light beam to sin of the angle of refraction will give the value of the relative refractive index n rel. The value of n rel. can also be defined as the ratio of the refractive indices of the media under consideration. n rel. = ----- = --- The value of the refractive index depends on 1) the nature of substances
The nature of a substance in this case is determined by the degree of deformability of its molecules under the action of light - the degree of polarizability. The more intense the polarizability, the stronger the refraction of light. 2)incident light wavelength
The measurement of the refractive index is carried out at a light wavelength of 589.3 nm (line D of the sodium spectrum). The dependence of the refractive index on the wavelength of light is called dispersion. The shorter the wavelength, the greater the refraction. Therefore, rays of different wavelengths are refracted differently. 3)temperature
at which the measurement is taken. A prerequisite for determining the refractive index is compliance with temperature regime. Usually the determination is performed at 20±0.3 0 С. As the temperature rises, the refractive index decreases, and as the temperature decreases, it increases.. The correction for the effect of temperature is calculated from following formula: n t \u003d n 20 + (20-t) 0.0002, where n t - Bye refractive agent at given temperature,
n 20 - refractive index at 20 0 C The influence of temperature on the values of the refractive indices of gases and liquids is related to the values of their coefficients of volumetric expansion. The volume of all gases and liquids increases when heated, the density decreases and, consequently, the indicator decreases The refractive index, measured at 20 0 C and a light wavelength of 589.3 nm, is indicated by the index n D 20 The dependence of the refractive index of a homogeneous two-component system on its state is established experimentally by determining the refractive index for a number of standard systems (for example, solutions), the content of components in which is known. 4) the concentration of a substance in a solution.
For many aqueous solutions of substances, the refractive indices at various concentrations and temperatures have been reliably measured, and in these cases reference data can be used. refractometric tables. Practice shows that when the content of the dissolved substance does not exceed 10-20%, along with graphic method in many cases you can use linear equation type: n=n o +FC, n- refractive index of the solution, no is the refractive index of the pure solvent, C- concentration of the dissolved substance,% F-empirical coefficient, the value of which is found by determining the refractive indices of solutions of known concentration. REFRACTOMETERS. Refractometers are devices used to measure the refractive index. There are 2 types of these instruments: Abbe type refractometer and Pulfrich type. Both in those and in others, the measurements are based on determining the magnitude of the limiting angle of refraction. In practice, refractometers are used various systems: laboratory-RL, universal RLU, etc. The refractive index of distilled water n 0 \u003d 1.33299, in practice, this indicator takes as reference as n 0 =1,333.
Hand refractometer This article reveals the essence of such a concept of optics as the refractive index. Formulas for obtaining this value are given, given short review application of the phenomenon of refraction of an electromagnetic wave. At the dawn of civilization, people asked the question: how does the eye see? It has been suggested that a person emits rays that feel the surrounding objects, or, conversely, all things emit such rays. The answer to this question was given in the seventeenth century. It is contained in optics and is related to what the refractive index is. Reflecting from various opaque surfaces and refracting at the border with transparent ones, light gives a person the opportunity to see. Our planet is shrouded in the light of the Sun. And it is precisely with the wave nature of photons that such a concept as the absolute refractive index is associated. When propagating in a vacuum, a photon encounters no obstacles. On the planet, light encounters many different denser media: the atmosphere (a mixture of gases), water, crystals. Being an electromagnetic wave, photons of light have one phase velocity in vacuum (denoted c), and in the environment - another (denoted v). The ratio of the first and second is what is called the absolute refractive index. The formula looks like this: n = c / v. It is worth giving a definition of the phase velocity of the electromagnetic medium. Otherwise understand what is the refractive index n, it is forbidden. A photon of light is a wave. So, it can be represented as a packet of energy that oscillates (imagine a segment of a sinusoid). Phase is that segment of the sinusoid that the wave passes in this moment time (recall that this is important for understanding such a quantity as the refractive index). For example, a phase can be a maximum of a sinusoid or some segment of its slope. The phase velocity of a wave is the speed at which that particular phase moves. As the definition of the refractive index explains, for a vacuum and for a medium, these values differ. Moreover, each environment has its own value of this quantity. Any transparent compound, whatever its composition, has a refractive index different from all other substances. It has already been shown above that the absolute value is measured relative to vacuum. However, this is difficult on our planet: light more often hits the border of air and water or quartz and spinel. For each of these media, as mentioned above, the refractive index is different. In air, a photon of light travels along one direction and has one phase velocity (v 1), but when it enters water, it changes the direction of propagation and phase velocity (v 2). However, both of these directions lie in the same plane. This is very important for understanding how the image of the surrounding world is formed on the retina of the eye or on the matrix of the camera. The ratio of the two absolute values gives the relative refractive index. The formula looks like this: n 12 \u003d v 1 / v 2. But what if the light, on the contrary, comes out of the water and enters the air? Then this value will be determined by the formula n 21 = v 2 / v 1. When multiplying the relative refractive indices, we get n 21 * n 12 \u003d (v 2 * v 1) / (v 1 * v 2) \u003d 1. This ratio is true for any pair of media. The relative refractive index can be found from the sines of the angles of incidence and refraction n 12 = sin Ɵ 1 / sin Ɵ 2. Do not forget that the angles are counted from the normal to the surface. A normal is a line that is perpendicular to the surface. That is, if the problem is given an angle α
falling relative to the surface itself, then the sine of (90 - α) must be considered. On a calm sunny day, glare plays at the bottom of the lake. Dark blue ice covers the rock. On a woman's hand, a diamond scatters thousands of sparks. These phenomena are a consequence of the fact that all boundaries of transparent media have a relative refractive index. In addition to aesthetic pleasure, this phenomenon can also be used for practical applications. Here are some examples: However, the Sun supplies us with photons not only in the visible spectrum. Infrared, ultraviolet, X-ray ranges are not perceived by human vision, but they affect our lives. IR rays keep us warm, UV photons ionize the upper atmosphere and enable plants to produce oxygen through photosynthesis. And what the refractive index is equal to depends not only on the substances between which the boundary lies, but also on the wavelength of the incident radiation. It is usually clear from the context which value is being referred to. That is, if the book considers X-rays and its effect on a person, then n there it is defined for this range. But usually the visible spectrum of electromagnetic waves is meant, unless otherwise specified. As it became clear from the above, we are talking about transparent media. As examples, we cited air, water, diamond. But what about wood, granite, plastic? Is there such a thing as a refractive index for them? The answer is complex, but in general yes. First of all, we should consider what kind of light we are dealing with. Those media that are opaque to visible photons are cut through by X-ray or gamma radiation. That is, if we were all supermen, then the whole world around us would be transparent to us, but to varying degrees. For example, walls made of concrete would be no denser than jelly, and metal fittings would look like pieces of denser fruit. For other elementary particles, muons, our planet is generally transparent through and through. At one time, scientists brought a lot of trouble to prove the very fact of their existence. Muons pierce us in millions every second, but the probability of a single particle colliding with matter is very small, and it is very difficult to fix this. By the way, Baikal will soon become a place for "catching" muons. Its deep and clear water is ideal for this - especially in winter. The main thing is that the sensors do not freeze. Thus, the refractive index of concrete, for example, for x-ray photons makes sense. Moreover, X-ray irradiation of a substance is one of the most accurate and important methods for studying the structure of crystals. It is also worth remembering that, in a mathematical sense, substances that are opaque for a given range have an imaginary refractive index. Finally, one must understand that the temperature of a substance can also affect its transparency. Light refraction- a phenomenon in which a beam of light, passing from one medium to another, changes direction at the boundary of these media. The refraction of light occurs according to the following law: When the angle of incidence changes, the angle of refraction also changes. The larger the angle of incidence, the larger the angle of refraction. absolute refractive index of a substance- a value equal to the ratio of the phase velocities of light (electromagnetic waves) in vacuum and in a given medium n=c/v The value n is the relative refractive index of medium B with respect to medium A, and n" = 1/n is the relative refractive index of medium A with respect to medium B. (Absolute - relative to vacuum. Total internal reflection- internal reflection, provided that the angle of incidence exceeds a certain critical angle. In this case, the incident wave is completely reflected, and the value of the reflection coefficient exceeds its most big values for polished surfaces. Reflection coefficient at full internal reflection does not depend on the wavelength. In optics, this phenomenon is observed for a wide range electromagnetic radiation, including the x-ray range. In geometric optics, the phenomenon is explained in terms of Snell's law. Considering that the angle of refraction cannot exceed 90°, we obtain that at an angle of incidence whose sine is greater than the ratio of the smaller refractive index to the larger index, electromagnetic wave should be fully reflected on the first Wednesday. In accordance with the wave theory of the phenomenon, the electromagnetic wave nevertheless penetrates into the second medium - the so-called “non-uniform wave” propagates there, which decays exponentially and does not carry away energy with it. The characteristic depth of penetration of an inhomogeneous wave into the second medium is of the order of the wavelength. Laws of refraction of light. From all that has been said, we conclude: Let MN- the interface between two transparent media, for example, air and water, JSC- falling beam OV- refracted beam, - angle of incidence, - angle of refraction, - speed of light propagation in the first medium, - speed of light propagation in the second medium.
Questions
Exercise
Fundamentals of a physical phenomenon
Reflection and refraction of light can be seen especially well in water.
The refraction of light is a physical phenomenon, which is characterized by a change in the direction of the solar beam at the moment of moving from one medium (structure) to another.
To improve the understanding of this process, consider the example of a beam falling from air into water (similarly for glass). By drawing a perpendicular along the interface, the angle of refraction and return of the light beam can be measured. This indicator (the angle of refraction) will change when the flow penetrates into the water (inside the glass).
Note! This parameter is understood as the angle that forms a perpendicular drawn to the separation of two substances when the beam penetrates from the first structure to the second.
At the same time, a change in the slope of the fall will also affect this indicator. But the relationship between them does not remain constant. At the same time, the ratio of their sines will remain constant, which is displayed by the following formula: sinα / sinγ = n, where:physical law
An important parameter for different objects
At the same time, when the value of the slope of the fall changes, the same situation will be typical for a similar indicator. This setting has great importance, since it is an integral characteristic of transparent substances.
Optical density of substances
In addition to the fact that this parameter is a constant value, it also reflects the ratio of the speed of light in two substances. physical meaning can be displayed as the following formula:Another important indicator
Full internal reflection
Conclusion
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The principle of operation on refractometers is based on the determination of the refractive index by the limiting angle method (angle total reflection Sveta).
Refractometer AbbeAbility to see and refractive index
Light and refractive index
Phase speed
Absolute and relative refractive index
The beauty of the refractive index and its applications
Wavelength
Refractive index and reflection
The incident and refracted rays and the perpendicular drawn to the interface between two media at the point of incidence of the beam lie in the same plane. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for two media:
,
Where α
- angle of incidence,
β
- angle of refraction
n - a constant value independent of the angle of incidence.
If light goes from an optically less dense medium to a denser medium, then the angle of refraction is always less than the angle of incidence: β < α.
A beam of light directed perpendicular to the interface between two media passes from one medium to another without breaking.
The value n included in the law of refraction is called the relative refractive index for a pair of media.
This value, ceteris paribus, is greater than unity when the beam passes from a denser medium to a less dense medium, and less than unity when the beam passes from a less dense medium to a denser medium (for example, from a gas or from vacuum to a liquid or solid). There are exceptions to this rule, and therefore it is customary to call a medium optically more or less dense than another.
A beam falling from airless space onto the surface of some medium B is refracted more strongly than when falling on it from another medium A; The refractive index of a ray incident on a medium from airless space is called its absolute refractive index.
Relative - relative to any other substance (the same air, for example).
The relative index of two substances is the ratio of their absolute indices.)
1 . At the interface between two media of different optical density, a beam of light changes its direction when passing from one medium to another.
2. When a light beam passes into a medium with a higher optical density, the angle of refraction is less than the angle of incidence; when a light beam passes from an optically denser medium to a less dense medium, the angle of refraction is greater than the angle of incidence.
The refraction of light is accompanied by reflection, and with an increase in the angle of incidence, the brightness of the reflected beam increases, while the refracted one weakens. This can be seen by conducting the experiment shown in the figure. Consequently, the reflected beam carries away with it the more light energy, the greater the angle of incidence.
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