This article reveals the essence of such an optics concept as refractive index. Formulas for obtaining this quantity are given, and a brief overview of the application of the phenomenon of electromagnetic wave refraction is given.
Vision and refractive index
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 surrounding objects, or, conversely, all things emit such rays. The answer to this question was given in the seventeenth century. It is found in optics and is related to what refractive index is. Reflecting from various opaque surfaces and refracting at the border with transparent ones, light gives a person the opportunity to see.
Light and refractive index
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. Propagating in a vacuum, a photon encounters no obstacles. On the planet, light encounters many different denser environments: the atmosphere (a mixture of gases), water, crystals. Being an electromagnetic wave, photons of light have one phase speed in a 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.
Phase speed
It is worth defining the phase velocity of the electromagnetic medium. Otherwise, understand what the refractive index is n, it is forbidden. A photon of light is a wave. This means that it can be represented as a packet of energy that oscillates (imagine a segment of a sine wave). The phase is the segment of the sinusoid that the wave travels at a given moment in time (remember that this is important for understanding such a quantity as the refractive index).
For example, the phase may be the maximum of a sinusoid or some segment of its slope. The phase speed of a wave is the speed at which that particular phase moves. As the definition of the refractive index explains, these values differ for a vacuum and for a medium. Moreover, each environment has its own value of this quantity. Any transparent compound, whatever its composition, has a refractive index that is different from all other substances.
Absolute and relative refractive index
It was already shown above that the absolute value is measured relative to the vacuum. However, this is difficult on our planet: light more often hits the boundary 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 speed (v 1), but when it gets into water, it changes the direction of propagation and phase speed (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 = v 1 / v 2.
But what if 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 obtain n 21 * n 12 = (v 2 * v 1) / (v 1 * v 2) = 1. This relationship is valid 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 angles are measured from the normal to the surface. A normal is a line perpendicular to the surface. That is, if the problem is given an angle α fall relative to the surface itself, then we must calculate the sine of (90 - α).
The beauty of refractive index and its applications
On a calm sunny day, reflections play on the bottom of the lake. Dark blue ice covers the rock. A diamond scatters thousands of sparks on a woman’s hand. 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 examples:
- A glass lens collects a beam of sunlight and sets the grass on fire.
- The laser beam focuses on the diseased organ and cuts off unnecessary tissue.
- Sunlight is refracted on the ancient stained glass window, creating a special atmosphere.
- A microscope magnifies images of very small details.
- Spectrophotometer lenses collect laser light reflected from the surface of the substance being studied. In this way, it is possible to understand the structure and then the properties of new materials.
- There is even a project for a photonic computer, where information will be transmitted not by electrons, as now, but by photons. Such a device will definitely require refractive elements.
Wavelength
However, the Sun supplies us with photons not only in the visible spectrum. Infrared, ultraviolet, and x-ray ranges are not perceived by human vision, but they affect our lives. IR rays warm us, UV photons ionize the upper layers of the 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. What exact value we are talking about is usually clear from the context. That is, if the book examines x-rays and its effect on humans, then n there it is defined specifically for this range. But usually the visible spectrum of electromagnetic waves is meant unless something else is specified.
Refractive index and reflection
As it became clear from what was written above, we are talking about transparent environments. We gave air, water, and diamond as examples. 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, concrete walls 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 had a lot of trouble proving the very fact of their existence. Millions of muons pierce us every second, but the probability of a single particle colliding with matter is very small, and it is very difficult to detect 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. So the refractive index of concrete, for example, for x-ray photons makes sense. Moreover, irradiating a substance with x-rays is one of the most accurate and important ways to study 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, we must understand that the temperature of a substance can also affect its transparency.
REFRACTION INDEX(refractive index) - optical. characteristic of the environment associated with refraction of light at the interface between two transparent optically homogeneous and isotropic media during its transition from one medium to another and due to the difference in the phase velocities of light propagation in the media. The value of P. p. is equal to the ratio of these speeds. relative
P. p. of these environments. If light falls on the second or first medium from (where is the speed of light With), then the quantities absolute pp of these averages. In this case, a the law of refraction can be written in the form where and are the angles of incidence and refraction.
The magnitude of the absolute power factor depends on the nature and structure of the substance, its state of aggregation, temperature, pressure, etc. At high intensities, the power factor depends on the intensity of light (see. Nonlinear optics). In a number of substances, P. changes under the influence of external influences. electric fields ( Kerr effect- in liquids and gases; electro-optical Pockels effect- in crystals).
For a given medium, the absorption band depends on the light wavelength l, and in the region of absorption bands this dependence is anomalous (see Fig. Light dispersion).In X-ray. region, the power factor for almost all media is close to 1, in the visible region for liquids and solids it is about 1.5; in the IR region for a number of transparent media 4.0 (for Ge).
Lit.: Landsberg G.S., Optics, 5th ed., M., 1976; Sivukhin D.V., General course, 2nd ed., [vol. 4] - Optics, M., 1985. V. I. Malyshev,
Laboratory work
Light refraction. Measuring the refractive index of a liquid
using a refractometer
Goal of the work: deepening understanding of the phenomenon of light refraction; study of methods for measuring the refractive index of liquid media; studying the principle of working with a refractometer.
Equipment: refractometer, sodium chloride solutions, pipette, soft cloth for wiping optical parts of instruments.
Theory
Laws of reflection and refraction of light. Refractive index.
At the interface between the media, light changes the direction of its propagation. Part of the light energy returns to the first medium, i.e. light is reflected. If the second medium is transparent, then part of the light, under certain conditions, passes through the interface between the media, usually changing the direction of propagation. This phenomenon is called refraction of light (Fig. 1).
Rice. 1. Reflection and refraction of light at a flat interface between two media.
The direction of reflected and refracted rays when light passes through a flat interface between two transparent media is determined by the laws of reflection and refraction of light.
Law of light reflection. The reflected ray lies in the same plane as the incident ray and the normal restored to the plane of separation of the media at the point of incidence. The angle of incidence is equal to the angle of reflection .
The law of light refraction. The refracted ray lies in the same plane as the incident ray and the normal restored to the plane of separation of the media at the point of incidence. Angle of incidence sine ratio α to the sine of the angle of refraction β there is a constant value for these two media, called the relative refractive index of the second medium in relation to the first:
Relative refractive index two media is equal to the ratio of the speed of light in the first medium v 1 to the speed of light in the second medium v 2:
If light comes from a vacuum into a medium, then the refractive index of the medium relative to the vacuum is called the absolute refractive index of this medium and is equal to the ratio of the speed of light in vacuum With to the speed of light in a given medium:
Absolute refractive indices are always greater than unity; for air n taken as one.
The relative refractive index of two media can be expressed in terms of their absolute indices n 1 And n 2 :
Determination of the refractive index of a liquid
To quickly and conveniently determine the refractive index of liquids, there are special optical instruments - refractometers, the main part of which are two prisms (Fig. 2): auxiliary Etc. 1 and measuring Pr.2. The liquid to be tested is poured into the gap between the prisms.
When measuring indicators, two methods can be used: the grazing beam method (for transparent liquids) and the total internal reflection method (for dark, turbid and colored solutions). In this work, the first of them is used.
In the grazing beam method, light from an external source passes through the face AB prisms Project 1, dissipates on its matte surface AC and then penetrates through the layer of the liquid under study into the prism Pr.2. The matte surface becomes a source of rays in all directions, so it can be observed through the edge EF prisms Pr.2. However, the edge AC can be seen through EF only at an angle greater than a certain minimum angle i. The magnitude of this angle is uniquely related to the refractive index of the liquid located between the prisms, which is the main idea behind the design of the refractometer.
Consider the passage of light through the face EF lower measuring prism Pr.2. As can be seen from Fig. 2, applying the law of light refraction twice, we can obtain two relationships:
Solving this system of equations, it is easy to come to the conclusion that the refractive index of the liquid
depends on four quantities: Q, r, r 1 And i. However, not all of them are independent. For example,
r+ s= R , (4)
Where R - refractive angle of prism Project 2. In addition, by setting the angle Q the maximum value is 90°, from equation (1) we obtain:
But the maximum angle value r , as can be seen from Fig. 2 and relations (3) and (4), the minimum angle values correspond i And r 1 , those. i min And r min .
Thus, the refractive index of a liquid for the case of “grazing” rays is associated only with the angle i. In this case, there is a minimum angle value i, when the edge AC is still visible, that is, in the field of view it appears mirror-white. For smaller viewing angles, the edge is not visible, and in the field of view this place appears black. Since the telescope of the device captures a relatively wide angular zone, light and black areas are simultaneously observed in the field of view, the boundary between which corresponds to the minimum observation angle and is uniquely related to the refractive index of the liquid. Using the final calculation formula:
(its conclusion is omitted) and a number of liquids with known refractive indices, you can calibrate the device, i.e., establish a unique correspondence between the refractive indices of liquids and angles i min . All formulas given are derived for rays of one particular wavelength.
Light of different wavelengths will be refracted taking into account the dispersion of the prism. Thus, when the prism is illuminated with white light, the interface will be blurred and colored in different colors due to dispersion. Therefore, every refractometer has a compensator that eliminates the result of dispersion. It may consist of one or two direct vision prisms - Amici prisms. Each Amici prism consists of three glass prisms with different refractive indices and different dispersion, for example, the outer prisms are made of crown glass, and the middle one is made of flint glass (crown glass and flint glass are types of glass). By rotating the compensator prism using a special device, a sharp, colorless image of the interface is achieved, the position of which corresponds to the refractive index value for the yellow sodium line λ =5893 Å (the prisms are designed so that rays with a wavelength of 5893 Å do not experience deflection).
The rays passing through the compensator enter the lens of the telescope, then pass through the reversing prism through the eyepiece of the telescope into the eye of the observer. The schematic path of the rays is shown in Fig. 3.
The refractometer scale is calibrated in the values of the refractive index and the concentration of the sucrose solution in water and is located in the focal plane of the eyepiece.
experimental part
Task 1. Checking the refractometer.
Direct the light using a mirror onto the refractometer's auxiliary prism. With the auxiliary prism raised, pipette a few drops of distilled water onto the measuring prism. By lowering the auxiliary prism, achieve the best illumination of the field of view and set the eyepiece so that the crosshair and refractive index scale are clearly visible. By rotating the camera of the measuring prism, you get the boundary of light and shadow in the field of view. Rotate the compensator head until the color of the border between light and shadow is eliminated. Align the light and shadow boundary with the crosshair point and measure the refractive index of water n change . If the refractometer is working properly, then for distilled water the value should be n 0 = 1.333, if the readings differ from this value, an amendment must be determined Δn= n change - 1.333, which should then be taken into account when further working with the refractometer. Please make corrections to Table 1.
Table 1.
|
n 0 |
n change |
Δ n |
|
|
N 2 ABOUT |
Task 2. Determination of the refractive index of a liquid.
Determine the refractive indices of solutions of known concentrations, taking into account the found correction.
Table 2.
|
C, vol. % |
n change |
n ist |
Plot a graph of the dependence of the refractive index of table salt solutions on the concentration based on the results obtained. Draw a conclusion about the dependence of n on C; draw conclusions about the accuracy of measurements using a refractometer.
Take a salt solution of unknown concentration WITH x , determine its refractive index and use the graph to find the concentration of the solution.
Clean the work area and carefully wipe the refractometer prisms with a damp, clean cloth.
Control questions
Reflection and refraction of light.
Absolute and relative refractive indices of the medium.
The principle of operation of a refractometer. Sliding beam method.
Schematic path of rays in a prism. Why are compensator prisms needed?
Propagation, reflection and refraction of light
The nature of light is electromagnetic. One proof of this is the coincidence of the speeds of electromagnetic waves and light in a vacuum.
In a homogeneous medium, light travels in a straight line. This statement is called the law of rectilinear propagation of light. An experimental proof of this law is the sharp shadows produced by point light sources.
The geometric line indicating the direction of propagation of light is called a light ray. In an isotropic medium, light rays are directed perpendicular to the wave front.
The geometric location of points in the medium oscillating in the same phase is called the wave surface, and the set of points to which the oscillation has reached at a given point in time is called the wave front. Depending on the type of wave front, plane and spherical waves are distinguished.
To explain the process of light propagation, the general principle of wave theory about the movement of a wave front in space, proposed by the Dutch physicist H. Huygens, is used. According to Huygens' principle, each point in the medium to which light excitation reaches is the center of spherical secondary waves, which also propagate at the speed of light. The surface surrounding the fronts of these secondary waves gives the position of the front of the actually propagating wave at that moment in time.
It is necessary to distinguish between light beams and light rays. A light beam is a part of a light wave that carries light energy in a given direction. When replacing a light beam with a light beam describing it, the latter must be taken to coincide with the axis of a sufficiently narrow, but at the same time having a finite width (the cross-sectional dimensions are much larger than the wavelength) light beam.
There are divergent, converging and quasi-parallel light beams. The terms beam of light rays or simply light rays are often used, meaning a set of light rays that describe a real light beam.
The speed of light in vacuum c = 3 108 m/s is a universal constant and does not depend on frequency. For the first time, the speed of light was experimentally determined by the astronomical method by the Danish scientist O. Roemer. More accurately, the speed of light was measured by A. Michelson.
In matter the speed of light is less than in vacuum. The ratio of the speed of light in a vacuum to its speed in a given medium is called the absolute refractive index of the medium:
where c is the speed of light in a vacuum, v is the speed of light in a given medium. The absolute refractive indices of all substances are greater than unity.
When light propagates through a medium, it is absorbed and scattered, and at the interface between the media it is reflected and refracted.
The law of light reflection: the incident beam, the reflected beam and the perpendicular to the interface between two media, restored at the point of incidence of the beam, lie in the same plane; the angle of reflection g is equal to the angle of incidence a (Fig. 1). This law coincides with the law of reflection for waves of any nature and can be obtained as a consequence of Huygens' principle.
The law of light refraction: the incident ray, the refracted ray and the perpendicular to the interface between two media, restored at the point of incidence of the ray, lie in the same plane; the ratio of the sine of the angle of incidence to the sine of the angle of refraction for a given frequency of light is a constant value called the relative refractive index of the second medium relative to the first:
The experimentally established law of light refraction is explained on the basis of Huygens' principle. According to wave concepts, refraction is a consequence of changes in the speed of wave propagation when passing from one medium to another, and the physical meaning of the relative refractive index is the ratio of the speed of propagation of waves in the first medium v1 to the speed of their propagation in the second medium
For media with absolute refractive indices n1 and n2, the relative refractive index of the second medium relative to the first is equal to the ratio of the absolute refractive index of the second medium to the absolute refractive index of the first medium:
The medium that has a higher refractive index is called optically denser; the speed of light propagation in it is lower. If light passes from an optically denser medium to an optically less dense one, then at a certain angle of incidence a0 the angle of refraction should become equal to p/2. The intensity of the refracted beam in this case becomes equal to zero. Light falling on the interface between two media is completely reflected from it.
The angle of incidence a0 at which total internal reflection of light occurs is called the limiting angle of total internal reflection. At all angles of incidence equal to and greater than a0, total reflection of light occurs.
The value of the limiting angle is found from the relation If n2 = 1 (vacuum), then
2 The refractive index of a substance is a value equal to the ratio of the phase speeds of light (electromagnetic waves) in a vacuum and in a given medium. They also talk about the refractive index for any other waves, for example, sound
The refractive index depends on the properties of the substance and the wavelength of the radiation; for some substances, the refractive index changes quite strongly when the frequency of electromagnetic waves changes from low frequencies to optical and beyond, and can also change even more sharply in certain areas of the frequency scale. The default usually refers to the optical range or the range determined by the context.
There are optically anisotropic substances in which the refractive index depends on the direction and polarization of light. Such substances are quite common, in particular, they are all crystals with a fairly low symmetry of the crystal lattice, as well as substances subjected to mechanical deformation.
The refractive index can be expressed as the root of the product of the magnetic and dielectric constants of the medium
(it should be taken into account that the values of magnetic permeability and absolute dielectric constant for the frequency range of interest - for example, optical - can differ very much from the static value of these values).
To measure the refractive index, manual and automatic refractometers are used. When a refractometer is used to determine the concentration of sugar in an aqueous solution, the device is called a saccharimeter.
The ratio of the sine of the angle of incidence () of the beam to the sine of the angle of refraction () when the beam passes from medium A to medium B is called the relative refractive index for this pair of media.
The quantity n is the relative refractive index of medium B in relation to medium A, аn" = 1/n is the relative refractive index of medium A in relation to medium B.
This value, other things being equal, is usually less than unity when a beam passes from a more dense medium to a less dense medium, and more than unity when a beam passes from a less dense medium to a denser medium (for example, from a gas or from a 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 (not to be confused with optical density as a measure of the opacity of a medium).
A ray 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 or simply the refractive index of a given medium; this is the refractive index, the definition of which is given at the beginning of the article. The refractive index of any gas, including air, under normal conditions is much less than the refractive index of liquids or solids, therefore, approximately (and with relatively good accuracy) the absolute refractive index can be judged by the refractive index relative to air.
Rice. 3. Operating principle of an interference refractometer. The light beam is divided so that its two parts pass through cuvettes of length l filled with substances with different refractive indices. At the exit from the cuvettes, the rays acquire a certain path difference and, being brought together, give on the screen a picture of interference maxima and minima with k orders (shown schematically on the right). Refractive index difference Dn=n2 –n1 =kl/2, where l is the wavelength of light.
Refractometers are instruments used to measure the refractive index of substances. The operating principle of a refractometer is based on the phenomenon of total reflection. If a scattered beam of light falls on the interface between two media with refractive indices and, from a more optically dense medium, then, starting from a certain angle of incidence, the rays do not enter the second medium, but are completely reflected from the interface in the first medium. This angle is called the limiting angle of total reflection. Figure 1 shows the behavior of rays when falling into a certain current of this surface. The beam comes at an extreme angle. From the law of refraction we can determine: , (since).
The magnitude of the limiting angle depends on the relative refractive index of the two media. If the rays reflected from the surface are directed to a collecting lens, then in the focal plane of the lens you can see the boundary of light and penumbra, and the position of this boundary depends on the value of the limiting angle, and therefore on the refractive index. A change in the refractive index of one of the media entails a change in the position of the interface. The interface between light and shadow can serve as an indicator when determining the refractive index, which is used in refractometers. This method of determining the refractive index is called the total reflection method
In addition to the total reflection method, refractometers use the grazing beam method. In this method, a scattered beam of light hits the boundary from a less optically dense medium at all possible angles (Fig. 2). The ray sliding along the surface () corresponds to the limiting angle of refraction (the ray in Fig. 2). If we place a lens in the path of the rays () refracted on the surface, then in the focal plane of the lens we will also see a sharp boundary between light and shadow.
Since the conditions determining the value of the limiting angle are the same in both methods, the position of the interface is the same. Both methods are equivalent, but the total reflection method allows you to measure the refractive index of opaque substances
Path of rays in a triangular prism
Figure 9 shows a cross section of a glass prism with a plane perpendicular to its side edges. The beam in the prism is deflected towards the base, refracting at the edges OA and 0B. The angle j between these faces is called the refractive angle of the prism. The angle of deflection of the beam depends on the refractive angle of the prismj, the refractive index n of the prism material and the angle of incidencea. It can be calculated using the law of refraction (1.4).
The refractometer uses a white light source 3. Due to dispersion, when light passes through prisms 1 and 2, the boundary of light and shadow turns out to be colored. To avoid this, a compensator 4 is placed in front of the telescope lens. It consists of two identical prisms, each of which is glued together from three prisms with different refractive indexes. Prisms are selected so that a monochromatic beam with a wavelength = 589.3 µm. (sodium yellow line wavelength) was not tested after passing the deflection compensator. Rays with other wavelengths are deflected by prisms in different directions. By moving the compensator prisms using a special handle, we ensure that the boundary between light and darkness becomes as clear as possible.
The light rays, having passed the compensator, enter the lens 6 of the telescope. The image of the light-shadow interface is viewed through the eyepiece 7 of the telescope. At the same time, scale 8 is viewed through the eyepiece. Since the limiting angle of refraction and the limiting angle of total reflection depend on the refractive index of the liquid, the values of this refractive index are immediately marked on the refractometer scale.
The optical system of the refractometer also contains a rotating prism 5. It allows you to position the axis of the telescope perpendicular to prisms 1 and 2, which makes observation more convenient.
Refractive index
Refractive index substances - a quantity equal to the ratio of the phase speeds of light (electromagnetic waves) in a vacuum and in a given medium. Also, the refractive index is sometimes spoken of for any other waves, for example, sound, although in cases such as the latter, the definition, of course, has to be modified somehow.
The refractive index depends on the properties of the substance and the wavelength of the radiation; for some substances, the refractive index changes quite strongly when the frequency of electromagnetic waves changes from low frequencies to optical and beyond, and can also change even more sharply in certain regions of the frequency scale. The default usually refers to the optical range or the range determined by the context.
Links
- RefractiveIndex.INFO refractive index database
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See what “Refractive Index” is in other dictionaries:
Relative of two media n21, dimensionless ratio of the propagation speeds of optical radiation (c light) in the first (c1) and second (c2) media: n21 = c1/c2. At the same time it relates. P. p. is the ratio of the sines of the g l a p a d e n i j and y g l ... ... Physical encyclopedia
See Refractive Index...
See refractive index. * * * REFRACTION INDEX REFRACTIVE INDEX, see Refractive Index (see REFRACTIVE INDEX) ... encyclopedic Dictionary- REFRACTIVE INDEX, a quantity characterizing the medium and equal to the ratio of the speed of light in a vacuum to the speed of light in the medium (absolute refractive index). The refractive index n depends on the dielectric e and magnetic permeability m... ... Illustrated Encyclopedic Dictionary
- (see REFRACTION INDEX). Physical encyclopedic dictionary. M.: Soviet Encyclopedia. Editor-in-chief A. M. Prokhorov. 1983 ... Physical encyclopedia
See Refractive index... Great Soviet Encyclopedia
The ratio of the speed of light in a vacuum to the speed of light in a medium (absolute refractive index). The relative refractive index of 2 media is the ratio of the speed of light in the medium from which light falls on the interface to the speed of light in the second... ... Big Encyclopedic Dictionary
Optics is one of the old branches of physics. Since the times of ancient Greece, many philosophers have been interested in the laws of the movement and propagation of light in various transparent materials, such as water, glass, diamond and air. This article discusses the phenomenon of light refraction, focusing on the refractive index of air.
Light beam refraction effect
Everyone in their life has encountered hundreds of times the manifestation of this effect when they looked at the bottom of a reservoir or at a glass of water with some object placed in it. At the same time, the pond did not seem as deep as it actually was, and the objects in the glass of water looked deformed or broken.
The phenomenon of refraction consists of a break in its rectilinear trajectory when it intersects the interface of two transparent materials. Summarizing a large amount of experimental data, at the beginning of the 17th century, the Dutchman Willebrord Snell obtained a mathematical expression that accurately described this phenomenon. This expression is usually written in the following form:
n 1 *sin(θ 1) = n 2 *sin(θ 2) = const.
Here n 1, n 2 are the absolute refractive indices of light in the corresponding material, θ 1 and θ 2 are the angles between the incident and refracted rays and the perpendicular to the interface plane, which is drawn through the intersection point of the ray and this plane.
This formula is called Snell's or Snell-Descartes' law (it was the Frenchman who wrote it down in the form presented, while the Dutchman used units of length rather than sines).
In addition to this formula, the phenomenon of refraction is described by another law, which is geometric in nature. It consists in the fact that the marked perpendicular to the plane and two rays (refracted and incident) lie in the same plane.
Absolute refractive index
This quantity is included in the Snell formula, and its value plays an important role. Mathematically, the refractive index n corresponds to the formula:
The symbol c is the speed of electromagnetic waves in a vacuum. It is approximately 3*10 8 m/s. The value v is the speed of light moving through the medium. Thus, the refractive index reflects the amount of retardation of light in a medium relative to airless space.
Two important conclusions follow from the formula above:
- the value of n is always greater than 1 (for vacuum it is equal to unity);
- it is a dimensionless quantity.
For example, the refractive index of air is 1.00029, while for water it is 1.33.
The refractive index is not a constant value for a particular medium. It depends on the temperature. Moreover, for each frequency of an electromagnetic wave it has its own meaning. Thus, the above figures correspond to a temperature of 20 o C and the yellow part of the visible spectrum (wavelength - about 580-590 nm).
The dependence of n on the frequency of light is manifested in the decomposition of white light by a prism into a number of colors, as well as in the formation of a rainbow in the sky during heavy rain.
Refractive index of light in air
Its value has already been given above (1.00029). Since the refractive index of air differs only in the fourth decimal place from zero, for solving practical problems it can be considered equal to one. A slight difference between n for air and unity indicates that light is practically not slowed down by air molecules, which is due to its relatively low density. Thus, the average air density is 1.225 kg/m 3, that is, it is more than 800 times lighter than fresh water.
Air is an optically weak medium. The process of slowing down the speed of light in a material is of a quantum nature and is associated with the acts of absorption and emission of photons by atoms of the substance.
Changes in the composition of air (for example, an increase in the content of water vapor in it) and changes in temperature lead to significant changes in the refractive index. A striking example is the mirage effect in the desert, which occurs due to differences in the refractive indices of air layers with different temperatures.
Glass-air interface
Glass is a much denser medium than air. Its absolute refractive index ranges from 1.5 to 1.66, depending on the type of glass. If we take the average value of 1.55, then the refraction of the beam at the air-glass interface can be calculated using the formula:
sin(θ 1)/sin(θ 2) = n 2 /n 1 = n 21 = 1.55.
The value n 21 is called the relative refractive index of air - glass. If the beam comes out of the glass into the air, then the following formula should be used:
sin(θ 1)/sin(θ 2) = n 2 /n 1 = n 21 = 1/1.55 = 0.645.
If the angle of the refracted ray in the latter case is equal to 90 o, then the corresponding one is called critical. For the glass-air boundary it is equal to:
θ 1 = arcsin(0.645) = 40.17 o.
If the beam falls on the glass-air boundary with larger angles than 40.17 o, then it will be reflected completely back into the glass. This phenomenon is called “total internal reflection”.
The critical angle exists only when the beam moves from a dense medium (from glass to air, but not vice versa).