Geometric optics – a branch of physics in which the laws of light propagation are considered on the basis of the idea of light rays (lines normal to the wave surfaces along which the flow of light energy propagates).
Total light reflection
Total reflection of light is a phenomenon in which a ray incident on the interface between two media is completely reflected without penetrating into the second medium.
Total reflection of light occurs at angles of incidence of light on the interface exceeding the limiting angle total reflection when light propagates from an optically denser medium to a less optically dense medium.
The phenomenon of complete reflection of light in our lives.
This phenomenon is used in fiber optics. Light, entering an optically transparent tube at a certain angle, and being repeatedly reflected from its walls from the inside, comes out through its other end (Fig. 5). This is how signals are transmitted.
When light passes from an optically less dense medium to a more dense one, for example from air to glass or water, 1 > 2 ; and according to the law of refraction (1.4) the refractive index n>1, therefore > (Fig. 10, a): the refracted ray approaches the perpendicular to the interface.
If you direct a ray of light in the opposite direction - from an optically more dense medium to an optically less dense one along the former refracted ray (Fig. 10, b), then the law of refraction will be written as follows:
Upon exiting the optically denser medium, the refracted ray will follow the line of the former incident ray, therefore < , т. е. преломленный луч отклоняется от перпендикуляра. По мере увеличения угла the angle of refraction increases, remaining always greater than the angle . Finally, at a certain angle of incidence, the value of the refraction angle will approach 90 and the refracted beam will go almost along the interface (Fig. 11). To the greatest possible angle refraction =90 corresponds to the angle of incidence 0 .
Let's try to figure out what will happen when > 0 . When light falls on the boundary of two media, the light beam, as already mentioned, is partially refracted and partially reflected from it. At > 0 refraction of light is impossible. This means that the beam must be completely reflected. This phenomenon is called complete reflection of light.
To observe total reflection, a glass half-cylinder with a frosted back surface can be used. The half-cylinder is fixed on the disk so that the middle of the flat surface of the half-cylinder coincides with the center of the disk (Fig. 12). A narrow beam of light from the illuminator is directed from below to lateral surface half-cylinder perpendicular to its surface. The beam is not refracted on this surface. On a flat surface, the beam is partially refracted and partially reflected. Reflection occurs in accordance with the law of reflection, and refraction occurs in accordance with the law of refraction
If you increase the angle of incidence, you will notice that the brightness (and therefore the energy) of the reflected beam increases, while the brightness (energy) of the refracted beam decreases. The energy of the refracted beam decreases especially quickly when the refraction angle approaches 90. Finally, when the angle of incidence becomes such that the refracted beam goes along the interface (see Fig. 11), the fraction of reflected energy is almost 100%. Let's rotate the illuminator, making the angle of incidence big 0 . We will see that the refracted beam has disappeared and all the light is reflected from the interface, i.e., total reflection of light occurs.
Figure 13 shows a beam of rays from a source placed in water near its surface. Greater light intensity is indicated by a thicker line representing the corresponding beam.
Angle of incidence 0 , corresponding to a refraction angle of 90, is called limiting angle of total reflection. At sin=1 formula (1.8) takes the form
From this equality the value of the limiting angle of total reflection can be found 0 . For water (n=1.33) it turns out to be 4835", for glass (n=1.5) it takes the value 4151", and for diamond (n=2.42) this angle is 2440 ". In all cases, the second medium is air.
The phenomenon of total reflection is easy to observe on simple experience. Pour water into a glass and raise it slightly above eye level. The surface of the water, when viewed from below through the wall, appears shiny, as if silvered due to the complete reflection of light.
Total reflection is used in the so-called fiber optics for transmitting light and images through bundles of transparent flexible fibers - light guides. The light guide is a glass fiber cylindrical, coated with a sheath of transparent material with a lower refractive index than the fiber. Due to multiple total reflection, light can be directed along any (straight or curved) path (Fig. 14).
The fibers are gathered into bundles. In this case, each of the fibers transmits some element of the image (Fig. 15). Fiber bundles are used, for example, in medicine to study internal organs.
As the technology for manufacturing long bundles of fibers - light guides - improves, communication (including television) using light rays is beginning to be used more and more widely.
Total reflection of light shows what rich possibilities for explaining the phenomena of the propagation of light are contained in the law of refraction. At first, total reflection was only a curious phenomenon. Now it is gradually leading to a revolution in transmission methods information.
Fiber optics
section of optics, which deals with the transmission of light and images through optical fibers and waveguides. range, in particular for multicore optical fibers and bundles of flexible fibers. V. o. arose in the 50s. 20th century
In fiber optic In detail, light signals are transmitted from one surface (the end of the light guide) to another (output) as a set
Element-by-element image transmission by a fiber part: 1 - image supplied to the input end; 2 - light-conducting core; 3 - insulating layer; 4 - mosaic image transmitted to the output end.
image elements, each of which is transmitted along its own light conductor (Fig.). In fiber parts, glass fiber is usually used, the light-carrying core of which is surrounded by a glass shell made of other glass with a lower refractive index. As a result, at the interface between the core and the cladding, rays incident at appropriate angles undergo complete inward. reflection and propagate along the light guide core. Despite the many such reflections, losses in fibers are due to Ch. arr. absorption of light in the glass core mass. When manufacturing light guides from highly pure materials, it is possible to reduce the attenuation of the light signal to several. tens and even units of dB/km. The diameter of the light-guide cores in details is varied. destinations lies in the region from several microns to several mm. The propagation of light through light guides, the diameter of which is large compared to the wavelength, occurs according to the laws of geometric optics; Only separate ones propagate along thinner fibers (on the order of wavelength). types of waves or their combinations, which is considered within the framework of wave optics.
To transfer the image to the V. o. Rigid multicore optical fibers and bundles with regular fiber placement are used. The quality of image transmission is determined by the diameter of the light-guide cores, their total number and manufacturing excellence. Any defects in the light guides spoil the image. Typically, the resolution of fiber bundles is 10-50 lines/mm, and in rigid multicore light guides and parts sintered from them - up to 100 lines/mm.
The image is projected onto the input end of the bundle using a lens. The exit end is viewed through the eyepiece. To increase or decrease valid. For images, focons are used - bundles of fibers with a gradually increasing or decreasing diameter. They concentrate the light flux incident on the wide end at the narrow output end. At the same time, the output illumination and inclination of the rays increase. An increase in the concentration of light energy is possible until the numerical aperture of the cone of rays at the output reaches the numerical aperture of the light guide (its usual value is 0.4-1). This limits the ratio of the input and output radii of the focon, which practically does not exceed five. Plates cut transversely from densely sintered fibers have also become widespread. They serve as the front glass of picture tubes and transfer the image to their external surface. surface, which allows it to be photographed in contact. At the same time, the base reaches the film. part of the light emitted by the phosphor, and the illumination created on it is tens of times greater than when shooting with a camera with a lens.
Light guides and other fiber optics. parts are used in technology, medicine and many other industries scientific research. Rigid straight or pre-bent single-core optical fibers and bundles of fibers dia. 15-50 microns are used in medical devices for indoor lighting. cavities of the nasopharynx, stomach, bronchi, etc. In such devices, light from electric. The lamp is collected by a condenser at the input end of the light guide or bundle and is fed through it into the illuminated cavity. Using a tourniquet with regular placement of glass fibers (flexible endoscope) allows you to see an image of the internal walls. cavities, diagnose diseases and, using flexible instruments, perform simple surgical procedures. operations without opening the cavity. Light guides with a given weave are used in high-speed filming to record tracks. h-ts, as scanning converters in phototelegraphy and television measurement. technology, as code converters and as encryption devices. Active (laser) fibers have been created that work like a quantum. amplifiers and quantum light generators designed for high-speed computing. machines and performing logical functions. elements, memory cells, etc. Particularly transparent thin fiber light guides with attenuation of several. dB/km are used as telephone and television communication cables both within an object (building, ship, etc.) and at a distance of tens of kilometers from it. Fiber communication is characterized by noise immunity, low weight of transmission lines, saves expensive copper and provides electrical isolation. chains.
Fiber parts are made from highly pure materials. A light guide and fiber are drawn from melts of suitable types of glass. A new optical fiber has been proposed. material - crystal fiber grown from melt. Light guides in crystal fibers. whiskers, and in layers - additives introduced into the melt.
Refractometry. Explain in detail the course of the experiment to determine the refractive index clear liquid refractometer.
38.
Refractometry(from Latin refractus - refracted and Greek metreo - measure) - this is a method of studying substances based on determining the index (coefficient) of refraction (refraction) and some of its functions .
Refractometry (refractometric method) is used to identify chemical compounds, quantitative and structural analysis, and determine the physical and chemical parameters of substances.
Refractive index n, is the ratio of the speeds of light in the surrounding media. For liquids and solids n usually determined relative to air, and for gases - relative to vacuum. Values n depend on the wavelength l of light and temperature, which are indicated in subscript and superscript, respectively. For example, the refractive index at 20°C for the D-line of the sodium spectrum (l = 589 nm) is n D 20. Hydrogen spectrum lines C (l = 656 nm) and F (l = 486 nm) are also often used. In the case of gases, it is also necessary to take into account the dependence of n on pressure (indicate it or reduce the data to normal pressure).
In ideal systems (formed without changing the volume and polarizability of the components), the dependence of the refractive index on the composition is close to linear if the composition is expressed in volume fractions (percentage)
n=n 1 V 1 +n 2 V 2 ,
Where n, n 1 , n 2- refractive indices of the mixture and components,
V 1 And V 2- volume fractions of components ( V 1+V 2 = 1).
For refractometry of solutions in wide concentration ranges, tables or empirical formulas are used, the most important of which (for solutions of sucrose, ethanol, etc.) are approved by international agreements and form the basis for the construction of specialized refractometer scales for the analysis of industrial and agricultural products.
Dependence of the refractive index of aqueous solutions of some substances on concentration:
The effect of temperature on the refractive index is determined by two factors: a change in the number of liquid particles per unit volume and the dependence of the polarizability of molecules on temperature. The second factor becomes significant only with a very large temperature change.
The temperature coefficient of the refractive index is proportional to the temperature coefficient of density. Since all liquids expand when heated, their refractive indices decrease as the temperature increases. The temperature coefficient depends on the temperature of the liquid, but in small temperature intervals it can be considered constant.
For the vast majority of liquids, the temperature coefficient lies within a narrow range from –0.0004 to –0.0006 1/deg. An important exception is water and dilute aqueous solutions (–0.0001), glycerin (–0.0002), glycol (–0.00026).
Linear extrapolation of the refractive index is acceptable for small temperature differences (10 – 20°C). Exact definition The refractive index in wide temperature ranges is calculated using empirical formulas of the form: n t =n 0 +at+bt 2 +…
Pressure affects the refractive index of liquids much less than temperature. When the pressure changes by 1 atm. the change in n is 1.48 × 10 -5 for water, 3.95 × 10 -5 for alcohol, and 4.8 × 10 -5 for benzene. That is, a change in temperature by 1°C affects the refractive index of a liquid in approximately the same way as a change in pressure by 10 atm.
Usually n liquid and solid bodies are determined by refractometry with an accuracy of 0.0001 per refractometers, in which the limiting angles of total internal reflection are measured. The most common are Abbe refractometers with prism blocks and dispersion compensators, which make it possible to determine nD in “white” light on a scale or digital indicator. The maximum accuracy of absolute measurements (10 -10) is achieved with goniometers using methods of deflecting rays with a prism made of the material under study. To measure n gases, interference methods are the most convenient. Interferometers are also used for precise (up to 10 -7) determination of differences n solutions. For the same purpose, differential refractometers are used, based on the deflection of rays by a system of two or three hollow prisms.
Automatic refractometers for continuous recording n in liquid flows used in production for control technological processes and automatic control of them, as well as in laboratories for control of rectification and as universal detectors of liquid chromatographs.
When waves propagate in a medium, including electromagnetic ones, to find a new wave front at any time, use Huygens' principle.
Each point on the wave front is a source of secondary waves.
In a homogeneous isotropic medium, the wave surfaces of secondary waves have the form of spheres of radius v×Dt, where v is the speed of wave propagation in the medium. By drawing the envelope of the wave fronts of the secondary waves, we obtain a new wave front in at the moment time (Fig. 7.1, a, b).
Law of Reflection
Using Huygens' principle we can prove the law of reflection electromagnetic waves at the interface between two dielectrics.
Angle of incidence equal to angle reflections. The incident and reflected rays, together with the perpendicular to the interface between the two dielectrics, lie in the same plane.Ð a = Ð b. (7.1)
Let a flat plane fall onto a flat boundary between two media. light wave(rays 1 and 2, Fig. 7.2). The angle a between the beam and the perpendicular to the LED is called the angle of incidence. If at a given moment in time the front of the incident OB wave reaches point O, then according to Huygens’ principle this point
 Rice. 7.2 |
begins to emit a secondary wave. During the time Dt = VO 1 /v, the incident beam 2 reaches point O 1. During the same time, the front of the secondary wave, after reflection in point O, propagating in the same medium, reaches points of the hemisphere with radius OA = v Dt = BO 1. The new wave front is depicted by the plane AO 1, and the direction of propagation by the ray OA. Angle b is called the angle of reflection. From the equality of triangles OAO 1 and OBO 1, the law of reflection follows: the angle of incidence is equal to the angle of reflection.
Law of refraction
An optically homogeneous medium 1 is characterized by , (7.2)
Ratio n 2 / n 1 = n 21 (7.4)
called
(7.5)
For vacuum n = 1.
Due to dispersion (light frequency n » 10 14 Hz), for example, for water n = 1.33, and not n = 9 (e = 81), as follows from electrodynamics for low frequencies. If the speed of light propagation in the first medium is v 1, and in the second - v 2,
 Rice. 7.3 |
then during the time Dt the incident plane wave travels the distance AO 1 in the first medium AO 1 = v 1 Dt. The front of the secondary wave, excited in the second medium (in accordance with Huygens' principle), reaches points of the hemisphere, the radius of which is OB = v 2 Dt. The new front of the wave propagating in the second medium is represented by the BO 1 plane (Fig. 7.3), and the direction of its propagation by the rays OB and O 1 C (perpendicular to the wave front). Angle b between the ray OB and the normal to the interface between two dielectrics at point O called the angle of refraction. From the triangles OAO 1 and OBO 1 it follows that AO 1 = OO 1 sin a, OB = OO 1 sin b.
Their attitude expresses law of refraction(law Snell):
. (7.6)
The ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the relative refractive index of the two media.
Total internal reflection
 Rice. 7.4 |
According to the law of refraction, at the interface between two media one can observe total internal reflection, if n 1 > n 2, i.e. Ðb > Ða (Fig. 7.4). Consequently, there is a limiting angle of incidence Ða pr when Ðb = 90 0 . Then the law of refraction (7.6) takes the following form:
sin a pr = , (sin 90 0 =1) (7.7)
With a further increase in the angle of incidence Ða > Ða pr, the light is completely reflected from the interface between the two media.
This phenomenon is called total internal reflection and are widely used in optics, for example, to change the direction of light rays (Fig. 7.5, a, b).
It is used in telescopes, binoculars, fiber optics and other optical instruments.
In classical wave processes, such as the phenomenon of total internal reflection of electromagnetic waves, phenomena similar to the tunnel effect in quantum mechanics, which is associated with the particle-wave properties of particles.
Indeed, when light passes from one medium to another, refraction of light is observed, associated with a change in the speed of its propagation in different media. At the interface between two media, a light beam is divided into two: refracted and reflected.
A ray of light falls perpendicularly onto face 1 of a rectangular isosceles glass prism and, without refraction, falls on face 2, total internal reflection is observed, since the angle of incidence (Ða = 45 0) of the beam on face 2 is greater than the limiting angle of total internal reflection (for glass n 2 = 1.5; Ða pr = 42 0).
If the same prism is placed at a certain distance H ~ l/2 from face 2, then a ray of light will pass through face 2 * and exit the prism through face 1 * parallel to the ray incident on face 1. Intensity J of the transmitted luminous flux decreases exponentially with increasing gap h between prisms according to the law:
,
where w is a certain probability of the beam passing into the second medium; d is the coefficient depending on the refractive index of the substance; l is the wavelength of the incident light
Therefore, the penetration of light into the “forbidden” region is an optical analogy of the quantum tunneling effect.
The phenomenon of total internal reflection is truly complete, since in this case all the energy of the incident light is reflected at the interface between two media than when reflected, for example, from the surface of metal mirrors. Using this phenomenon, one can trace another analogy between the refraction and reflection of light, on the one hand, and Vavilov-Cherenkov radiation, on the other hand.
WAVE INTERFERENCE
7.2.1. The role of vectors and
In practice, several waves can propagate simultaneously in real media. As a result of the addition of waves, a series of interesting phenomena: interference, diffraction, reflection and refraction of waves etc.
These wave phenomena are characteristic not only of mechanical waves, but also of electrical, magnetic, light, etc. Wave properties are also exhibited by all elementary particles, which has been proven by quantum mechanics.
One of the most interesting wave phenomena, which is observed when two or more waves propagate in a medium, is called interference. An optically homogeneous medium 1 is characterized by absolute refractive index , (7.8)
where c is the speed of light in vacuum; v 1 - speed of light in the first medium.
Medium 2 is characterized by the absolute refractive index
where v 2 is the speed of light in the second medium.
Attitude (7.10)
called the relative refractive index of the second medium relative to the first. For transparent dielectrics in which m = 1, using Maxwell's theory, or
where e 1, e 2 are the dielectric constants of the first and second media.
For vacuum n = 1. Due to dispersion (light frequency n » 10 14 Hz), for example, for water n = 1.33, and not n = 9 (e = 81), as follows from electrodynamics for low frequencies. Light is electromagnetic waves. Therefore, the electromagnetic field is determined by the vectors and , which characterize the strengths of the electric and magnetic fields, respectively. However, in many processes of interaction of light with matter, for example, such as the effect of light on the organs of vision, photocells and other devices, the decisive role belongs to the vector, which in optics is called the light vector.
The propagation of electromagnetic waves in various media is subject to the laws of reflection and refraction. From these laws, under certain conditions, one follows interesting effect, which in physics is called total internal reflection of light. Let's take a closer look at what this effect is.
Reflection and refraction
Before proceeding directly to the consideration of internal total reflection of light, it is necessary to explain the processes of reflection and refraction.
Reflection refers to the change in direction of movement of a light ray in the same medium when it encounters any interface. For example, if you send from laser pointer on the mirror, you can observe the described effect.
Refraction is, just like reflection, a change in the direction of movement of light, but not in the first, but in the second medium. The result of this phenomenon will be a distortion of the outlines of objects and their spatial arrangement. A common example of refraction is when a pencil or pen breaks when placed in a glass of water.
Refraction and reflection are related to each other. They are almost always present together: part of the beam's energy is reflected, and the other part is refracted.
Both phenomena are the result of the application of Fermat's principle. He states that light moves along the path between two points that will take it the least amount of time.
Since reflection is an effect that occurs in one medium, and refraction occurs in two media, it is important for the latter that both media are transparent to electromagnetic waves.
The concept of refractive index
The refractive index is an important quantity for mathematical description the phenomena under consideration. The refractive index of a particular medium is determined as follows:
Where c and v are the speeds of light in vacuum and matter, respectively. The value of v is always less than c, so the exponent n will be greater than one. The dimensionless coefficient n shows how much light in a substance (medium) will lag behind light in a vacuum. The difference between these speeds leads to the occurrence of the phenomenon of refraction.
The speed of light in matter correlates with the density of the latter. The denser the medium, the harder it is for light to move through it. For example, for air n = 1.00029, that is, almost like for a vacuum, for water n = 1.333.
Reflections, refraction and their laws
A prime example of the result of total reflection is the shiny surface of a diamond. The refractive index for diamond is 2.43, so many rays of light hitting gem, experience multiple total reflections before emerging from it.
Problem of determining the critical angle θc for diamond
Let's consider simple task, where we will show how to use the given formulas. It is necessary to calculate how much the critical angle of total reflection will change if a diamond is placed from air into water.
Having looked at the values for the refractive indices of the indicated media in the table, we write them down:
- for air: n 1 = 1.00029;
- for water: n 2 = 1.333;
- for diamond: n 3 = 2.43.
The critical angle for the diamond-air pair is:
θ c1 = arcsin(n 1 /n 3) = arcsin(1.00029/2.43) ≈ 24.31 o.
As you can see, the critical angle for this pair of media is quite small, that is, only those rays can exit the diamond into the air that are closer to the normal than 24.31 o.
For the case of diamond in water we obtain:
θ c2 = arcsin(n 2 /n 3) = arcsin(1.333/2.43) ≈ 33.27 o.
The increase in the critical angle was:
Δθ c = θ c2 - θ c1 ≈ 33.27 o - 24.31 o = 8.96 o.
This slight increase in the critical angle for complete reflection of light in a diamond causes it to shine in water almost the same as in air.
In the picture Ashows a normal ray that passes through the air-Plexiglas interface and exits the Plexiglas plate without undergoing any deflection as it passes through the two boundaries between the Plexiglas and the air. In the picture b shows a ray of light entering a semicircular plate normally without deflection, but making an angle y with the normal at point O inside the plexiglass plate. When the beam leaves a denser medium (plexiglass), its speed of propagation in a less dense medium (air) increases. Therefore, it is refracted, making an angle x with respect to the normal in air, which is greater than y.
Based on the fact that n = sin (the angle that the beam makes with the normal in the air) / sin (the angle that the beam makes with the normal in the medium), plexiglass n n = sin x/sin y. If multiple measurements of x and y are made, the refractive index of the plexiglass can be calculated by averaging the results for each pair of values. Angle y can be increased by moving the light source in an arc of a circle centered at point O.
The effect of this is to increase the angle x until the position shown in the figure is reached V, i.e. until x becomes equal to 90 o. It is clear that the angle x cannot be greater. The angle that the ray now makes with the normal inside the plexiglass is called critical or limiting angle with(this is the angle of incidence on the boundary from a denser medium to a less dense one, when the angle of refraction in the less dense medium is 90°).
A weak reflected beam is usually observed, as is a bright beam that is refracted along the straight edge of the plate. This is a consequence of partial internal reflection. Note also that when used white light, then the light appearing along the straight edge is decomposed into the colors of the spectrum. If the light source is moved further around the arc, as in the figure G, so that I inside the plexiglass becomes greater than the critical angle c and refraction does not occur at the boundary of the two media. Instead, the beam experiences total internal reflection at an angle r with respect to the normal, where r = i.
To make it happen total internal reflection, the angle of incidence i must be measured inside a denser medium (plexiglass) and it must be greater than the critical angle c. Note that the law of reflection is also valid for all angles of incidence greater than the critical angle.
Diamond critical angle is only 24°38". Its "flare" therefore depends on the ease with which multiple total internal reflection occurs when it is illuminated by light, which depends largely on the skillful cutting and polishing which enhances this effect. Previously it was It is determined that n = 1 /sin c, so an accurate measurement of the critical angle c will determine n.
Study 1. Determine n for plexiglass by finding the critical angle
Place a half-circle piece of plexiglass in the center of a large piece of white paper and carefully trace its outline. Find the midpoint O of the straight edge of the plate. Using a protractor, construct a normal NO perpendicular to this straight edge at point O. Place the plate again in its outline. Move the light source around the arc to the left of NO, all the time directing the incident ray to point O. When the refracted ray goes along the straight edge, as shown in the figure, mark the path of the incident ray with three points P 1, P 2, and P 3.
Temporarily remove the plate and connect these three points with a straight line that should pass through O. Using a protractor, measure the critical angle c between the drawn incident ray and the normal. Carefully place the plate again in its outline and repeat what was done before, but this time move the light source around the arc to the right of NO, continuously directing the beam to point O. Record the two measured values of c in the results table and determine the average value of the critical angle c. Then determine the refractive index n n for plexiglass using the formula n n = 1 /sin s.
The apparatus for Study 1 can also be used to show that for rays of light propagating in a denser medium (Plexiglas) and incident on the Plexiglas-air interface at angles greater than the critical angle c, the angle of incidence i is equal to the angle reflections r.
Study 2. Check the law of light reflection for angles of incidence greater than the critical angle
Place the semi-circular plexiglass plate on a large piece of white paper and carefully trace its outline. As in the first case, find the midpoint O and construct the normal NO. For plexiglass, the critical angle c = 42°, therefore, angles of incidence i > 42° are greater than the critical angle. Using a protractor, construct rays at angles of 45°, 50°, 60°, 70° and 80° to the normal NO.
Carefully place the plexiglass plate back into its outline and direct the light beam from the light source along the 45° line. The beam will go to point O, be reflected and appear on the arc-shaped side of the plate on the other side of the normal. Mark three points P 1, P 2 and P 3 on the reflected ray. Temporarily remove the plate and connect the three points with a straight line that should pass through point O.
Using a protractor, measure the angle of reflection r between and the reflected ray, recording the results in a table. Carefully place the plate into its outline and repeat for angles of 50°, 60°, 70° and 80° to the normal. Record the value of r in the appropriate space in the results table. Plot a graph of the angle of reflection r versus the angle of incidence i. A straight line graph drawn over the range of incidence angles from 45° to 80° will be sufficient to show that angle i is equal to angle r.
Physical meaning of the refractive index. Light is refracted due to changes in the speed of its propagation when passing from one medium to another. The refractive index of the second medium relative to the first is numerically equal to the ratio of the speed of light in the first medium to the speed of light in the second medium:
Thus, the refractive index shows how many times the speed of light in the medium from which the beam exits is greater (smaller) than the speed of light in the medium into which it enters.
Since the speed of propagation of electromagnetic waves in a vacuum is constant, it is advisable to determine the refractive indices of various media relative to vacuum. Speed ratio With propagation of light in a vacuum to the speed of its propagation in a given medium is called absolute refractive index of this substance() and is the main characteristic of its optical properties,
,
those. the refractive index of the second medium relative to the first is equal to the ratio of the absolute indices of these media.
Typically, the optical properties of a substance are characterized by its refractive index n relative to air, which differs little from the absolute refractive index. In this case, a medium with a larger absolute index is called optically denser.
Limit angle of refraction. If light passes from a medium with a lower refractive index to a medium with a higher refractive index ( n 1< n 2 ), then the angle of refraction is less than the angle of incidence
r< i (Fig. 3).
Rice. 3. Refraction of light during transition
from an optically less dense medium to a medium
optically denser.
When the angle of incidence increases to i m = 90° (beam 3, Fig. 2) light in the second medium will propagate only within the angle r pr called limiting angle of refraction. In the region of the second medium within an angle additional to the limiting angle of refraction (90° - i pr ), light does not penetrate (in Fig. 3 this area is shaded).
Limit angle of refraction r pr
But sin i m = 1, therefore .
The phenomenon of total internal reflection. When light comes from a medium with a high refractive index n 1 > n 2 (Fig. 4), then the angle of refraction is greater than the angle of incidence. Light is refracted (passes into a second medium) only within the angle of incidence i pr , which corresponds to the angle of refraction r m = 90°.
Rice. 4. Refraction of light when passing from an optically denser medium to a medium
optically less dense.
Light falling under high angle, is completely reflected from the boundary of the media (Fig. 4, ray 3). This phenomenon is called total internal reflection, and the angle of incidence i pr – limiting angle of total internal reflection.
Limiting angle of total internal reflection i pr determined according to the condition:
, then sin r m =1, therefore, .
If light comes from any medium into a vacuum or air, then
Due to the reversibility of the ray path for two given media, the limiting angle of refraction during the transition from the first medium to the second is equal to the limiting angle of total internal reflection when the ray passes from the second medium to the first.
The limiting angle of total internal reflection for glass is less than 42°. Therefore, rays traveling through glass and falling on its surface at an angle of 45° are completely reflected. This property of glass is used in rotating (Fig. 5a) and reversible (Fig. 4b) prisms, often used in optical instruments.
 |
Rice. 5: a – rotary prism; b – reversible prism.
Fiber optics. Total internal reflection is used in the construction of flexible light guides. Light, entering a transparent fiber surrounded by a substance with a lower refractive index, is reflected many times and propagates along this fiber (Fig. 6).
Fig.6. Passage of light inside a transparent fiber surrounded by a substance
with a lower refractive index.
To transmit large light fluxes and maintain the flexibility of the light-conducting system, individual fibers are collected into bundles - light guides. The branch of optics that deals with the transmission of light and images through optical fibers is called fiber optics. The same term is used to refer to the fiber optic parts and devices themselves. In medicine, light guides are used to illuminate internal cavities with cold light and transmit images.
Practical part
Devices for determining the refractive index of substances are called refractometers(Fig. 7).
Fig.7. Optical design refractometer.
1 – mirror, 2 – measuring head, 3 – prism system to eliminate dispersion, 4 – lens, 5 – rotating prism (beam rotation by 90 0), 6 – scale (in some refractometers
there are two scales: the refractive index scale and the solution concentration scale),
7 – eyepiece.
The main part of the refractometer is the measuring head, which consists of two prisms: the lighting one, which is located in the folding part of the head, and the measuring one.
At the exit of the lighting prism, its matte surface creates a scattered beam of light, which passes through the liquid under study (2-3 drops) between the prisms. The rays fall onto the surface of the measuring prism at different angles, including at an angle of 90 0 . In the measuring prism, the rays are collected in the region of the limiting angle of refraction, which explains the formation of the light-shadow boundary on the device screen.
Fig.8. Beam path in the measuring head:
1 – lighting prism, 2 – test liquid,
3 – measuring prism, 4 – screen.
