The nature of light icon

The nature of light



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THE NATURE OF LIGHT

Lesson I


Until about the middle of the I7th century, it was generally believed that light consisted of a stream of corpuscles. These corpuscles were emitted by light sources, such as the sun or a candle flame, and travelled outward from the source in straight lines. They could penetrate transparent materials and were reflected from the surfaces of opaque materials. When the corpuscles entered the eye, the sense of light was stimulated. This theory was called on to explain why light ap­peared to travel in straight lines, why it was reflected from a smooth surface such as a mirror with the angle of reflection equal to the angle of incidence, and why and how it was refracted at a boundary surface such as that between air and water or air and glass.

For all of these phenomena, a corpuscular theory provides a simple explana­tion.

Newton (1687) explained the facts of refraction on the basis of the corpuscular the­ory (in which light was supposed to consist of small particles which in their motions along straight lines finally struck the eye and produced the sensation of light). He assumed that the particles moved with greater speed in water than in air, an assumption which could neither be proved nor disproved at the time.

Newton's experiment, with the prism, however, constituted a great forward stride. It had been believed that white light was changed in its fundamental nature by passage through a prism. Earlier writers had associated the colours of the rain­bow in some way with refraction, but it was not until Newton's experiment that anything definite was known.

Newton had proved that white light is a mixture of colours and that rays of light of the various colours are bent by varying amounts when passing obliguely from one medium to another of different density, each colour having a different index of refraction.

Newton's discoveries relating to colour and refraction were later to have an important bearing on the wave theory of light. We know colour to be determined by the length of the


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light waves, red light having a longer wave length than blue light. Newton explained eve­rything on, the basis of his corpuscular the­ory, which he had invented to satisfy the re­quirements that light must travel in straight lines.

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THE NATURE OF LIGHT

Lesson 2


By the middle of the I7th century, while most workers in the field of optics accepted the corpuscular theory, the idea had begun to develop that light might be a wave motion of some sort.

In I670 Huygens showed that the laws of reflection and refraction could be explained on the basis of a wave theory and that such a theory furnished a simple explanation of the recently discovered phenomenon of double refraction.


Lomonosov studied the phenomena of light and believed it to be a wave mo­tion. In 1753 Lomonosov informed the Academy of Science of his intention to make experiments with strings in vacuum to prove that the vibrations of strings emitted light, the wave theory of Huygens and Lomonosov failed of immediate acceptance, however. For one thing, it was objected that if light were a wave motion one should be able to see around cor­ners, since waves can bend around obstacles in their path.

We know now that the wave lengths of light waves are so short that the bend­ing, while it does actually take place, is so small that it is not ordinarily observed. As the mat­ter of fact, the bending of a light wave around the edges of an object, a phenomenon known as diffraction, was noted as early as 1665, but the signifi­cance of these observa­tions was not realized at the time. It was not until 1827 that the experiments on inter­fer­ence and the measurements of the velocity of light in li­quids, at a somewhat later date, demonstrated the existence of optical phenomena for whose explanation a corpuscular theory was inadequate. These experiments enabled the physicists to measure the wave length of the waves and it was proved that the rectilinear propagation of light, as well as the diffraction effects, could be accounted for by the behaviour of waves of short wave lengths.


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THE NATURE OP LIGHT

Lesson 3


The next great forward step in the theory of light was made by Hertz who suc­ceeded in producing short wave length waves of undoubted electromagnetic ori­gin and showed that they possessed all the properties of light waves. They could be ref­lected, refracted, fo­cussed by a lens, polarized, and so on, just as could waves of light. The wave theory of light seemed to have defeated the particle theory. However, in 1888 Stoletov, Russian physicist, discovered the phenome­non of photo­electric emission.

Early in the twentieth century it was found that light could cause atoms to emit elec­trons and that the energy po­ssessed by the electron very greatly exceeded that which the atom could have received according to electromagnetic-wave the­ory. It was at this point that the wave theory failed to suggest an explanation,

A return, at least to some extent, to the particle theory of light appeared to be neces­sary. In 1905 Einstein suggested that the energy of a light beam is concen­trated in the form of small particles proportional to the frequency of light. These localized concentrations of energy he called "photons" or "light quanta". Thus, on the one hand, all the phenomena of interference, dif­fraction and polarization are described by the wave theory. On the other hand, there are many phenomena of the interaction of light with matter in the processes of emission and absorption, which are readily described in terms of photons.

According to the present concept light has a dual character such that it may be repre­sented equally well by waves or by particles. The wave and particle proper­ties of light are found by modern scientists to be two different aspects of the same thing. These two as­pects are to be regarded as complementary rather than antogonistic, each being correct when dealing with the phenomena in its own domain.

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REFLECTION AND REFRACTION

Lesson 4


In the passage of a beam of light through a medium, some


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of the radiant energy is absorbed and transformed into heat; some of the radi­ant energy is also scattered in all directions. Light, because of its electromagnetic character, sets the elec­trons of the medium into vibration, thus giving up some of its energy. These electrons re-emit some of this energy in the form of radia­tion, either of the same wave length as the incident ra­diation, or of different wave lengths. Absorption and scatter­ing of light take place even in the most transpar­ent media such as air and glass. The colour of the sky, for example, is due to the small amount of scattering of sunlight by the molecules of the air. These mole­cules are more effective in scattering the shorter wave lengths such as the vio­let and blue light. When we look away from the sun, we see this scattered light, and the sky thus appears blue. If we were in the stratosphere, where there are fewer scattering par­ticles, the sky would appear much darker, almost black. Since blue and violet light are scattered from the direct beam, sunlight should appear redder as it goes through thicker layers of air. It is for this reason that the setting sun looks redder than the moonday sun.

When a beam of light strikes the surface separating one medium from another - for example, the surface between air and glass - some of the light is reflected back into the first me­dium at the surface of separation and the remainder enters the second medium. The light which passes from one medium into ano­ther is said to be refracted. If the surface of separation bet­ween the two media is smooth and polished, the light which is thrown back into the first medium is said to be regularly re­flected; if the surface is rough, the light is diffusely reflec­ted. Unless otherwise stated, we shall assume that the surface between two media is smooth and polished. In general, smooth, polished metal surfaces will reflect about 90 per cent of the incident light, while smooth polished glass surfaces will ref­lect from 4 to I0% for angles of incidence from 0° to 60°.

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LAWS OP REFLECTION

Lesson 5


When a beam of light strikes a polished surface separating two media, such as air and glass, part is reflected and part is refracted. The angles of incidence, re­flection and refrac­tion are all measured from a normal to the surface; a normal to sur-


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face at a given point is a line drawn perpendicular to the sur­face at that point. The two laws of reflection are as follows: 1)The incident ray, the normal, and the reflected ray all
lie in one plane. 2) The angles of incidence and reflection are equal.

These two laws can easily be verified experimentally. These laws enable us to construct the reflected rays when the incident rays and the position and shape of the reflection surface are given. Rotating mirrors provide an interesting application of the laws of reflection. Such mirrors are used for measuring the deflection of a galvanometer coil and other rotating devices.

When the mirror turns through a small angle, say 1°, the angle
of incidence is increased by 10 and so is the angle of reflection. If the incident beam comes from a stationary source, the reflected beam will travel through 2°. In general, the angle through which the reflected beam rotates is twice the angle through which the mir­ror rotates.


^

Reflection at a Plane Surface



On looking into a plane reflecting surface one sees, appa­rently behind the sur­face, images of any objects that are in front of the surface. Some of the light from each object point is reflected at the surface, and enters the eye as though it were coming from points behind the surface. Apparent images of this kind from which the light is diverging are termed virtual images. When, by reflection or refraction at a curved surface, the light from object point is made to converge again through points, an image is formed that actually exists at the position to which the light converges. Such images, which can be received on a screen, as with the image formed by the lens of a camera or projection lantern, are termed real images. The position of the image of any object before a plane reflecting surface can be determined from the law of reflection, or it may be found by using Huygen's construction to determine the form of the reflec­ted wave front. The image formed by a plane mirror is situated as far behind the mirror as the object is in front, and the line joining the object and image is perpen­dicular to the plane of the mirror surface. It is a simple matter, therefore, to find graphi­cally the position of the image formed by a plane mirror, and as the reflected light is trav­elling apparently


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from the image, the path of the light by which an eye in a gi­ven position sees the im­age can readily be found. It follows that in shape and size, the image will be an exact re­production of the object. The point of the object nearest the mirror is represented by the point of the image nearest the mirror, and the top and bot­tom of the image correspond with the top and bottom of the object, that is the image is erect. The question of whether the im­age is or is not reversed left for right, or perverted, as it is sometimes called, depends on the position of the ob­server in viewing both object and image. As may be readily seen by experiment, the extent of image in a plane mirror that can be seen by an eye in any posi­tion will depend on the size of the mirror and the position of the eye. This extent of im­age seen is termed the field of view of the mirror.

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DEVIATION ON REFLECTION AT TWO MIRRORS IN SUCCESSION

Lesson 6

When a ray incident in a plane containing the normals of the two mirrors is reflected from two mirrors in succession, it undergoes a total de­viation that depends only on the angle between the mirrors. The total de­viation produced is, therefore, independent of the angle of incidence at the first mirror and a rotation of the mirrors about an axis perpendicular to the plane containing their normals, and keeping the angle between them constant, produces no change in the final direc­tion of the re­flected light. Successive reflection from two mirrors is used in all possible cases where considerable accuracy is required
in the direction of a reflected beam. Providing the angle between the reflectors is accu­rately fixed, and this is frequently done by making them the surfaces of a prism, the cor­rect placing of the mirrors with respect to the incident light need not be made with any great accuracy. A further advantage of the use of two reflectors is that the incident and reflected beams may be separated by any distance, thus making it possible to put
lenses, prisms or other reflectors in either of the beams.


Refraction


When light is incident obliquely on the surface between two media of different re­fractive index, its direction is changed on passing into the new medium, and it is said to be refracted. Refraction obeys two basic laws:


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1) A ray of light, which, passing from a rarer medium to a denser medium, makes a certain angle with the perpendicular to the plane at which the two media meet, will on en­tering the denser medium make a smaller angle with the perpen­dicular than that which it made whilst traversing the rare medium. Converse­ly, of course, a ray passing from a denser medium to a rarer medium will make a larger angle with the perpendicular to that which it made whilst traversing the denser medium. In optics, this perpendicular to the plane of junction of two media is called the normal.

A clearer understanding of the nature of refraction will be obtained if one visualises the case of a ray of light pass­ing from a rare medium, such as air, into a denser medium, such as water. Here we have a ray which may be represented by a wave front of a certain amplitude and angle to the normal, which on enter­ing the denser medium encounters a re­sistance to its mo­tion and is refracted downwards towards the normal. Perhaps, the point will be made clearer by imagining the wave front to be represented by a strip of wood, say 2 feet long by 5 inches wide, the thickness is immaterial. If the wood is travelling towards the surface of the water at an angle to the normal, flat side forward then it will be seen that when it strikes the water the lower edge of the strip would strike first and be re­sisted, bringing the upper edge round and so virtually redirec­ting its path from the original straight line to a new straight line whose angle to the nor­mal would be smaller than the origi­nal angle. Although this is not precisely true, it will serve the purpose of illustrating the point.

2) The second law may be briefly stated by saying that the sine of the angle of inci­dence (i.e., the angle of the incident ray with the normal) divided by the sine of the angle of re­fraction, is a constant quantity for any two given media.

If one of the media is a vacuum, then this ratio of sines is called the absolute refrac­tive index of the medium and it fallows that as there is no other medium less dense than a va­cuum, the angle of refraction for any other medium paired with it will be less than the incident angle in the vacuum. There­fore the ratio of sines will always be greater than unity, i.e. the refractive index will be greater than unity.


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REFRACTIVE INDEX

Lesson 7


Prom the behaviour of light on passing from one medium to another, it is evi­dent that the light undergoes a change in velocity and that the velocity of light is different in dif­feren media. It was determined experimentally that the velocity was less in water than in air. This important result was in accor­dance with the wave theory explanation of the be­haviour of the light passing between these two media. The action of lenses and prisms is entirely due to this change of velocity in diffe­rent media; and it is necessary to have some means of express­ing the relative velocity of the light in any medium. If we take the veloc­ity of light, in vacuo as a standard, then its re­lative velocity in any other medium maybe ex­pressed in terms of the ratio velocity in vacuo/velocity in medium.

This ratio is known as the absolute refractive index and will be denoted by n. As the velocity of any transparent medi­um is less than that in vacuo, the value of the absolute re­fractive index of any medium is greater than unity and, with the exception of gases, will be between 1.33, the refractive index of water, and 2.42, that of the diamond. When the light parses from one medium to another, such as from air to glass, glass to water, etc., it is sometimes convenient to express the change in velocity as the ratio of the velocities in the two media, thus velocity in air/velocity in glass = ang, this is called the relative refractive index from air to glass. Hence the relative refractive index from one medium to another is the ratio of the absolute refractive index of the second, medium to that of the first. As the velocity of light in air is very near­ly that in vacuo, the average absolute refractive index of air being I.00029, the relative refractive index from air to any substance is usually given as the refractive index of that sub­stance. The term "rare" and "dense" are frequently used in a comparative sense in referring to media of low and high refrac­tive index respectively. It will be seen, when we consider the ac­tion of a prism, that the dispersion of white light is due to the refractive index being different for each of the colours composing the white light, the refractive index being highest for the violet and lowest for the red in all sub­stances with a


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few exceptions. In stating any refractive index, therefore, it is necessary that the col­our of the light shall be specified. Usually, a mean value of refractive in­dex is taken as that for a particular yellow, the light emitted by incandescent so­dium vapour. This particular light may be very easily obtained by placing com­mon salt in the colourless flame of a spirit lamp. Unless otherwise stated, given refractive indices are assumed to be for this sodium light.
^

The Principle of Least Time


The laws of reflection and refraction may be summed up in a general law which is known as the principle of least time; this may be stated as follows. The actual path travelled by light, in going from one point to another is that, which, under the given condi­tions, requires the least time. In certain ca­ses, however, when the bounding surface is curved, the time may be a maximum instead of a minimum, but must always be one or the other.

PRISMS


Lesson 8

By a prism in optical work is meant a transparent substan­ce bounded by plane pol­ished surfaces inclined to one another. . In the simplest form of prism, as used for refrac­tion, only two surfaces, the refracting surfaces, need be considered, the light entering the prism at the first and leaving at the second. In the case however of the various reflecting prisms, there are a variety of forms having three or more polished surfaces at which the light is refracted or reflected. In a simple refract­ing prism the line of intersection of the two refracting surfaces is the, refracting edge or apex of the prism. Any section through the prism perpendicular to the, edge is a principal section, and the angle of such a section is the refracting or apical angle.


Total Reflection in a Prism.

In certain cases, the angle of incidence at the first sur­face of a prism will be such that the light meets the second surface at an angle greater than the critical angle, and is the­re­fore totally reflected. This reflected light will meet a third sur­face of the prism and, if this is a plane polished surface, the light will emerge or again be totally reflected. Its direc­tion after leaving the third surface may easily be found. It


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should be noted that total reflection will occur when the value obtained from expres­sion "sin i2 = n·sin i2", is greater than unity. For any given prism there will be a limiting angle of incidence at the first sur­face at which light can pass through the prism, and for a given glass there will be a maxi­mum limi­ting value of the angle between the faces of the prism through which any light can pass. As the greatest possible angle of emergence i2 is 90°, i2 is the critical angle iC between the glass and air, then i1 = a - iC and sin i1 = n·sin(a - iC) this value of i1 gives the smallest angle of incidence for a ray that will pass through the prism; any ray closer to the normal will be totally reflected at the second surface. When the angle a is smaller than iC the limiting direction of the incident ray lies on the other side of the normal. The greatest angle that a prism may have for light to pass through it will be such that the incident and emergent light is grazing the sur­face. Hence no light can pass through a prism, the refract­ing angle of which is greater than twice the critical angle. For a prism of crown glass in air, the refracting angle must not ex­ceed about 82°.

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