1COMPOSSED AND WRITTEN BY PROF. NAJEEB MUGHAL. GOVT. MUSLIM SCIENCE DEGREE COLLEGE HYD. 1
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CHAPTER 9
NATURE OF LIGHT
Contents:
1. DUAL NATURE OF LIGHT.
2. INTEREFERNCE OF LIGHT.
3.YOUNG’S DOUBLE SLIT EXPERIMENT.
4.INTERFEROMETER.
5.THIN FLIM
6.DIFFRACTION
7. DIRRECTION GRATTING
8.X-RAYS DIFFRACTION
9.POLORIZATION OF LIGHT
10.SHORT DEFINITIONS.
11.EQUATIONS
12. SUMMARY
13. SHORT QUESTIONS AND ANSWERS.
TECHNECHAL TERM RELATIVE DEFINITIONS
1: Dual nature of light:
Light is an external cause responsible for sensation of visionLight is a form of energy. Energy can be transferred from one point to another point either by particle motion or by wave motion. Accordingly, different theories on the nature of light have been proposed. The important theories are as follows: Aristotle was one of the first to publicly hypothesize as to the nature of light, proposing that it was a disturbance in the element air. At the beginning of the 11th century, the Arabic scientist Alhazen wrote the first comprehensive treatise on optics; describing refraction, reflection, and the operation of a pinhole lens via rays of light traveling from the point of emission to the eye. He asserted that these rays were composed of particles of light.
Newton's Corpuscular Theory:
According to Sir Issac Newton's Corpuscular Theory, a luminous body continuously emits tiny, light and elastic particles called corpuscles in all directions. When these particles fall on the retina of the eye they produce the sensation of vision.
This theory could explain a number of phenomena concerning light like rectilinear propagation reflection and refraction. Reflection was explained by assuming that the corpuscles which fall on a smooth surface would bounce back like rubber balls hitting a wall. When this theory was used to explain refraction scientists found that the velocity of light in a denser medium would be more than that in a rarer medium. However, the experimental findings of Foucault pushed back the corpuscular theory of Newton. This corpuscular theory could not explain satisfactorily certain other phenomena
Huygens' Wave Theory:
In 1967 Christian Huygens proposed the wave theory of light. According to this, a luminous body is a source of disturbance in hypothetical medium called ether. The disturbance from the source is propagated in the form of waves through space and the energy is distributed equally in all directions Even though this theory could satisfactorily explain several optical phenomena, the presence of ether could not be detected
Young's Double-Slit Experiment:
In 1803,Thomas Young studied the interference of light waves by shining light through a screen with two slits equally separated, the light emerging from the two slits, spread out according to Huygen's principle.Eventually the two wave fronts will overlap with each other, if a screen was placed at the point of the overlapping waves, you would see the production of light and dark areas (see interference). Later in 1815, Augustin Fresnel supported Young's experiments with mathematical calculations.
Maxwell's Electromagnetic Theory:
Electromagnetic theory of light was put forward by James Clerk Maxwell in 1873. According to this theory, light consists of fluctuating electric and magnetic fields propagating in the form of electromagnetic waves. But this theory failed to explain the photoelectric effect.
Planck's Quantum Theory:
In 1900 According to Max Planck's Quantum theory, radiation is not continuous but is made up of tiny packets of energy called photons. However, this theory could not explain other optical phenomena From all the above theories it is clear that certain optical phenomena can be explained clearly only if light is considered to be made up of particles, while certain other phenomena can be explained only if we consider light as a wave.
In 1905 Albert Einstein had proposed a solution to the problem of observations made on the behavior of light having characteristics of both wave and particle theory. From work of Plank on emission of light from hot bodies, Einstein suggested that light is composed of tiny particles called photons, and each photon has energy.
Light Wave Theory:
Light can exhibit both a wave theory and a particle theory at the same time. Much of the time, light behaves like a wave. Light waves are also called electromagnetic waves because they are made up of both electric (E) and magnetic (H) fields. Electromagnetic fields oscillate perpendicular to the direction of wave travel, and perpendicular to each other. Light waves are known as transverse waves as they oscillate in the direction traverse to the direction of wave travel.
De Broglie's wavelength: In 1924, Louis-Victor de Broglie formulated the de Broglie hypothesis, claiming that all matter,[6][7] not just light, has a wave-like nature; he related wavelength, and momentum . The Speed of Light:
The speed of light in a vacuum is a universal constant, about 300,000 km/s or 186,000 miles per second. The exact speed of light is: 299,792.458 km/s It takes approximately 8.3 min for light from the sun the reach the earth.Taking the distance of the sun from Earth into account, which is 150,000,000 km, and the fact that light travels at 300,000 km/s,
With the use of the SI units for wavelength (l), frequency (¦) and speed of light (c), we can derive some simple equations relating to wavelength, frequency and speed of light:
Photon Model of Light:
As proposed by Einstein, light is composed of photons, very small packets of energy. The reason that photons are able to travel at light speeds is due to the fact that they have no mass and therefore, Einstein's infamous equation - E=mc2cannot be used. Another formula devised by Planck, is used to describe the relation between photon energy and frequency - Planck's constant (h) = 6.63x10-34 Joule-Second. E = h f
Thus,, here,E is the photonic energy in Joules, h is Planks constantand f is the frequency in Hz
Sources:
Light is produced by one of two methods1. Incandescence is the emission of light from "hot" matter (T≳800K).
2. Luminescence is the emission of light when excited electrons fall to lower energy levels (in matter that may or may not be "hot").
Huygen’s principle and Wave front:
According to the “Huygen’s principle”,
“Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave itself. The new wave front is the envelope of all the wavelets (that is the tangent to all of them).The tangent will give a secondary spherical wave front”.
The energy flow equally in all directions of waves propagated. The direction of the energy,
in which the waves travel, is called a “ray”.
A “plane wave front” is a small portion of the spherical wave front, which is far away from the source.
Light year:
The distance traveled by light in one year is called light year. Thus light-year is a unit of distance.
One light year = velocity time (in seconds in one year)
One light year = 3 108 m /sec (365.25 24 3600 sec)or light year = 9.461 1015 meter = 9.461 1012 km
2. Interference of light:
The modification in the distribution of light energy due to superposition of two light waves is called “Interference of light”.
There are two types interference. 1. Constructive interference and 2) Destructive interference.
Constructive interference:
Constructive interference occurs when the crests and the troughs of the two wave trains coincide (the wave fronts are in phase. The resultant is the sum of the two amplitudes.
Destructive interference:
Destructive interference occurs when the crests of one wave coincide with the troughs of the other the wave fronts are not in phase. The resultant is the difference between the two amplitudes Conditions of interference of light: 1. the sources should be monochromatic (a light of single wave length.) 2. The sources should be coherent (the two sources having same phase difference. They emit light waves of same frequencies and amplitude, with same wavelength.) 3. The sources should be narrow (the source should be as pinhole.) The sources should be closer (the sources are placed near to one another.)
DESCRIPTIVE PART
3. Young’s Double Slit Experiment: Introduction: A British physicist in 1801 named Thomas Young was proved the wave nature of light by double slit experiment. In this experiment, a single source is split in two, to generate two coherent sources. When the light from the two sources is projected on a screen, an interference pattern is observed. Experiment:
Light from a point monochromatic source travel, towards two coherent sources S1 and S2, after passing interfere each other finally the waves are made to fall on to screen and visible pattern is obtained on to screen. At the center of the screen the waves from the two sources are in phase. As we move away from the center, the path traveled by the light from one source is larger than that traveled by the light from the other source. When the difference in path is equal to half a wavelength, destructive interference occurs. Instead, when the difference in path length is equal to a wavelength, constructive interference occurs. The screen consists a series of light having, dark and bright bands; they are parallel to one another .The bands are known as “fringes”. Description:
Two light of wavelength “”, pass through two slits, separated by a distance “d” and strike a screen a distance, “L”, from the slits. You can change these parameters and see the interference on the screen on which bands are observed, the fringe spacing is “y”. The path difference between two light waves is d sin, that light wave covered more from S2 as compared light from S1.
Mathematical derivation:
For constructive interference, d sin = m ------►eq.(1)
Where, m = 1,2, - - -n, is called order of the interference fringe.
Thus bright bands are observed, also called ‘maxima”.
for destructive interference ------►(2).
Where m= 1,2,- - - - n
Then dark bands are observed, also called “minima”.
Consider OPC right-angled triangle
Sin = tan = , Because CP = CO ( base = hyp.)
, The equation # 1, for brightness can be written as,
And equation # 2, for darkness will be,
The distance between two adjacent bright or dark fringes is called “fringe spacing”.
If, m = n and , m = ( n+1),
Then, , for m = n
And , for m = (n+1)
Fringe spacing = Yb ( at n+1th fringe) - Yb ( at n th fringe)
x = –
Hence, Fringe spacing =
4 : Michelson interferometer:
Introduction:
The American scientist Albert A. Michelson invented this interferometer. He designed this instrument for the measurement of interference fringes. There are two paths from the light source to the detector. One reflects off the semi-transparent mirror, goes to the top mirror and then reflects back, goes through the semi-transparent mirror, to the detector. The other first goes through the semi-transparent mirror, to the mirror on the right, reflects back to the semi-transparent mirror, then reflects from the semi-transparent mirror into the detector
Construction:
An interferometer constructed using a half-silvered mirror inclined at a 45° angle to the incoming beam. Half the light is reflected perpendicularly and bounces
off a beam splitter; half passes through and is reflected from a second beam splitter.
The light passing through the mirror must also pass through an inclined
compensator plate to compensate for the fact that the other ray
passes through the mirror glass three times instead of one.
Working:
A monochromatic light from a single point source is striking a half–
silvered mirror placed at 45o with incident beam. Light splits in to two equal intensity rays, after reflection and refraction. After breaking half
of the beam, say ray-1 falls on to fixed mirror M1 , where it is reflected back. The
other half is refracted, say ray-2 falls on to movable mirror M2. Both mirrors are perpendicular to one another, the rays cover equal distances after reflection and recombine on to silvered glass plate. At this stage the path difference is zero between two rays. They interfere constructively, the bright fringe appears. The movable mirror M2 is moved a distance /4, one beam will travel an extra distance say, path difference changes /2. The two beams will destructively interfere and dark fringe appears. Again the movable mirror is moved /2, the path difference becomes , so that bright fringe appears. This shows that alternatively bright and dark fringe appear. The reflected rays after striking with plane mirrors; they recombine and produce interference pattern, which can be seen. The wavelength of light is the measured by counting the number of fringes “m”.
Suppose a movable mirror is moved “x’ distance and ‘m” bright or
dark fringes are appears.
Therefore, 2 x = m
Applications;
Interferometers can be used for many different purposes. Some examples are: 1 :for the measurement of a distance with an accuracy of better than an optical wavelength 2 :for measuring the wavelength e.g. of a laser beam. 3: for monitoring slight changes in an optical wavelength or frequency
4: for measuring rotations
5: or measuring slight deviations of an optical surface from perfect flatness
6: for measuring the line width of a laser
7: for revealing tiny refractive index variations or induced index changes
in a transparent medium
8: for measurements of the chromatic dispersion of optical components
9: as an optical filter
10: for the full characterization of ultra short pulses
6. Interference of light by Thin Films:
In everyday life, the interference of light most commonly gives rise to easily observable effects when light impinges on a thin film of some transparent material. For instance, the brilliant colors seen in soap bubbles, in oil films floating on puddles of water. A very thin film of air is trapped between two pieces of glass, as shown If monochromatic light is incident normally to the film then some of the light is reflected from the interface between the bottom of the upper plate and the air, and some is reflected from the interface between the air and the top of the lower plate. The eye focuses these two parallel light beams. The two beams produce either destructive or constructive interference, depending on whether their path difference. Let “t” be the thickness of the air film. The difference in path-lengths between the two light rays shown in the figure is. Naively, we might expect that constructive interference, and, hence, brightness, would occur if, where “m” is an integer, and destructive interference, and, hence, darkness, would occur if. An additional phase difference is introduced between the two rays on reflection. The first ray is reflected at an interface between an optically dense medium (glass), through which the ray travels, and a less dense medium (air). There is no phase change on reflection from such an interface, just as there is no phase change when a wave on a string is reflected from a free end of the string. The second ray is reflected at an interface between an optically less dense medium (air), through which the ray travels, and a dense medium (glass). There is an 180o phase change on reflection from such an interface, just as there is an 180o phase change when a wave on a string is reflected from a fixed end. Thus, an additional 180o phase change is introduced between the two rays, which is equivalent to an additional path difference of. When this additional phase change is taken into account, the condition for constructive interference becomes where “m” is an integer. Similarly, the condition for destructive interference becomes If the thin film consists of water, oil, or some other transparent material of refractive index “n” then the results are basically the same as those for an air film, except that the wavelength of the light in the film is reduced from (the vacuum wavelength) to. It follows that the modified criteria for constructive and destructive interference are and
7. Newton Ring:
Arrangement:
The convex surface of a long focal length lens (large radius of curvature) is placed in contact with a plane glass plate. A thin film of air is formed between the two surfaces of glass in contact. There is no phase change at the glass-air surface of the convex lens (because the wave is going from a higher to a lower refractive index medium)
Explanation
Suppose light of wave length '' falls on the lens, the radius of curvature of the convex lens is Rand the radius of ring is 'r'. After refraction and reflection two rays 1 and 2 are obtained. These rays interfere each other producing alternate bright and dark rings. At the point of contact the thickness of air film is zero and the path difference is also zero and as an 180O path difference occurs, so they cancel each other and a dark ring is obtained at the centre.
From the figure AB=t, BC =2R-t and BD = r
Where “t” is very small as compared to r, therefore t2 is negligible.
------► (1).
In thin films, path difference for constructive interference is:
Where n= refractive index. For air n = 1
------► (2).
For first bright ring m = 0 for second bright ring m = 1 for third bright ring m = 2
Similarly for Nth bright ring m = (N-1) Putting the value of m in equation (2)