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Engineering Physics For Computer Science Engineering (2024-2025) Chapter-1: Interference Class -01 By Dr. K. Yadagiri Department of Physics Interference Principle of Superposition, Coherence and Coherent...

Engineering Physics For Computer Science Engineering (2024-2025) Chapter-1: Interference Class -01 By Dr. K. Yadagiri Department of Physics Interference Principle of Superposition, Coherence and Coherent Sources,  Production of Coherent Light, Young’s Double Slit Experiment, Concept of interference, Newton’s Rings, working of Michelson Interferometer, Fabry-Perot Interferometer, and its application as wavelength filter. Light: Light is a type of electromagnetic radiation that allows the human eye to see or makes objects visible. It is also defined as visible radiation to the human eye. Photons, which are tiny packets of energy, are found in light.  Light always moves in a straight line.  Light travels at a faster rate than sound. The speed of light is 3×10 8m/s.  Light is a transverse wave that travels without the use of a medium.  Light does not require a physical medium to travel. That is, it can also move through a vacuum.  Wave: Wave is a form of disturbance which travels through a material medium due to the repeated periodic motion of the particles of the medium about their mean positions without any actual transportation of matter.  Characteristics of wave: The characteristics of waves are as follows:  The particles of the medium traversed by a wave execute relatively small vibrations about their mean positions but the particles are not permanently displaced in the direction of propagation of the wave.  Each successive particle of the medium executes a motion quite similar to its predecessors along/perpendicular to the line of travel of the wave.  During wave motion only transfer of energy takes place but not that of a portion of the medium.  Waves are mainly of three types:  Mechanical or elastic waves  Electromagnetic waves and  Matter waves.  Mechanical waves Mechanical waves can be produced or propagated only in a material medium. These waves are governed by Newton’s laws of motion. For example, waves on water surface, waves on strings, sound waves etc.  Electromagnetic waves These are the waves which require no material medium for their production and propagation, i.e., they can pass through vacuum and any other material medium.  Common examples of electromagnetic waves are visible light; ultra-violet light; radiowaves, microwaves etc.  Matter waves These waves are associated with moving particles of matter, like electrons, protons, neutrons etc.  waves are of two types: (i) Transverse wave motion (ii) Longitudinal wave motion Wave equation for 1D & solution : y=f(vt- x) Wave equation for 3D & solution : = = Since harmonic wave nature y= y= Superposition Principle The principle of superposition, in wave motion, the principle that when two or more waves overlap in space, the resulting disturbance is equal to the algebraic sum of the individual disturbances. This principle holds for many different kinds of waves, such as waves in water, sound waves, and electromagnetic waves. Types of Superposition of Waves According to the phase difference in superimposing waves, interference is divided into two categories as follows. Constructive Interference If two waves superimpose with each other in the same phase, the amplitude of the resultant is equal to the sum of the amplitudes of individual waves resulting in the maximum intensity of light; this is known as constructive interference. Destructive Interference If two waves superimpose with each other in opposite phases, the amplitude of the resultant is equal to the difference in amplitude of individual waves, resulting in the minimum intensity of light; this is known as destructive interference. Interference When a number of waves passes through a point in a medium at the same time, they combine to produce a resultant wave having a different amplitude and hence different intensity than the individual waves at that point. This phenomenon is known as interference. The resultant intensity at a point is due to the combined influence of all the waves pass through that point. Interference produces modification in the distribution of intensity of light, and it has been observed with light waves, sound waves, water waves, etc. Interference can be explained using the principle of superposition of waves conditions for sustained Interference To produce a sustained interference pattern, the two coherent sources of light used for interference should be derived from a single source of light, usually by amplitude division of a single source of light. The two coherent light beams that have been obtained in this method are used to produce interference. Some more conditions necessary for the interference of light are given below: (i) The two waves must have equal amplitudes. (ii) The two coherent sources must be closely placed. (iii) The light must be continuously emitted. Phase Difference and Path Difference : Phase difference is defined as the difference in phase angles of two vibrating particles, i.e. φ =2 π /λ (path difference) If μx is the optical path difference between two particles, then the phase difference is φ =2 π /λ μx where the optical path difference μx is the distance travelled in vacuum containing the same number of waves as the actual path travelled in the medium Coherent source: The source which emits a light wave with the same frequency, wavelength, and phase or has a constant phase difference is known as a coherent source. Methods of Producing Interference can be produced by two following methods: (a) Division of wavefront In this method, the wavefront is divided into two parts, either by reflection, refraction or by diffraction by using mirror, lens, prism or grating. These two parts of the same wave front travel unequal distances and reunite at some angles, thus producing interference fringes, e.g. Young’s double slit experiment, Fresnel’s biprism and Lloyd’s mirror. (b) Division of amplitude The amplitude of the incoming beam is divided into two parts, either by parallel reflection or by refraction. These two parts travel unequal distances and reunite to produce interference, e.g. Newton’s rings and Michelson’s interferometer. Young’s double slit experiment Analytical Treatment of Interference Let the amplitudes of the waves from S1 and S2 be a1 and a2. Let the phase difference between the waves at P be φ. Suppose that Y1 and Y2 are the displacements of these waves at P. Theory of Interference Fringes Coherence: To produce interference, coherent sources of light are required. When two or more electromagnetic waves are said to be coherent, they have same frequency and are in phase or maintain a constant phase difference between them. In general, the phase can vary from point to point or can change from time to time. So we have two different kinds of coherences, namely (i) temporal coherence and (ii) spatial coherence. (i) Temporal coherence: This refers to the correlation between the field of a wave at a point at some time and the field at the same point at a later time. For example, at a point, (x,y,z ) let the fields at times t1 and t2 be E(x, y, z, t1) and E (x, y, z, t2). If the phase difference between the two fields is constant during the period normally covered by observations, then the wave is said to be temporally coherent. On the other hand, if the phase difference changes many times and also there exists irregularity during the short period of time, then it is said to be non coherent. Eg: Michelson Experiment; Newton rings (ii) Spatial coherence: If a constant phase difference exists at different points in space between the waves over a time t, then they are said to be spatially coherent. Temporal coherence refers to a single beam of light, whereas spatial coherence refers to the relationship between two separate beams of light. Eg: Young’s double sit experiment Chapter-1: Interference Class -02 Principle of Superposition, Coherence and Coherent Sources,  Production of Coherent Light, Young’s Double Slit Experiment, Concept of interference, Newton’s Rings, &working of Michelson Interferometer Fabry-Perot Interferometer, and its application as wavelength filter. Displacement of Fringes S1 sources and t thickness of glass plate (μ); ν be velocity of light in glass plate the time taken for the journey from S1to P is given as Now, at any point P, the effective path difference Interference in parallel thin films A ray of monochromatic light SA be incident at an angle i on a parallel- sided transparent thin film of thickness t and refractive index μ >1. Parallel reflected rays AR1, CR2, … and a set of transmitted rays BT1, DT2, Let CN and BM be perpendicular to AR1 and AC. As the path of the rays AR1 and CR2 beyond CN is equal, the path difference between them is Interference Due to Reflected Light The two rays will reinforce each other if the path difference between them is an integral multiple of “According to Stoke’s law, when a light is conditions of maxima and minima in reflected reflected at the surface of an optically light. The two rays will reinforce each other if the denser medium, it suffers a phase path difference between them is an integral change of π, i.e a path change of λ/2.” multiple of λ, i.e., for maxima Again the two rays will destroy each other if the path difference between them is an odd multiple of λ/2 i.e. for minima Interference Due to Transmitted Light the path difference between the transmitted rays BT 1 and DT2 is given by In this case, there is no phase change due to reflection B or C because in either case the light is travelling from denser to rarer medium. Hence, the effective path difference between BT 1 and DT2 is also 2μt cos(r). Conditions for maxima and minima in transmitted light Newton’s Rings lens (L) having long focal length, f (≈100 cm) is placed with its convex surface a plano convex on a plane glass plate (G). A gradually increasing thickness of air film will be formed between plane glass plate and convex surface of plano convex lens. The thickness of air film will be zero at the point of contact and symmetrically increases as we go radially from the point of contact. A monochromatic light of wavelength ‘λ’ is allowed to fall normally on the lens with the help of a glass plate ‘P’ kept at 45° to the incident monochromatic beam. A part of the incident light rays is reflected up at the convex surface of the lens and the remaining light is transmitted through the air film. Again a part of this transmitted light is reflected at on the top surface of the glass plate (G). Both the reflected rays combine to produce an interference pattern in the form of alternate bright and dark concentric circular rings, known as Newton’s rings, because Newton first demonstrated and showed these rings. The rings are circular because the air film has circular symmetry. These rings can be seen through the travelling microscope M D Theory: Newton’s rings by reflected light Let the lens be in contact with glass plate at O and let the radius of curvature of the lens be R. Let a vertical light ray be partially reflected and partially transmitted at ‘P’. The transmitted light is again reflected at Q on glass plate G. Let the thickness of air film at P be PQ = t and the radius of Newton’s ring at Q be rn. The ray reflected at Q suffers an additional phase change of π or path difference λ/2. O Q The total path difference between the two reflected rays at ‘P’ and ‘Q’ is (1) (2) From (1) & (2) (3) (4) (4) (5) (5) From equation (3) (6) (7) nclusions derive from Newton's rings Experiment’ s  At the point of contact of lens and glass plate [at ‘O’], the path difference is zero and phase change π takes place due to reflection on glass plate; hence, dark spot will be formed at the center of ring system.  From Eq. (7), we know the diameter of rings is proportional to square root of the order of rings (i.e., n).  Hence, the spacing between consecutive rings goes on decreasing with an increase of order of rings.  The theory of Newton’s rings can be used to determine the wavelength of monochromatic light and the refractive index of a given liquid. Applications:  Determination of the wavelength of monochromatic light  Determination of the refractive index of a given liquid Principle of Superposition, Coherence and Coherent Sources,  Production of Coherent Light, Young’s Double Slit Experiment, Concept of interference, Newton’s Rings, & Working of Michelson Interferometer Fabry-Perot Interferometer, and its application as wavelength filter.

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