# 1 INTERFERENCE 2 Topics Two source interference Double-slit interference Coherence Intensity in...

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Slide 2 1 INTERFERENCE Slide 3 2 Topics Two source interference Double-slit interference Coherence Intensity in double slit interference Interference from thin film Michelsons Interferometer Text Book: PHYSICS VOL 2 by Halliday, Resnick and Krane (5 th Edition) BE-PHYSICS- INTERFERENCE-2010-11MIT-MANIPAL Slide 4 What is an Electromagnetic wave (EM)? The electromagnetic waves consist of the electric and magnetic field oscillations. In the electromagnetic waves, electric field is perpendicular to the magnetic field and both are perpendicular to the direction of propagation of the waves. 90 0 Electric field (E) Magnetic field (B) Slide 5 Examples: Light waves Heat waves Radio and television Waves Ultraviolet waves Gamma rays, X- rays Electromagnetic waves are non-mechanical waves i.e they do not require material medium for propagation. They are transverse waves. ie. They travel in the form of crests and troughs. Properties of electromagnetic waves (EM) Slide 6 They differ from each other in wavelength ( ) and frequency (f). In vacuum, all electromagnetic waves (EM) move at the same speed and differ from one another in their frequency (f). Speed=c=Frequency x wavelength i.e c= f x c= 3 x 10 8 m/s Slide 7 Electromagnetic spectrum NameFrequency range (Hz)Wavelength range Gamma rays(-rays)5 x 10 20 - 3 x 10 19 0.00006 -0.1nm X-rays3 x 10 19 - 1 x 10 16 0.1 nm-30nm Ultraviolet light1 x 10 16 - 8 x 10 14 30nm-400nm Visible light8 x 10 14 - 4 x 10 14 400nm-800nm Infra-red4 x 10 14 - 1 x 10 13 800nm-30000nm Radio frequencies3 x 10 7 - 3 x 10 4 10 10 -10 13 nm More frequency (f) more energy (E), and lesser wavelength(). Slide 8 Albert Einstein proposed that light not only behaves as a wave, but as a particle too. Light is a particle in addition to a wave-Dual nature of light. Dual Nature of Light Dual nature of light - treated as 1) a wave or 2) as a particle Light as a stream of particles Dual nature of light successfully explains all the phenomena connected with light. Slide 9 The wave nature of light dominates when light interacts with light. f When light behaves as a Wave? The wave nature of light explains the following properties of light: Refraction of light Reflection of light Interference of light Diffraction of light Polarization light Slide 10 When light behaves as a stream of particles? The particle nature of light dominates when the light interacts with matter (like solids, liquids and gases). Particle nature - Photoelectric, Compton Effect, Black body radiation.. The light is propagated in bundles of small energy, each bundle being called a quantum. Each quantum is composed of many small particles called quanta or photon. Light as a stream of particles Quantum (bundles/packets of energy) (Photon/quantum) Photon energy E = hf h = Plancks constant = 6.626x10 -34 Js f = frequency of radiation Slide 11 Light as a wave: c= f Light as a particle: E = hf photon Energy of a photon or light wave: Where h = Plancks constant = 6.626x10 -34 Js f = frequency of a light wave - c = velocity of light = wavelength of a light wave -distance between successive crests Slide 12 Visible Light 400435 nmViolet 435 nm-440nm Indigo 440480 nmBlue 480530 nmGreen 530590 nmYellow 590630 nmOrange 630700 nmRed The color of visible light is determined by its wavelength. White light is a mixture of all colors. We can separate out individual colors with a prism. Slide 13 Wave Function of Sinusoidal Waves y(x,t) = y m sin(kx- t) y m : amplitude kx- t : phase k: wave number : angular frequency Slide 14 13 PRINCIPLE OF SUPERPOSITION When two waves traveling almost in the same direction superpose, the resulting displacement at a given point is the algebraic sum of the individual displacements. i.e. when waves, y 1 =A sin t & y 2 =A sin (t + ) superpose, the resultant displacement is y= y 1 +y 2 = a sin (t) + a sin (t+ ) Slide 15 14 INTERFERENCE OF LIGHT Slide 16 TWO-SSOURCE INTERFERENCE When identical waves from two sources overlap at a point in space, the combined wave intensity at that point can be greater or less than the intensity of either of the two waves. This effect is called interference. When two waves of same frequency (or wavelength) with zero initial phase difference or constant phase difference superimpose over each other, then the resultant amplitude (or intensity) in the region of superposition is different than the amplitude (or intensity) of individual waves. OR Slide 17 16 At certain points either two crests or two troughs interact giving rise to maximum amplitude resulting in maximum intensity. (Constructive interference). At certain points a crest and a trough interact giving rise to minimum or zero amplitude resulting in minimum or zero intensity. (Destructive interference). Slide 18 Constructive Interference Destructive interference Two waves (of the same wavelength) are said to be in phase if the crests (and troughs) of one wave coincide with the crests (and troughs) of the other. The net intensity of the resultant wave is greater than the individual waves. (Constructive interference). If the crest of one wave coincides with the trough of the second, they are said to be completely out of phase. The net intensity of the resultant wave is less than the individual waves. (Destructive interference). TWO-SOURCE INTERFERENCE Slide 19 INTERFERENCE PATTERN PRODUCED BY WATER WAVES IN A RIPPLE TANK 18 Maxima: where the shadows show the crests and valleys (or troughs). Minima: where the shadows are less clearly visible BE-PHYSICS- INTERFERENCE-2010-11 TWO-SOURCE INTERFERENCE MIT-MANIPAL Slide 20 Phase: Phase of a vibrating particle at any instant indicates its state of vibration. Phase may be expressed in terms of angle as a fraction of 2. PHASE AND PATH DIFFERENCE F C A G B /2 3/2 D E 22 O Path difference corresponds to phase difference of 2. /4 /2 3/4 t=0 Slide 21 Constructive interference path difference p= 0 or phase difference = 0 path difference p = 1 or phase difference =2 path difference p =2 or phase difference = 4 General condition: Path difference p = m or phase difference = 2m where m = 0, 1, 2, 3, order of interference. 22 Slide 22 Maximal constructive interference of two waves occurs when their: path difference between the two waves is a whole number multiple of wavelength. OR Phase difference is 0, 2, 4, (the waves are in-phase). Constructive interference Slide 23 22 path difference p= /2 phase difference = 1 path difference p = 3 /2 or phase difference =3 DISTRUCTIVE INTERFERENCE path difference p = 5 /2 phase difference = 5 General condition: Path difference p=(m+1/2) or phase difference =(2m+1) where m = 0, 1, 2, 3, Slide 24 23 Complete destructive interference of two waves occur when the path difference between the two waves is an odd number multiple of half wavelength. Or the phase difference is, 3, 5, (the waves are 180 o out of phase). Slide 25 24 Coherence necessary condition for interference to occur. Two waves are called coherent when they are of : same amplitude same frequency/wavelength same phase or are at a constant phase difference COHERENCE Slide 26 25 A SECTION OF INFINITE WAVE A WAVE TRAIN OF FINITE LENGTH L COHERENCE No two independent sources can act as coherent sources, because the emission of light by the atoms of one source is independent of that the other. If the two sources are completely independent light sources, no fringes appear on the screen (uniform illumination). This is because the two sources are completely incoherent. For interference pattern to occur, the phase difference at point on the screen must not change with time. This is possible only when the two sources are completely coherent. Slide 27 26 A SECTION OF INFINITE WAVE A WAVE TRAIN OF FINITE LENGTH L BE-PHYSICS- INTERFERENCE-2010-11 COHERENCE Common sources of visible light emit light wave trains of finite length rather than an infinite wave. The degree of coherence decreases as the length of wave train decreases. MIT-MANIPAL Slide 28 27 BE-PHYSICS- INTERFERENCE-2010-11 COHERENCE Common sources of visible light emit light wave trains of finite length rather than an infinite wave. MIT-MANIPAL Laser light is highly coherent whereas a laboratory monochromatic light source (sodium vapor lamp) may be partially coherent. Slide 29 28 (2) Division of Amplitude: In this method, the amplitude of the incoming beam is divided into two or more parts by partial reflection with the help of mirrors, lenses and prisms. These divided parts travel different paths and finally brought together to produce interference. The common methods are a.Newtons rings, b. Michelsons interferometer. COHERENCE ( 1). Division of wave front: In this method, the wave front is divided into two or more parts with the help of mirrors, lenses and prisms. The common methods are: a.Youngs double slit arrangement, b. Lloyd's single mirror method. Methods of producing coherent sources: Slide 30 29 DOUBLE SLIT INTERFERENCE Screen Two narrow slits (can be considered as two sources of coherent light waves). If the widths of the slits are small compared with the wavelength distance a ( 34 For D>>d, we can approximate rays r 1 and r 2 as being parallel. The line S 2 b is drawn so that the lines PS 2 and Pb have equal lengths. Path length (S 1 b) between the rays r 1 and r 2 reaching the point P decides the intensity at P. (i.e. maximum/minimum). DOUBLE SLIT INTERFERENCE Slide 36 Path difference between two waves from S 1 & S 2 (separated by a distance d) on reaching a point P on a screen at a distance D from the sources is d sin. The path difference (S 1 b=d sin ) determines whether the two waves are in phase or out of phase when they arrive at point P. If path length (S 1 b= d sin ) is either zero or some integer multiple of the wavelength, constructive interference results at P. (d sin) DOUBLE SLIT INTERFERENCE Slide 37 Constructive Interference: Maximum at P: P O The condition for constr

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