The wave nature of lightChristian Huygens (1629 - 1695) was a Dutch Physicist who proposed a wave theory of ight ong !efore "a#we$s incredi!e discoveries% &aveet 'heory &aveet 'heory(n 1)*1+ the first e#peri,enta evidence for the wave nature of ight ca,e fro, an e#peri,ent devised !y 'ho,as -oung (1../ 0 1)29)-oung1s dou!e sits -oung1s dou!e sits Interference Principle of SuperpositionCoherent SourcesYoungs Double slitDiffractionGratingsPolarization (covered in the previous lesson)The wave nature of light c = f on is the refractive index of the mediumv is the speed of light in a mediumIn any other medium the speed of propagation is given byWave FundamentalsWave Equationc the speed of light f frequencyo wavelength fncv = = Two points are said to be in-phase if the behave e!actl the sa"e# that is$ if the are a ,utipe of a waveength apart% &f two points are not in'phase$ then the are out-of-phase% Since a wavelength corresponds to one co"plete vibration$ one wavelength is often e!pressed as 2 radians%So in'phase points are separated b 2n% (ut'of'phase points can be an nu"ber of radians apart% )g *+$ rad%Wave Fundamentals Interference is the superposing of two or "ore waves to give a resultant wave whose a"plitude is given b the Principe of 2uperposition% Principe of 2uperposition%Interference of Light WavePrinciple of SuperpositionPrinciple of Superposition The total displacement at a point equal to the sum of the individual displacements at that point. There are two types of interference:constructive and destructive! Interference of Light Wave"onstructive Interferenceoccurs when the wave amplitudes reinforce each other, building a wave of even greater amplitude. There are two types of interference:constructive and destructive! Interference of Light WaveDestructive Interferenceoccurs when the wave amplitudes oppose each other, resulting in waves of reduced reduced amplitudeamplitude. http://id.mind.net/~zona/mstm/physics/waves/interference/waveInterference2/WaveInterference2.htmlinterference n interference pattern is produced provided a constant phase difference is maintained between the sources of the waves so that the points of cancellation and of reinforcement do do notnot move about. Interference of Light Wave#ources giving rise to these interference pattern are said to be coherent$ i!e!$ having the same frequencysame frequency and a constant phase constant phase differencedifference! eg! when one source emits a crest$ the other always emits a crest a set time later! ,onochro,atic light has a uni,ue wavelength and is represented b a perfect sine wave which would e!tend to infinit in ti"e and space%3aser light is an extremely good appro!i"ation to "onochro"atic light$ so"e possessing a coherence length of several -ilo"etres%&hite light$ on the other hand$ is a "i!ture of "onochro"atic waves of widely different wavelengths Interference of Light Wave %oung&s Double #lit %oung&s Double #lit %oung&s Double #lit "onstructive interference at P"onstructive interference at P'Destructive interference at P( %oung&s Double #lit ) r( * r' ) d sin path difference path difference4 22P 021P%oung&s Double #lit &f the ras were in phase when the passed through the slits$ then the condition for constructive interference at the screen is. #(P * #'P ) d sin+ ) n,bright fringesn = 1,2,...... %oung&s Double #lit the condition for destructive interference at the screen is#(P * #'P ) d sin+ ) !"n# $% ,dar- fringesn = 1,2,...... %oung&s Double #lit The points of constructive interference will appear as !right!right !ands !ands on the screen and the points of destructive interference will appear as dar5 !ands dar5 !ands% These dar- and bright spots are called interference fringes interference fringes% n 4 *dar5 fringen 4 61dar5 fringe+ etc%n 4 0 1dar5 fringen 4 *n 4 61n 4 62n 4 6/n 4 01n 4 *2n 4 */Centra !right fringenth !right fringenth !right fringe %oung&s Double #lit sinor L L yLy ==tantanwhere is very smalld d n = = sindLy n= & !distance from the screento double slit

d !slit separation y !distance of bright fringe from center &nterference patterns of overlapping water waves fro" two vibrating spherical sources%E.ample of interference http://id.mind.net/~zona/mstm/physics/waves/interference/two'ource/(wo'ourceInterference).html(wo sources interference *veryday *+amples of Interference(a) Colours of oil fil"s on water(b) Pulsing of the picture on a televisionThis occurs when an aircraft passes low overhead% The signal travelling directl fro" the trans"itting to the receiving aerial interferes with that reflected fro" the aircraft