ContentsIntroductionHuygen’s PrincipleApplications of Huygen’s Principle to the studyRefraction And ReflectionTotal Internal ReflectionDiffuse ReflectionSummary
IntroductionThe wave theory of light was 1st forward by ChristiaanHuygens in 1678.During that period , everyone believed in Newton’sCorpuscular theory, which had satisfactorily explain thephenomena of reflection, refraction, the rectilinearpropagation of light and the fact that light light couldpropagate through vacuum.The Corpuscular model predicted that if the ray of light(on refraction) bends towards the normal then the speedof light would be greater in the second medium.In 1678, the Dutch Physicist Christiaan Huygens putforward the wave theory of light-it is wave model of light.The wave model could satisfactorily explain the
Phenomena of reflection and refraction;However, it predicted that on refraction if the waveBends towards the normal then the speed of light would beless in second medium.According to Maxwell, light waves are associated withchanging electric & magnetic field; changing electric fieldproduces a time and space varying magnetic field & achanging magnetic field produces a time and spacevarying electric field.The changing electric & magnetic field result in thepropagation of electromagnetic waves (or light waves)even in vaccum.
Huygen’s TheoryWavefrontItisthelocusofpointsonawavehavingsanephase.Directionofwavesisalwaysperpendiculartothewavefront.o Forapointsourcewavefrontisspherical,o Foralinesourcewavefrontisalwayscylindericalo Incaseofplanesoutcewavefrontisalwayspalne.If point source & line source placed at ∞ then wave frontalways appears to be plane.For ExampleIf we drop a small stone in a calm pool of water, circular ripplesspread out from the point of impact, each point on thecircumference of the circle (whose centre as at the point ofimpact) oscillates with the same amplitudes & same phase
and same phase and thus we a circularwave front.At large distance from the source, a small portion of thesphere can be considered as a plane and we havewhat is known as a plane wave .Sphericalwavefront Cylindricalwavefront PlanewavefrontSphericalwavefront Cylindrecialwavefront
Huygen’s PrincipleIt is a Geometric Constructions used to find theshape and position of new wave fronts at a giveninstant of time . It is base on the followingassumption:-All points are primary wave front act as a source forthe formation of secondary wave front.Velocity of wave from primary to secondary wavefront is same as that from the source of the primarywave front. Wealways taking to consideration the forward wave front and ignorethebackward wave front because energy always propagate in forwarddirection. Reasons :-
In Huygen’s theory , the presence of the backwardIs avoided by assuming that the amplitude of the secondarywavelets is not uniform an all directions ; it is maximum in theforward direction & zero in the backward direction.Reflection of a plane wave by a plane surfaceConsider a beam of light incident on a planesurface at points P,Q,R and getting reflectedAs shown in fig.Primary & Secondary wave front are drawn alongperpendicular to the incident and reflected rays.
Time = Distance/SpeedT= MQ+QS/CT= PQ sini + QR sinr/CT= PQ sini + (PR-PQ)sinr/C
T= PQ(sini + sinr) + PR sinr/CPosition of Q is not fixed , time taken will not depend uponterm PQ.PQ(sini + sinr) = 0But PQ is not equal to zeroSini – sinr = 0Sini = sinrHence , angle of incidence is equal to the angle of reflection.( Henced Proved)Refraction of a Plane Wave
T= PQ(sini/C + sinr/V) + PR sinr/VPosition of Q is not fixed , time taken will not dependupon term PQPQ(sini/C + sinr/V) = 0But PQ is nor equal to zeroSini/C + sinr/VSini/C = sinr/VSini/sinr = C/V=µHence, snell’s law is proved(Henced Proved)
Total Internal Reflection (TIR)In above fig. the angle of incidence has been shown tobe greater than the angle of incidence. Thiscorresponds to the case when V2<V1, i.e, the lightwave is incident on denser medium.If the second medium is a rare medium (i.e, V1<V2)then the angle of refraction will be greater than theangle of incidence. Where B1B2= V1t and A1A2= V2t.Clearly , if the angle of incidence id such that V2t is >than A1B2 , then the refracted wave front will be absentand we will have, what is known as , TIR.THE CRITICAL ANGLE WILL CORRESPONDS TOA1B2 = V2t
Thus sinic = B1B2/A1B2 = V1/V2 = n12Where, ic denotes the critical angle and n12 represents therefractive index of the second medium w.r.t the 1st.For all angles of incidence greater than ic , we will have totalinternal reflection.Diffuse Reflection In the above we considered the reflection of light from asmooth surface. This is known as specular reflection.If the surface is irregular we have , what is known as diffusereflection.The secondary wavelets emanating from the irregular surfacetravel in many directions and we do not have a well definedreflected wave.
If the irregularity in the surface is considerably greaterthan the wavelength, wee will have diffuse reflection.
SummaryAccording to Hugyen’s Principle, each point of a wave front is asource of secondary disturbance and the wavelets emanatingfrom these points s[read out in all directions with the speed ofthe wave. The envelope of these wavelets gives the shape ofthe new wave front.Huygen’s Principle along with the fact that the secondarywavelets mutually interfere , is known as the Huygen’s –Fresenel Principle.Law’s of reflection and Snell’s law of refraction can be derivedusing Huygen’s Principle.Using Huygen’s Principle one can derived the lens fomula1/v – 1/u = 1/f.