1 Waves 9 Lecture 9 Wave propagation. D Aims: ëHuygen’s Principle: > Reflection and refraction. > Problems ëHuygen’s-Fresnel principle ëFraunhofer diffraction (waves in the “far field”). > Young’s double slits > Three slits > N slits and diffraction gratings > A single broad slit > General formula - Fourier transform. This lecture

2 Waves 9 Huygens’ Principle ëRemember the concept of wavefront - a surface of constant phase. D 1690 “Treatise on light”, Huygens. ë“Every point of a primary wavefront behaves as the source of spherical, secondary wavelets, such that the primary wavefront at a later time is the envelope of these wavelets; the wavelets have the same frequency and velocity as the incoming wave” ë Rectilinear propagation ëSpherical propagation

3 Waves 9 Reflection and refraction   r =  i  Result follows from the 2 right-angled triangles with same hypotenuse, both having one side of length vt. Thus  r =  i. D Snell’s Law

4 Waves 9 Huygen’s-Fresnel principle D Shortcomings D Shortcomings It is easy to criticise Huygens: > No theoretical basis; > Why neglect parts of the wavelet other than those forming the envelope; > Why don’t wavelets propogate backwards; > It is no help in predicting amplitudes; etc... ëNone detract from its historical significnce and the fact that it works. D Fresnel (1818) (See handout). ëHe built in Young’s concept of interference. “Every unobstructed point of a wavefront … serves as a source of spherical secondary wavelets … The amplitude of the optical field at any point beyond is the superposition of all these wavelets (considering their amplitudes and relative phases)” ëNote backward travelling wavelets tend to interfere destructively D Kirchoff ( ) ëProvided theoretical foundation by connecting the wave equation to a surface integral of spherical wavelets. ëSee Optics course, next term.