Week 15 Day 1 Concept Question Double Slit Superposition Principle Interference Diffraction Interference and Diffraction Huygens Fresnel Principle Interference Intensity Distribution Interference Phase shift Correct answer 1 Coherent monochromatic plane waves impinge on two apertures separated by a distance d An approximate formula for the path length differences between the two rays is dsin When two or more beams of radiation are superimposed the distribution of the intensity in the region of the intersection of the two beams varies from point to point between maxima which exceed the sum of the individual intensities and minima which may have zero intensity Diffraction the spending of waves as they pass by certain obstacles or by a small aperture in a screen Diffraction and interference are both manifestations of the superposition of waves The term interference usually applies where only a few beams are allowed to interact while diffraction is usually applied to situations where many beams interact All points on a wave front act as point sources of spherical secondary wavelets which propagate outward with speeds characteristic of waves in that medium At some later time the new wave front is the surface tangent to all the wavelets Interference Combination of two or more waves to form composite wave use superposition principle Conditions for interference Coherence the sources must maintain a constant phase with respect to each other Monochromaticity the sources consist of waves of a single wavelength What is intensity of the superposition of two waves The intensity is the sum of the intensities of beam one beam two and the interference term Consider two traveling waves moving through space When the two waves are in phase there is constrictive interference When the two waves have a 180 phase shift there is destructive interference Extra Path length Constructive interference Extra path length integer multiples of wavelength L m m 0 1 2 Extra Path length Destructive interference Extra path length half integer multiples of wavelength L m m m 0 1 2 Young s Experiment Coherent Light of Fixed Wavelength Bright fringes constructive interference Dark fringes destructive interference Interference Phase Shift and Path length What can introduce a phase shift between two waves each of wavelength Assuming L d we get y Ltan Lsin Constructive interference dsin m and y m L d Destructive interference dsin m and y m L d Concept Question Changing Wavelengths Group Problem Intensity Distribution for Double Slit interference What is the intensity of two waves out of phase Intensity Superposition E E E Phase 2 dsin Intensity I I cos dsin Diffraction Through a Single Slit Intensity Distribution Diffraction minima asin m m 1 2 Correct answer 1 You just observed an interference pattern using a red laser What if instead you had a blue laser In that case the interference maxima you just was would be closer because the blue light has a smaller wavelength Two Slits with Finite Width Concept Question Interference and diffraction With more than one slit having a nite width a we must consider diffraction due to the individual slit and interference of waves from different slits Correct answer 1 Coherent monochromatic plane waves impinge on two long narrow apertures width a that are separated by a distance d with d a The resulting pattern on a screen far away is shown above with distantly spaced zeroes of the envelope as indicated by the length X above and closely spaced zeroes of the rapidly varying fringes as indicated by the length Y above Which length in the pattern above is due to the nite width a of the apertures
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