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2054Lecture16

# 2054Lecture16 - Interference Young's Double Slit...

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Unformatted text preview: Interference, Young's Double Slit Experiment & Diffraction Gratings Topics of Discussion Wave/Particle Duality Interference & the Principle of Superposition Diffraction & Huygens' Principle Single Slits Resolving Power & Rayleigh's Criterion Young's Double Slit Experiment WaveParticle Duality Wave-particle duality says that light can be viewed as a particle or as a wave. Wave Phenomenon: Interference and Diffraction. Particle Phenomenon: Photoelectric Effect and Compton Effect Interference Interference is the phenomenon that occurs as the result of the interaction of two or more light sources. The conditions for interference are: All sources must maintain a constant phase with respect to one another. The source is then called coherent. The light must have the same wavelength. The Mathematical Description of a Wave When a wave travels from one location to another, we will call such a wave a traveling wave. This type of wave is described by y ( x, t ) = y m sin ( kx - t ) where ym is the amplitude, x is the position, is the angular frequency, t is time, and kx t is the phase of the wave. Principle of Superposition When N sources are simultaneously present at the same place, the resulting disturbance is the sum of the disturbances from the individual waves, that is y ( x, t ) = N i= 1 y m , i sin ( k i x - i t ) . Types of Interference Constructive interference occurs when light from sources reinforce each other using the principle of linear superposition. Destructive interference occurs when light from sources cancel each other using the principle of linear superposition. Diffraction Diffraction is interference produced by light scattering from an object or objects. A pattern of light and dark bands at an observation screen using the principle of superposition, which we call a diffraction pattern. Types of Diffraction Frauanhoffer diffraction occurs when the observation screen that is located far from the source. Fresnel diffraction occurs when the observation screen is located near the source. Single Slit Diffraction If light of wavelength strikes the single slit of width W then the condition for destructive interference is given by Wsin = m for m=1,2,3,.... Huygens' Principle Every point on a wave front acts as a source of tiny sources that travel at the same speed as the incident wave. Derivation of Single Slit Destructive Interference Diffraction Number Path Length Order of Sources Difference 1 2 m 2 4 2m W/2sin = /2 W/4sin = /2 W/2msin = /2 Young's Double Slit Experiment If light of wavelength strikes two slits spaced d apart then the condition for constructive interference for m=0,1,2,3,...is given by dsin = m. If light of wavelength strikes two slits spaced d apart then the condition for destructive interference for m=0,1,2,3,...is given by dsin = (m + 1/2) . Resolving Power The resolving power of an optical system is its ability to distinguish two closely spaced objects. If light of wavelength strikes the single slit of diameter D then the condition for destructive interference is given by Dsin = 1.22 where is the angle between the first dark circular fringe and the central bright circular fringe. Rayleigh Criterion Two point objects are just resolved when the first dark fringe in the diffraction pattern of one falls directly on the central bright fringe in the diffraction pattern of the other. If light of wavelength strikes the single slit of diameter D then the minimum angle min between the two objects is min 1.22 / D Diffraction Gratings An optical component that produces a diffraction pattern is called a diffraction grating. If light of wavelength strikes a diffraction grating of grating spacing d then the condition for constructive interference for m=0,1,2,3,...is given by dsin = m. ...
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