![]() ![]() Here n d=a the slit width, therefore we can say first minima occurs at We can see the term sin(nφ/2) (blue) is changing faster than term sin(φ/2) (dashed red).įirst minima will be where term sin(nφ/2) will have first minima or when n φ/2=π Let us first look at the plot of sin(nφ/2) and sin(φ/2) as a function of θ. That means that all the oscillators are in phase and there is a strong intensity in the direction θ = 0. In the first place there will be maxima when φ=π (a/n) sinθ/λ=0. Intensity in a given direction θ can be rewritten as Here we have assumed that initial constant phase α = 0. Let us now examine the diffraction pattern of a plane wave of light of wavelength λ through a narrow slit of width a.Īccording to Huygens' principle, we can divide the slit in n equidistant point sources.Īccording to our formula for n interfering sources, Intensity at any point in a given direction θ is Intensity at any point is proportional to energy density, therefore intensity in a given direction θ is These all terms can be added geometrically using phasor diagram. If we are observing in a given direction θ, the phase term φ can be computed from the path difference. Let us consider n equally spaced oscillators, all of equal amplitude E, but different from one another in phase as shown This bright spot is called Fresnel bright spot. To the surprise of every one Poisson's prediction indeed turns out to be true. Poisson, pointed out that if Fresnel's explanation is correct, then in the center of the shadow of a opaque sphere or disk, there should be a bright spot.Ĭompetition committee arranged an experiment to verify this prediction. To challenge wave theory, they arranged an assay competition.Īugustin Fresnel presented his experiments on light and his wave theory explanation of those experiments. Newton's theory was that light is a stream of particles.Įven in 1819, scientific circles were dominated by Newton's supporters. In this chapter we will learn following topics.Īmplitude due to interference of n equal light (electromagnetic wave) sources.ĭiffraction can only be explained by wave theory of light. If there are larger number of sources, word Diffraction is more often used. When there are only a few interfering sources, say two, then the result is usually called Interference. There is no specific, important physical difference between the two. No one has ever been able to define the difference between interference and diffraction satisfactorily. ![]()
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