Experiment 5 – Diffraction of Light 1Experiment 5Diffraction of Light1 IntroductionWe will look at the wave nature of light in a set of experiments wherediffraction and interference patterns are produced when laser light isincident on various obstacles.2 Background - see Pedrotti3, Chapter 11The general arrangement that will produce a diffraction pattern is il-lustrated schematically in Fig. 1. At a distance D from the obstacle,the intensity of the diffracted light will be measured as a function of thex coordinate. The diffraction patterns are relatively simple in the farfield limit, where a2/Dλ 1, where a is the characteristic dimensionof the obstacle (such as the width of a slit) and λ is the wavelengthof light. This is the Fraunhofer diffraction limit, and the diffractionpatterns are simply Fourier transforms of the diffracting object. Closerto the object, the diffraction patterns are more complicated and aredescribed by Fresnel diffraction theory.2.1 Slit DiffractionConsider a single slit with width a illuminated by a laser with wave-length λ. The diffraction pattern is observed on a screen a distance Daway. The intensity as a function of θ that appears on the screen (inthe far field) is given byI(θ) = I(0)sin αα2(1)where I(0) is the intensity at θ = 0 andα =πaλsin θ. (2)Experiment 5 – Diffraction of Light 2LaserbeamxI(x)I(0)!DFigure 1: Schematic layout for diffractionThis is an Airy function, which is the Fourier transform of a tophat function. For light passing through N slits, with widths a andseparations d, the intensity is given byI(θ) = N2I(0)sin αα2sin NβN sin β2, (3)where I(0) is the intensity at θ = 0 passing through one slit, α is definedin Eq. (2), and β is given byβ = πdλsin θ. (4)Notice that the α dependent term of Eq. (3) is related to the single slitdiffraction pattern and the β is due to interference between the lightemanating from the multiple slits. Note the N2dependence, whichcomes from the coherent addition of N sources.3 ExperimentIn the following experiments, you will scan the diffraction patterns witha linearly driven photodiode and record the data with the computer.Measure the diffraction patterns from single and multiple slits. Inthe far field limit, you should be able to extract the slit parameters byanalysis of your diffraction patterns. Verify the N2dependence for themultiple slits. Compare your results with a measurement of the slitwidths with the microscope.Using a razor blade, measure the diffraction pattern from an edge,and compare it to the expected pattern. Do not cut yourself!Using Babinet’s principle (which relates the diffraction pattern of amask to its complement, see Pedrotti3page 330) measure the diameterof a human hair (your own if you have one to spare).Experiment 5 – Diffraction of Light 3Using a lens, show that imaging can undo what diffraction does.Hint- place the lens to magnify the image so that it is large enough toresolve. Moving slightly away from the imaging condition allows youto record a near-field diffraction pattern, governed by the much morecomplex Fresnel diffraction
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