Physics 2020 Lab: Diffraction and Interference page 1 of 12Lab: Diffraction and InterferenceINTRODUCTION & BACKGROUND:Light is an electromagnetic wave, and under the proper circumstances, it exhibits wavephenomena, such as constructive and destructive interference. The wavelength ofvisible light ranges from about 400-750 nm = 0.0004-0.00075 mm, and this wavelength sets the scale for the appearance of wave-like effects. For instance, if a broad beamof light partly passes through a wide slit (i.e. a slit which is very large compared to ),then the wave effects are negligible, the light acts like a ray, and the slit casts ageometrical shadow. However, if the slit is small enough (i.e. around the same size as), then the wave properties of light become apparent and a diffraction pattern isprojected.plane wave wavefrontsFigure 1a. Slit large compared to . Figure 1b. Slit small compared to . Now consider the light from two coherentlight sources a distance d apart. Coherentsources emit light waves that are in phase, orin sync. If we think of light like a water wave,we can imagine that coherent sources emit anidentical succession of wave crests andtroughs, with both emitting crests at the sametime. One way to create such coherentsources is to illuminate a pair of narrow slitswith a distant light source.Interference from two slits: Consider the light rays from the two coherent pointsources made from slits a distance d apart (see fig. 3). We assume that the sourcesare emitting monochromatic (single wavelength) light of wavelength . The rays areemitted in all forward directions, but let’s concentrate on the rays that are emitted in adirection toward a distant screen ( measured from the normal to the screen, diagrambelow). One of these rays has further to travel to reach the screen, and the pathdifference is given by sind. University of Colorado at Boulder, Department of PhysicsA B Points A and B are coherent sources. Figure 2. Points A and B act likecoherent sources.Physics 2020 Lab: Diffraction and Interference page 2 of 12What happens if this path difference isexactly one wavelength (or any integernumber of wavelengths)? If you lookcarefully, this is what is represented in fig. 3.What happens if the path difference is /2, or 3/2, or 5/2, etc.?A complete analysis yields a pattern of intensity vs. angle that looks like:Intensity0/d/dDouble slit,infinitesimalwidthd2.. 1, 0, = m .)(sin :sin :21mdDarkmdBrightWhat happens to the above interference pattern if d is increased? What if d isdecreased?University of Colorado at Boulder, Department of PhysicsFigure 3.Physics 2020 Lab: Diffraction and Interference page 3 of 12Small angle simplification: If is small (<< 1 rad), then sin (in radians), andmaxima occur on the screen at dm; minima occur at dm21. As shown below, the angle (measured from the center of the screen) is related to thedistance x measured on the screen by tan()=x/L, where L is the distance from thescreen to the source of light (the aperture).laseraperturescreenLx/LtanxIf the angle is small (less than a few degrees), then to an excellent approximation,sin() tan() (in radians) so the locations of the interference maxima are given bydmLx.Single slit diffraction: The uniform 2-slit interference pattern shown above is seldomobserved in practice, because real slits always have finite width (not an infinitesimalwidth). We now ask: what is the intensity pattern from a single slit of finite width D?Huygens’ Principle states that the light coming from an aperture is the same as the lightthat would come from a collection of coherent point sources filling the space of theaperture. It's as if we constructed the large slit out of a whole set of small slits, alladjacent to each other. To see what pattern the entire array produces, consider firstjust two of these imaginary sources: one at the edge of the slit and one in the center.These two sources are separated by a distance D/2.The path difference for the rays fromthese two sources, going to the screenat an angle , is sin2D, and theserays will interfere destructively if22sinD. But the same can besaid for every pair of sourcesseparated by D/2. Consequently, therays from all the sources filling theaperture cancel in pairs, producingzero intensity on the screen whenD22sin or, if is small,University of Colorado at Boulder, Department of PhysicsDto screenD/2sin 2_Daperture filled with imaginary sourcesPhysics 2020 Lab: Diffraction and Interference page 4 of 12D. (First minimum in single slit pattern.)The complete intensity pattern, called a diffraction pattern, looks like...0IntensityDSingle slit. D/ D/ D/ D/ D/ D/[The central maximum is actually much higher than shown here. It was reduced by afactor of 6, for clarity.] The single slit diffraction pattern has minima at D D D, , , ...2 3 (Minima of single slit pattern.)So the separation of minima is /D, except for the first minimum on either side of thecentral maximum, which are separated by 2/D. If x is the distance on the screenbetween minima, then DLx.Combining 2-slit interference with finite-width single-slit diffraction: When theaperture consists of two finite slits, each of width D, separated by a distance d, thenthe intensity pattern is a combination of both the single-slit pattern and the double slitpattern: the amplitude of the two slit interference pattern is modulated by a single slitdiffraction pattern: dDDouble slit,finite width/d/D/D2University of Colorado at Boulder, Department of PhysicsPhysics 2020 Lab: Diffraction and Interference page 5 of 12In this full pattern, the finely spaced interference maxima are spaced d apart,while the more widely spaced minima of the single-slit diffraction pattern areseparated by D or 2D. Note that an interference maximum
View Full Document
Unlocking...