Physics 342 LaboratoryThe Wave Nature of Light: Interference and DiffractionRR July 2000SS Dec 2001 Physics 342 LaboratoryThe Wave Nature of Light: Interference and DiffractionObjectives: To demonstrate the wave nature of light, in particular diffraction andinterference, using a He-Ne laser as a coherent, monochromatic light source. Apparatus: He-Ne laser with spatial filter; photodiode with automatic drive, highvoltage power supply for the laser, amplifier, computer with CASSY interface (no pre-amp boxes required), slits on a photographic plate, spherical and cylindrical lenses,diaphragm, and a razor blade. References: 1. D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics; 5th Edition,Wiley and Sons, New York, 1997; Part 4, pgs. 901-957.2. E. Hecht, Optics, 2nd Edition, Addison-Wesley, Reading Massachusetts, 1974.Chapter 9 on interference, Chapter 10 on diffraction.3. D.C. O’Shea, W.R. Callen and W.T. Rhodes, Introduction to Lasers and TheirApplications, Addison-Wesley, Reading Massachusetts, 1978.Introduction In 1678, Christian Huygens wrote a remarkable paper in which he proposed a theoryfor light based on wave propagation phenomena, providing a very early theoretical basisfor the wave theory of light. Because Huygens’ theory could not explain the origin ofcolors or any polarization phenomena, it was largely discarded for over 100 years.During the early 1800’s, Thomas Young revived interest in Huygens theory byperforming a series of now famous experiments in which he provided solid experimentalevidence that light behaves as a wave. In 1801, Young introduced the interferenceprinciple for light which proved to be an important landmark and was hailed as one of thegreatest contributions to physical optics since the work of Isaac Newton.The interference principle was independently discovered by Augustin Fresnel in 1814.Unlike Young, Fresnel performed extensive numerical calculations to explain hisexperimental observations and thereby set the wave theory of light on a firm theoreticalbasis.The interference and diffraction experiments performed by Young and Fresnel requirethe use of a coherent light source. While coherent light is difficult to produce usingconventional sources, the invention of the laser now makes intense coherent light readily1available. In this experiment, you will reproduce some of Young and Fresnel’s importantdiscoveries using light from a He-Ne laser. In this way, you will become familiar with afew of the basic principles surrounding the wave theory of light. The remarkablesuccesses of this theory explains why it was so prominent throughout the 1800’s and whyit was so difficult to challenge, even when convincing evidence for a quantized radiationfield began to emerge in the 1890’s.Theoretical Considerations Fraunhoffer diffraction, Fresnel diffraction Diffraction phenomena are conveniently divided into two general classes, 1. Those in which the light falling on an aperture and the diffracted wavefalling on the screen consists of parallel rays. For historical reasons, opticalphenomena falling under this category are referred to as Fraunhoffer diffraction.2. Those in which the light falling on an aperture and the diffracted wavefalling on the screen consists of diverging and converging rays. For historical reasons,optical phenomena falling under this category are referred to as Fresnel diffraction.A simple schematic illustrating the important differences between these two cases isshown in Fig. 1.Figure 1: Qualitatively, Fraunhoffer diffraction (a) occurs when both the incident anddiffracted waves can be described using plane waves. This will be the case when thedistances from the source to the diffracting object and from the object to the receivingpoint are both large enough so that the curvature of the incident and diffracted waves canbe neglected. For the case of Fresnel diffraction (b), this assumption is not true and thecurvature of the wave front is significant and can not be neglected. Fraunhoffer diffraction is much simpler to treat theoretically. It is easily observed inpractice by rendering the light from a source parallel with a lens, and focusing it on a2screen with another lens placed behind the aperture, an arrangement which effectivelyremoves the source and screen to infinity. In the observation of Fresnel diffraction, on theother hand, no lens are necessary, but here the wave fronts are divergent instead of plane,and the theoretical treatment is consequently more complex. The important guiding principal of all interference and diffraction phenomena is thephase  of a light wave. For light having a wavelength , the phase of the light wave at agiven instant in time is represented by d2. (1)where d is distance travelled by light. If a light beam is equally split and the two splitbeams travel along two different paths 1 and 2, then the phase difference  between thetwo beams when they are recombined (after traveling distances x1 and x2) can be definedas 12122xx . (2)In the wave theory of light, the spatial variation of the electric (or magnetic) field isdescribed by a sinusoidal oscillation. When discussing interference and diffraction effects, appears in the argument of this sinusoidal function. Since the intensity I of a lightwave is proportional to the square of its electric field vector, the intensity of two beamsinterfering with each other will be determined by factors proportional to sin2() orcos2(). The exact expression for  depends on the detailed geometry involved, but ingeneral, (geometrical factor). A few important cases have been worked out in detail and the relative intensityvariation I(x)/I(0) produced by a coherent, monochromatic light beam as a function ofposition x along a viewing screen are given below. Because of the periodic nature ofsinusoidal functions, they exhibit local maximums and zeros as the phase varies. Theprecise location of the maximums and zeroes can often be established by a calculation ofthe phase difference . Single Slit (Fraunhoffer limit)If coherent light having a wavelength  is made to