1RR July 2000 SS Dec 2001 Physics 342 Laboratory The Wave Nature of Light: Interference and Diffraction Objectives: To demonstrate the wave nature of light, in particular diffraction and interference, using a He-Ne laser as a coherent, monochromatic light source. Apparatus: He-Ne laser with spatial filter; photodiode with automatic drive, high voltage 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 Their Applications, Addison-Wesley, Reading Massachusetts, 1978. Introduction In 1678, Christian Huygens wrote a remarkable paper in which he proposed a theory for light based on wave propagation phenomena, providing a very early theoretical basis for the wave theory of light. Because Huygens’ theory could not explain the origin of colors or any polarization phenomena, it was largely discarded for over 100 years. During the early 1800’s, Thomas Young revived interest in Huygens theory by performing a series of now famous experiments in which he provided solid experimental evidence that light behaves as a wave. In 1801, Young introduced the interference principle for light which proved to be an important landmark and was hailed as one of the greatest 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 his experimental observations and thereby set the wave theory of light on a firm theoretical basis. The interference and diffraction experiments performed by Young and Fresnel require the use of a coherent light source. While coherent light is difficult to produce using conventional sources, the invention of the laser now makes intense coherent light readily available. In this experiment, you will reproduce some of Young and Fresnel’s important discoveries using light from a He-Ne laser. In this way, you will become familiar with a few of the basic principles surrounding the wave theory of light. The remarkable successes of this theory explains why it was so prominent throughout the 1800’s and why it was so difficult to challenge, even when convincing evidence for a quantized radiation field began to emerge in the 1890’s.2Theoretical 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 wave falling on the screen consists of parallel rays. For historical reasons, optical phenomena falling under this category are referred to as Fraunhoffer diffraction. 2. Those in which the light falling on an aperture and the diffracted wave falling 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 is shown in Fig. 1. Figure 1: Qualitatively, Fraunhoffer diffraction (a) occurs when both the incident and diffracted waves can be described using plane waves. This will be the case when the distances from the source to the diffracting object and from the object to the receiving point are both large enough so that the curvature of the incident and diffracted waves can be neglected. For the case of Fresnel diffraction (b), this assumption is not true and the curvature of the wave front is significant and can not be neglected. Fraunhoffer diffraction is much simpler to treat theoretically. It is easily observed in practice by rendering the light from a source parallel with a lens, and focusing it on a screen with another lens placed behind the aperture, an arrangement which effectively removes the source and screen to infinity. In the observation of Fresnel diffraction, on the other 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 the phase φ of a light wave. For light having a wavelength λ, the phase of the light wave at a given instant in time is represented by d×=λπφ2. (1)3where d is distance travelled by light. If a light beam is equally split and the two split beams travel along two different paths 1 and 2, then the phase difference ∆φ between the two beams when they are recombined (after traveling distances x1 and x2) can be defined as ( )12122xx −×=−=∆λπφφφ. (2) In the wave theory of light, the spatial variation of the electric (or magnetic) field is described by a sinusoidal oscillation. When discussing interference and diffraction effects, ∆φ appears in the argument of this sinusoidal function. Since the intensity I of a light wave is proportional to the square of its electric field vector, the intensity of two beams interfering with each other will be determined by factors proportional to sin2(∆φ) or cos2(∆φ). The exact expression for ∆φ depends on the detailed geometry involved, but in general, ∆φ=π/λ × (geometrical factor). A few important cases have been worked out in detail and the relative intensity variation I(x)/I(0) produced by a coherent, monochromatic light beam as a function of position x along a viewing screen are given below. Because of the periodic nature of sinusoidal functions, they exhibit local maximums and zeros as the phase varies. The precise location of the maximums and zeroes can often be established by a calculation of the phase difference ∆φ. Single Slit (Fraunhoffer limit) If coherent light having a wavelength λ is made to pass through a long narrow slit of width a, then the relative light intensity as a function of lateral displacement x