From: V Laxmanan (vlaxmanan@hotmail.com)
Date: Thu Sep 04 2003 - 14:38:50 PDT
Eratosthenes Experiments and Young's Interference Experiment Posted by V. Laxmanan, September 4, 2003 Thomas Young performed a very simple experiment using natural sunlight, back in 1801, which provided support for the wave nature of light. Many of Young's contemporaries, on the other hand, held the competing view, championed by Newton, that light was a stream of particles that obeyed his laws of mechanics. The different colors of the rainbow were simply due to different particles of light that had different masses and has different values of the momentum (mass time velocity, with velocity being the same for all the colors). The wave view point was championed by the Englishman Robert Hooke and was the Dutch physicist, Chrisitaan Huygens, both contemporaries of Newton. Huygens developed the mathematical aspects of the wave theory, in 1678, and showed how the then known laws of reflection and refraction could be explained readily on the basis of the wave theory. The ratio of the sines of the angle of incidence to the angle of refraction could be related to the speed of the light wave as it travels from one medium (say air) into another (say glass or water). However, because of Newton's great authority and prestige, the wave theory found very little support during his lifetime. Young's experiment, however, seemed to prove conclusively that light must be a wave. Even today this experiment cannot be rationalized on the basis of the particle theory of light. In the middle of the 19th century, Foucault showed, quite convincingly, that the relative values of the speeds of light in air and water was exactly as predicted by the wave theory (and inconsistent with the conclusions of the particle theory, and Newton's predictions). The speed of a light c = Lf where f is the frequency and L the wavelength. The wavelength L is the distance between any two adjacent crests, troughs, or nodes of the wave. The light wave travels a distance L in the time t = 1/f, the period of vibration of the wave. Amazingly, as in the case of the Eratosthenes experiments, we must make the assumption that light rays are parallel in order to calculate the (then unknown) wavelength of light from Young's observations. In Young's experiment, two light rays emerge from two small pinholes, or slits, in screen number one, see Figure 3 in the attached Microsoft PowerPoint file. These rays travel slightly different distances to arrive at the same time t at the point P on a second screen, where Young observed alternate bands of light and dark (or interference fringes). The wavelength is obtained using geometrical arguments familiar to all high school students. Amazingly, we cannot determine the wavelength without assuming that the two rays are parallel although they meet at a finite distance D. This point is discussed in more detail in the attached file (see Parallels1.doc). Are the dark fringes that Young observed similar to the shadows cast by vertical sticks? This seems like an intriguing train of thought and, perhaps, merits some consideration. Thus, we must make the assumption of parallel light rays to 1. Determine the latitude using the Pole star. 2. Determine the radius of the earth in Eratosthenes Experiment. 3. Determine the wavelength of light in Young's Interference Experiment. Can we therefore use shadow length measurements to test the validity of the parallel rays hypothesis. Since we cannot determine the latitude of a place, without this assumption, we cannot proceed to step 2, viz. the Eratosthenes Experiment. The role played by time itself in the formation of interference fringes in discussed in detail in Ref. [18] cited in the attached Microsoft Word file. Likewise, if we consider two adjacent points on the surface of the earth (not necessarily in different cities, see Figure 2), where two vertical sticks are placed, the role played by time in the formation of a shadow will become obvious. Light waves must travel different distances from the top of the stick to the tip of the shadow because of the curvature of the earth's surface. These distances increase as the latitude increases, since all rays of the sun are deemed to be parallel. Because of the very high speed with which a light ray, or wave, travels, we are unable to see the formation of the shadow at high noon. However, when the sun rises or sets, we can see the shadow growing or shrinking. All observations suggest that this takes place at a finite speed. This must be related to the speed of light and also the daily rotational speed of the earth. No attempts seem to have been made to analyze these problems mathematically. There is still much to be done in developing the mathematical theory that describes how shadow lengths change on a sundial. Perhaps, renewed interest in the Worldwide Eratosthenes Experiment might call the attention of physicists to such problems. Attachments: Parallels1.doc and Parallel1.ppt. _________________________________________________________________ Try MSN Messenger 6.0 with integrated webcam functionality! http://www.msnmessenger-download.com/tracking/reach_webcam