|MadSci Network: Physics|
Greetings: The interference between rays of white light, as illustrated in most text books, is in reality very difficult to duplicate because they tend to be simplifications that are designed to explain a particular topic and not to describe an experimental procedure. To demonstrate the wave like interference effects caused by two beams of white light interacting, which Young demonstrated in 1800, requires that the light in the two paths have exactly the same distribution of wavelengths and that each wavelength (color) in one path be exactly in step (in phase) with the same wavelength in the second path to within a fraction of a wavelength in distance. Scientists call this SPATIAL COHERENCE between the beams. Until the development of the first laser in 1960, coherent sources of light, particularly white light, were very difficult to obtain. The spectrum of white light ranges from red wavelengths that are about 0.7 micrometers long to violet wavelengths that are about 0.4 micrometers long. Quantum mechanics teaches us that there are over 320 thousand, million (trillion) different wave lengths of light (colors) in the white light visible spectrum. The red waves are almost two times as long as violet waves and wavelength dependent interference and diffraction phenomena are easily obscured and smeared by this large number of wavelengths in white light, each of ray of which must have the correct phase relative to its neighbor in the beam . Today, single wavelength, coherent, laser light makes it very easy to duplicate Youngs experiments. Red wavelength diode laser pointers are now available for less than $10 in many electronics and hardware stores. To duplicate Youngs experiment with a laser pointer we can we poke two very small pin holes, spaced about 1/2 millimeter (about 1/64 inch) apart, in a sheet of aluminum foil. Then we can tape the foil and a laser pointer to a table surface with the laser pointer about one meter (3 feet) from the aluminum foil and with the laser beam illuminating the two pinholes. By projecting the resultant beams passing through the pinholes onto a white sheet of paper located about two or more meters (6 feet) away from the pin holes in the foil, we can see dark and bright interference bands in the projected laser spot. Scientists call these bands fringes. If you conduct the laser experiment you will notice that the fringes of the interference pattern do not form until the paper is about a meter (3 feet) away from the pinholes and that the fringes become much more distinct as you move the paper greater distances from the pinholes. After the coherence problem, sufficient light intensity for experimentation was another problem faced by Young in his white light experiments. You must reach the Fraunhofer (far field) region of the pinholes before the interference fringes between two beams can be formed as variations in light intensity. The Fresnel (near field) region, which begins at the pinholes and extends to the begining of the far field, is the reqion in which the fringes are being generated; however they are not visible as variations in light intensity. The Fraunhofer distance (F) from the pinholes can be calculated by dividing the square of the distance between the pinholes (D) by the wavelength of the light source (L) divided by 2. F = (2 x D^2) /L For example: If the distance between the pinholes is one millimeter and the laser pointer operates at a wavelength of 0.63 micrometers, the far field begins about 317 cm (125 in) from the pin holes. If the pin holes are spaced 1/2 millimeter apart, the far field begins about 80 cm (32 in) from the pin holes. While the tight laser beam can form bright fringes projected on the paper, doing this same experiment with white light passing through the pin holes would form extremely faint fringe patterns. However with a bright light bulb or sunlight we can still demonstrate Youngs experiment. Let me describe a simple experiment that Young used to observe white light interference effects that overcomes the problems with coherence that I have discussed above. The materials required for a white light experiment are : 1) a cardboard or plastic tube or pipe approximately 5 cm (2 in) diameter and about 1 meter (3 feet) long. 2) Several 10 cm (4 in) squares of aluminum foil. 3) Masking tape or Scotch tape. 4) A sharp needle or pin. 5) A table top or similar surface on which to mount the experiment. 6) A clear glass light bulb with a linear filament. Form a tight aluminum foil diaphragm over one end of the tube and tape the outside of excess foil tightly around the tube to make a cap so that you can slide the foil diaphragm on and off the tube while aligning the light rays during the experiment. With a needle or a pin, poke the smallest hole possible in the center of the foil diaphragm. Do not push the pin all the way through the diaphragm for the pinhole will then be to large. Next look into the open end of the dark tube and practice aiming the pinhole toward a hot light bulb filament, that is located about 3 meters (9 feet ) away from the pin hole (later you might try a candle). You should be able to see the projection of the pin hole on the dark inside walls of the tube to help you align the beam. When you use a candle in place of the bulb you will observe that they are a very weak source of light, especially after passing through the small pinhole. This is why scientists such as Newton and Young used mirrors to direct sun light into their darkened laboratories for a light source in place of candles. However, on cloudy days they still had to use candles or stop experimenting. Using a pinhole is a technique that makes all of the white light rays inside of the tube have the same distribution of wavelengths and phases (spatial coherence), because all of the rays reaching the end of the tube come from the same bundle of light entering the tube from the light source. The pin hole rejects other off axis light rays from the light source that will have different wavelength and phase distributions that would spoil the inteference effect. The spatial coherence produced by the pinhole light source is not as good as that obtained with a laser, but it was good enough for Young to first demonstrate the wavelike nature of light. Now make a second aluminum foil diaphragm and cap on the open end of the tube and secure it with tape. Poke two small pin holes, side by side, in the center of the diaphragm spaced about one half of a millimeter (about 1/64 inch) apart. Now to observe Youngs interference fringes you will need to tape the tube onto a rigid surface or tripod and align the beam from the single pin hole so that it illuminates the two pin holes on the second diaphragm. This is best done by moving the light bulb back and forth or by tilting and rotating the tube on the head of a tripod. The projected white light beams that emerge from the two pin holes will be extremely dim at the far field distance and it is amazing that Young could see and study them. To see the dim fringes you must mask out all of the extraneous light from the bulb and be sure that your eyes are dark adapted, and then you might be able to see the fringes in the white light beam projected onto a paper. However, we can more easily view the white light interference fringes in a slightly different manner. A lens can be used to transform near field light beam patterns into the far the field patterns in a very short distance. This method also makes a much brighter light spot with which to conduct experiments. Our eyes have an excellent lens to do this transformation of the near field pattern into the far field patteren required to observe fringes. This transformation occurs in a distance of 2.5 cm (1 in), the focal distance distance from the lens to the retina! If we look very closely through the two pin holes and observe the lighted single pin hole at the other end of the tube, with proper alignment, we will observe a long band of bright and dark fringes extending on each side of the single pinhole. These are Youngs fringes being transformed and generated inside of our eye. You might also observe that the fringes have slightly rainbow colored edges because the different colors in the beam are slightly out of step (out of phase) with each other. With patience and a very dark room I was also able to use this experiment to see fringes from a candle flame as Young observed them. Best regards, Your Mad Scientist Adrian Popa
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