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Experiment 1 1. Wave Nature of Light: Interference and Diffraction of Laser Light PHY 134 (Section 11) 2 Purpose The experiment was done to help observe and establish the wave-like nature of light. Apparatus Two rulers, Magnetic bench, Straight edge/Opaque disks slide, Helium-neon laser, 48mm focal length lens, Slide with several narrow single slits, Slide with double slits, Diffraction grating slide, Hologram, and Calculator. Theory In the laboratory experiment, diffraction of light, a form of interference, is investigated using a laser. The light from a laser is collimated, monochromatic, and coherent. Which means that the beam does not diverge very much, the wavelength is constant, and all the oscillators in the beam are in phase with each other. The relationship between wavelength (), frequency (f), and speed of light (c) can be expressed c = f. Light travels with a constant speed within the same indices of refraction, and in air light travels with a speed of 3.0 * 108 m/s. Figure 1. Diagram of the narrow slit experiment 3 For the first two experiments, quantitative analysis is not required. But for narrow slit experiment, the formula = aw/2L is used, where is wavelength, a is the width of the slit, w is the width of the central peak, and L is the distance to screen (Fig 1). The formula is derived from a sin =, tan = w/2L, and using the right triangle. Since the angle is very small, sin and tan can be set equal to each other. Figure 2. Diagram of the double slit experiment In the double slit experiment, two slits are separated by a distance d, and two beams interfere with each other. When the two beams arrive at the screen in phase, bright spots can be observed, and it is called constructive interference. For this experiment, the condition is dsin = m, where m is the order of the bright band (Figure 2). Using the small angle approximation, = dy/mL can be derived. The Diffraction grating makes a very accurate wavelength measurement. Formulas d = 1/n (where n is number of slits per mm), and dsin = m are used to derive dy/L = m, which is the formula used in the experiment. 4 The hologram is an advanced form of photography that allows an image to be recorded in three dimensions. The technique of holography can also be used to optically store, retrieve, and process information and it only works with laser. Procedure This experiment was composed of six different experiments. All six experiments required semi-dark conditions, so the light was turned off. The first experiment was "Diffraction by a Straight Edge." The slide marked "straight edge/opaque disks" with a fairly well-defined edge was placed on the magnetic holder and the laser on the screen was observed. For the second experiment, "Superposition of Waves and Diffraction by a Disk," the 48mm focal length lens was places on the magnetic holder and the opaque disk slide was placed on as well. Then, the diffraction pattern of the laser was observed. Then, the third experiment, "Diffraction by a Narrow Slit" was done by first using the slide with several narrow single slits into the holder and recording the theoretical a. The slide was then illuminated with the laser. With the given wavelength, and the value of L and w measured by rulers, experimental a was calculated and was compared to the theoretical a. For the fourth experiment, "Interference: the Double Slit," the slide with double slits were used. Again, theoretical d was recorded, and L and y were measured. Then, with the given , experimental d was calculated and compared to the known value. For the fifth experiment, "The Diffraction Grating," an optically flat glass with a large number of narrow parallel slits was used. The grating was mounted on the bench and illuminated with the laser. The distance between the first order spots, as well as the distance L was measured for the first order. Then using the formula derived, the wavelength was calculated. same The 5 procedure was repeated for the second order. Then, the last experiment "The Hologram" was done by observing the three-dimensional image. Precautions Do not look directly into the laser beam, and do not remove it from the optical bench. Also, do not slide the component holders to protect the magnetic surfaces of the optical bench. Results and Conclusions A. Diffraction by a Straight Edge The light bended around the opaque part of the slide and went into the shadow region. This was interesting, since me and my partner expected the result to be only half of the circle. This showed that the light wave is capable of bending around sharp edges, if the boundary of the edge is not too much larger than the wavelength of the light. B. Superposition of Waves and Diffraction by a Disk In this experiment, a bright spot was observed at the center as shown in figure 3. This could be explained by superposition, which occurs when two waves arrive at the same point at the same time. Superposition is a form of constructive interference. Figure 3. The result of "Superposition of Waves and Diffraction by a Disk" 6 C. Diffraction by a Narrow Slit The value of the wavelength of the laser was given: 632.8nm. The theoretical a was obtained from the narrow single slits slide. My partner and I chose atheo = 0.04mm. From the experiment, w and L were each measured, 28mm and 94cm. With the data and the formula = aw/2L, experimental a was calculated. [Calculation] atheo = 0.04mm * 1m / 1000mm = 4 * 10-5 m = 632.8nm * 1m / 109nm = 6.32 * 10-7 m w = 28mm * 1m / 1000mm = 0.028 m L = 94 cm * 1m /100 cm =0.94 m = aw/2L aexpt = 2L / w = (2 * 0.94m * 6.32 * 10-7 m) / 0.028 m = 4.2 * 10-5 m Then value of atheo and aexpt were compared. They were atheo = 4.0 * 10-5 m and aexpt = 4.2 * 10-5 m, which were very small difference. D. Interference: the Double Slit Like the single slit experiment, of the laser was given: 632.8nm. From the slide, d theo was obtained, which was 0.250mm. The value of L remained the same, and y was 7 measured to be 2.7 mm using the first order. Again, using the formula = dy/mL, dexpt was calculated. [Calculation] dtheo = 0.250mm * 1m / 1000mm = 2.5 * 10-4 m = 632.8nm * 1m / 109nm = 6.32 * 10-7 m y = 2.7 mm * 1m / 1000mm = 0.0027 m L = 94 cm * 1m /100 cm =0.94 m = dy/mL dexpt = mL / y = (1 * 0.94m * 6.32 * 10-7 m) / 0.0027 m = 2.2 * 10-4 m The value of dtheo (2.5 * 10-4 m) and dexpt (2.2 * 10-4 m) were compared, and they turned out to be having a very small difference as well. E. The Diffraction Grating For this experiment, d was given on the grating: 3.3 * 10 -4 m. To compute the wavelength , L and y was measured. Then, using the formulas, tan = y/2L, = dsin / m, and the small angle approximation, were calculated for both 1 st and 2nd order. [Calculation] d (given) = 3.3 * 10-4 m ym=1 = 188 mm * 1m / 1000mm = 0.188 m ym=2 = 418 mm * 1m / 1000mm = 0.418 m L = 94 cm * 1m /100 cm =0.94 m 8 <1st order> tan = ym=1 /2L =0.188 m/ (2 * 0.94m) =0.1 tan =sin (small angle approximation) = dsin/m m=1 = (3.3 * 10-4 m * 0.1) / 1 = 3.3 * 10-5 m <2nd order> tan = ym=2 /2L =0.418 m/ (2 * 0.94m) =0.22 tan =sin (small angle approximation) = dsin/m m=2 = (3.3 * 10-4 m * 0.22) / 2 = 3.6 * 10-5 m Again, the wavelength of the first order and the second order were only off by a very small number. This shows that the wavelength of the laser did change but by the same amount when it went through the grating. F. The Hologram In this experiment, I observed 3D image of a telephone. At first, I thought the information was coming from the laser, but it turned out I was wrong. The image was actually coming from the lens. Based on the observations and calculations of the diffraction of light, I could prove that light is has a wave property. All the calculation using the formulas of wave fit almost perfectly into the experiments with very small percent errors.

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