![]() The experimental result was found that the linear coefficient of thermal expansion of aluminium is 22.512 × 10 -6 (C°) -1, giving a 2.545 % error. The value of the linear coefficient of thermal expansion of the material can then be calculated using the principle knowledge of diffraction equation and thermal expansion. A He-Ne laser with a wavelength of 632.8 nm was used to obtain a diffraction pattern for the single slit. For both the single slit(S.S.) and double slit(D.S.) experiment similar equations are used, d sin() n. The increase in the slit width, hence the linear expansion, can be determined by measuring the fringe width. The design of the apparatus for this method allows for the width of a single slit to increase by the same amount as the thermal expansion of a length of a strip or a rod of a material. In this work, we made an effort to determine linear coefficient of thermal expansion of metal using single-slit diffraction. Thermal expansion coefficient, single-slit diffraction, aluminium Abstract So I took the amplitude function (for the. and on approximating: r D + 1 2 D ( x + l) 2. where r is the distance between the point of origin on the slit and point of contact on the screen (and k is the angular wave-number). As seen in the figure, the difference in path length for rays from either side of the slit is D sin, and we see that a destructive minimum is obtained when this distance is an integral multiple of the wavelength.Department of Physics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangmod, Bangkok 10140, Thailand. The amplitude for a wave originating from a point on the slit should be: y a sin k r. Finally, in part (d), the angle shown is large enough to produce a second minimum. Lets assume that the slit is constant width and very tall compared. However, not all rays interfere constructively for this situation, so the maximum is not as intense as the central maximum. The sketch shows the view from above a single slit. Most rays from the slit have another ray to interfere with constructively, and a maximum in intensity occurs at this angle. Two rays, each from slightly above those two, also add constructively. One ray travels a distance different from the ray from the bottom and arrives in phase, interfering constructively. Īt the larger angle shown in part (c), the path lengths differ by for rays from the top and bottom of the slit. The difference in path length for rays from either side of the slit is seen to be D sin. Light passing through a single slit is diffracted in all directions and may interfere constructively or destructively, depending on the angle. By symmetry, another minimum occurs at the same angle to the right of the incident direction (toward the bottom of the figure) of the light. In other words, a pair-wise cancellation of all rays results in a dark minimum in intensity at this angle. In fact, each ray from the slit interferes destructively with another ray. A ray from slightly above the center and one from slightly above the bottom also cancel one another. Thus, a ray from the center travels a distance less than the one at the bottom edge of the slit, arrives out of phase, and interferes destructively. In part (b), the ray from the bottom travels a distance of one wavelength farther than the ray from the top. However, when rays travel at an angle relative to the original direction of the beam, each ray travels a different distance to a common location, and they can arrive in or out of phase. When they travel straight ahead, as in part (a) of the figure, they remain in phase, and we observe a central maximum. (Each ray is perpendicular to the wave front of a wavelet.) Assuming the screen is very far away compared with the size of the slit, rays heading toward a common destination are nearly parallel. Knowing the wavelength of the laser light, the equation (3) can be used to determine the. ![]() These are like rays that start out in phase and head in all directions. the minima of a single-slit diffraction pattern are. According to Huygens’s principle, every part of the wave front in the slit emits wavelets, as we discussed in The Nature of Light. ![]() We then consider light propagating onwards from different parts of the same slit. Here, the light arrives at the slit, illuminating it uniformly and is in phase across its width. The analysis of single-slit diffraction is illustrated in (Figure). (b) The diagram shows the bright central maximum, and the dimmer and thinner maxima on either side. The central maximum is six times higher than shown. This is an approximate description of an actual slit of. (a) Monochromatic light passing through a single slit has a central maximum and many smaller and dimmer maxima on either side. General considerations Following Giancoli, section 35-2 (and quoting some of the text), we consider the single slit divided up into N very thin strips of width y as indicated in the gure below.
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