When slits are used, the laser superposes itself and creates constructive interference. The resulting spots are measured to give data that allows one to find the wavelength using the equation λm = dais θ. These diffraction and interference with such slits was successful because of low percent errors in the wavelengths calculated. Additionally, a diffraction gradient creates better-defined spots, and more accurate measurements, yielding the lowest uncertainties. A. Diffraction by a Straight Edge Using the slide marked “straight edge/opaque disks,” a laser is positioned so that it falls on the edge.
The light does go into the shadow region, it bends around the edge and spreads out into the shadow region. The picture below shows what happens when the laser beam falls on a straight edge. B. Superposition of Waves and Diffraction by a Disk A mm focal length lens and opaque disk slide are used to observe superposition and the diffraction patterns. Due to symmetry, all waves that arrive from the edge of the disk at the same point on the axis will be in phase, causing a bright spot on the center of the pattern. The first disk used created concentric circles of bright light. The next disk produced a dark circle in the enter.
The pictures below show the patterns of diffraction. C. Diffraction by a Narrow Slit The slide with several narrow slits is placed in the holder, and this causes diffraction fringes. These fringes are caused by the interference of wavelets from the various areas of the slit. An equation relating the first dark band to the wavelength and angular position is given by Asianθ = λ. The width of the slit is marked on the disk, and represents the a value. The value of L is kept at mm throughout the experiment to maintain consistency, and w is the width between the central peaks. See the diagram below.
The angle θ is given by the equation = w/AL. The known value of the wavelength is 632. NM. The experimental value for the wavelength is 559. NM, which has a percent error of approximately 1 1. 5%. There are however some uncertainties in the experiment that may account for this error. When measuring the value for L, object may move or the edge of the meter stick could yield an inaccurate reading, which accounts for about +1-0. Mm of error. Also, the value of w may be slightly off because oaf worn ruler, or difficulties in measuring the distance of peaks on the wall without blocking the easer beam.
The measurement was also supposed to be horizontal, which is hard to maintain, so this may attribute +1-0. Mm of error. W = 0. CACM L = 1. Mm a= 0. NM= E-mm Tan = w/AL Tan-I = 559. NM Using the known value of the wavelength, one may also calculate the value for a. This value is compared to the given actual value of E-5 and has an error of about 13%. Again, this is accounted for by the uncertainties in the values of w and L. = 632. NM/sin(O. 401) = 9. EYE 05 D. Interference: The Double Slit This part of the experiment uses two slits, and a laser goes through both of hem, allowing them to superpose and interfere with one another.
When the two beams are in phase, a bright dot is created on the wall, called constructive interference. The equation used is dais θ= m λ for all orders of m. Because there are several bands in this section, one must remember that tan θ= (Y/5) x (I/L). The diagram below shows how the constructive interference is created. The L for this part is 1. Mm, and there is about +1-0. Mm of uncertainty, as there was in the previous part, due to objects being moved slightly, or a meter stick that is worn at the end. The Y value for this part, the distance between two bright bands, may be off by about +1-0. CM due to the difficulty in measuring a horizontal distance on the wall without interrupting the laser beam. 1. Mm Y- 0. Mm d- 0. NM- 2. Mm = dais Tan Y/AL = 699. NM Tan-1= (0. 014/5) = (run=l) When the experimental value of the wavelength is compared to the actual value, there is a percent error of about 10. 6%. This may be due to the uncertainties in the values of Y or L. The error may also be due to not measuring the value of Y entirely, because it is difficult to see the difference between where the light egging ends, its actually past where one may have measured.
Therefore, the uncertainty of Y may be greater then earlier mentioned and a more reasonable value would be +/- 0. Mm. E. The Diffraction Grating The diffraction grating of this part allows for a more accurate measurement of the spacing between the bright spots. The procedure is similar to the previous section, with the value for θ being tan θ= Y/AL. There is also two measurements taken, for the first order (m=l) and the second order (m=2). The table below summarizes the data for both orders. M=l m=2 L 1. Mm 1. Mm YOU. Mm 0. Mm 11. 31 30. 47 Experimental 647. NM 836. NM Percent Error 2. 32. % As with the previous sections, there is an uncertainty of about +1- 0. Mommy the value of L, due to objects moving or a worn meter stick. In addition, Y has an uncertainty of about +1- 0. Mother uncertainty is smaller than in previous sections because the diffraction grating is better defined and easier to get an accurate measurement. This is reflected in the low percent error. Conclusion The lab was successful in investigating the ability of light to act as a wave in the form of interference. It was interesting to see how light bends around a straight edge, allowing light to enter an area of shadow.
Superposition was also examined, as one is able to see how waves add together to form resultant waves. Disks are able to diffract the light into various patterns of brightness, because they superpose the light differently. Perhaps using a few more different disks in future experiments would be interesting. Diffraction of a narrow slit yields fairly good results in determining either the wavelength or slit width, depending on the data available. The equation Asian#952; = λ relates the data and is an easy ay to calculate either value.