![]() Order of magnitude of the known value (1☐) × 10-6 m. The groove spacing of the CD was found to be (1☐) × 10-6 m, which is consistent with the The error was again calculated using fractional errors with the equation, ∆d=√¿ ¿ ¿ , d for the unknown diffraction grating is Using this value in the rearranged equationd= nλ sinθ Taking an average from these two results (6☐) ×10-7 m was determined to be the best estimateįor the wavelength of the laser beam. Standard error wasn’t representative of a larger data set, were the standard error would have been This was probably a result of the initial measurement being very consistent, so the ![]() The large standard error on the mean at higher values of n which is perpetuated into the error in dsinθ.Ĭonversely, the chi squared value for the fit of 08543 was 4, suggesting the errors were Showing the data does not have a good fit and that the errors were overestimated. Underestimation in the errors as shown by the chi squared value discussed below.įrom the graph, the gradient can be used to determine a value for the wavelength. It is worth noting that the error bars on figure 2 are present but may not be visible, this is due to an The error on dsinθ was calculated using fractional errors in quadrature ∆dsinθ= √ (∆sinθ sinθ ) From the equationnλ=dsinθ, a graph can be plotted for the first two diffraction gratings in order to find the wavelength of the laser using λ= dsinθ n. ![]() The errors were calculated using the standard error on the mean. The value for the slit separation on grating 08540 was (9☐) х 10-5 m and the slit separation forĠ8543 was (1☐) х 10-5 m. If this time constraint was eliminated in a repeatĮxperiment, the statistical error on the value for the CD grating would be significantly reduced. Time was a large limitation in this experiment and restricted the number of measurements that wereĪble to be taken, especially regarding the CD. Involved a large degree of human error as the definition of the diffraction pattern was difficult to read. In the x direction and along the grooves where information is stored. Marking the maxima with a pencil mark before measurements were taken.įinally, we used the same method to then determine the slit separation between grooves in a CD both Of human error was introduced that was not accounted for. The measurement was taken directly off the screen, so a degree To determine the value of the slit separation for the unknown grating, the distance between the gratingĪnd the screen was varied and the distance between the first order maxima recorded at each point,Īgain with two more repeat readings. This method was repeated for gratingĠ8543, considering the different value for d, the distance between slits. For small angles tan that is equal to sin theta. Values for x and l, which then could be used to find a value for the wavelength by plotting a graph of nĪgainst dsinθ. Dividing each measurement by 2 gave a value for x and an average was taken.īoth these steps were taken to reduce the statistical error. Using a Vernier calliper, a measurement between eachįirst order maxima was recorded three times and repeated for each order of maxima that could be A note of the distanceīetween the grating and the screen was taken. To determine the wavelength of the laser, by clamping the first grating in front of the laser so that aĭiffraction pattern caused by superposition was displayed on the screen behind. Using the two known values of the diffraction gratings for 0856, a procedure was set up It was determined that a measurement for the third grating could not be taken as Track pitch can then be found for any unknown diffraction grating, in this case, a CD.įirst the value for the distance between slits in three unknown diffraction gratings, 08540, 08543 andĠ8546, were measured using a travelling microscope, taking an average of distance d from three The waves emitted by the laser undergo superposition at increments of nλ. The value of the de Broglie wavelength of a laser can be found by shining the beam through aĭiffraction grating with a known slit spacing by measuring the distance between maxima lines where From this the best estimate for the track pitch of the CD The wavelength of the laser beam was (6☐) ×10-7 m, and the The experiment undergone was an attempt to determine the track pitch of a CD and its separationīetween storage grooves by first determining the wavelength of a laser beam and the value for the We can solve for \(y_V\) and \(y_R\).Investigating laser diffraction with applications to CD disks
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