Every color on the visible light spectrum has a distinct wavelength. These wavelengths can be measured by using the diffraction pattern of the light. In this experiment we used a HeNe laser and a green laser pointer with known wavelengths of 632.8x10-9m and 532.0x10-9m respectively. We aimed the lasers at a slight angle from horizontal onto a precision steel ruler with 0.5x10-3m and 1.0x10-3m rulings. When the laser is incident on the rulings, it reflects onto a surface showing the diffraction pattern. After measuring the spacing between each bright spot, we calculated the wavelength for each ruling used for the HeNe laser and for the green laser pointer. The ...view middle of the document...
The ruler was then moved out of the path of the laser giving us a value for –y0. Half the distance between the y0 and –y0 gave us the zero point on the y axis. The angle between zero and y0 was α and the angles between each zero and yn was βn.
III. Results and Analysis
Using a nonlinear curve fit allowed us to determine a more accurate wavelength of both the HeNe laser and the green laser pointer. To determine the wavelength of the laser:
nλ=d(cos(α)-sin(β_n )) (1)
y_n^2=1/(1/√(x_0^2 〖+y〗_0^2 )-nλ/(dx_0 ))^2 -x_0^2 (2)
To determine the absolute error for yn:
(σ_(y_n )/y_n )^2=2×σ_(y_n )/y_n (3)
σ_(y_n )=2×σ_(y_n )× y_n (4)
When taking the measurements, there was an error associated to each yn measurement. The ruler used to measure Δyn has an error of ±2.0x10-4m. Determining the brightest spot of the laser for each yn had an error of 3.0x10-3m (for both lasers), along with a smaller error of
8.0x10-4m due to the pen markings for each bright spot. The error associated to each yn measurement was 4.0x10-3m. Since the ruler was a precision (machined) steel ruler the error was negligible and x0 was extremely large compared to its error, this allowed us to use d and x0 as a fixed value in our nonlinear fit.
The two sets of data collected using the HeNe laser, used two different spacing’s between rulings that are being analyzed, while all the other parameters were constant. These values were d=0.50x10-3m, 1.0x10-3m, x0=5.69 m±1.00x10-2m,...