Physics NYC Report7

Lab 7 - Light Emitting Diode (LED) Experiment Physics NYC: Waves, Optics and Modern Physics Hubert Camirand April 9 th , 2021 Analysis: 1.) Table 1: Recorded and Calculated Results of Diodes at L Distance 0.092 m. d (m) = 0.000001 L (m) = 0.092 Diode Colour Order, m Position, x (m) d*x m*sqrt(x^2+L^2) Wavelength, λ (m) Purple 1 0.046 4.60E-08 1.03E-01 4.47E-07 Blue 0.0535 5.35E-08 1.06E-01 5.05E-07 Green 0.061 6.10E-08 1.10E-01 5.55E-07 Yellow 0.071 7.10E-08 1.16E-01 6.12E-07 Red 0.082 8.20E-08 1.23E-01 6.67E-07 Purple -1 -0.044 -4.40E-08 -1.02E-01 4.31E-07 Blue -0.0565 -5.65E-08 -1.08E-01 5.23E-07 Green -0.064 -6.40E-08 -1.12E-01 5.71E-07 Yellow -0.073 -7.30E-08 -1.17E-01 6.24E-07 Red -0.0875 -8.75E-08 -1.27E-01 6.89E-07 Figure 1: Spectral Image of 1000 lines per mm diffraction grating at a distance of 0.092 m from the wall.

Figure 2: Relationship of the wavelength of the 1000 line per mm diffraction grating at a distance of 0.092 m from the wall. Table 2: Recorded and Calculated Results of Diodes at L Distance 0.104 m. d (m)= 0.000001 L (m)= 0.104 Diode Colour Order, m Position, x (m) d*x m*sqrt(x^2+L^2) Wavelength, λ (m) Purple 1 0.051 5.10E-08 1.16E-01 4.40E-07 Blue 0.057 5.70E-08 1.19E-01 4.79E-07 Green 0.0685 6.85E-08 1.25E-01 5.48E-07 Yellow 0.0785 7.85E-08 1.30E-01 6.04E-07 Red 0.089 8.90E-08 1.37E-01 6.50E-07 Purple -1 -0.0495 -4.95E-08 -1.15E-01 4.30E-07 Blue -0.058 -5.80E-08 -1.19E-01 4.87E-07 Green -0.071 -7.10E-08 -1.26E-01 5.63E-07 Yellow -0.082 -8.20E-08 -1.32E-01 6.21E-07 Red -0.09 -9.00E-08 -1.38E-01 6.52E-07

Blue -0.0635 -6.35E-08 -1.32E-01 4.81E-07 Green -0.075 -7.50E-08 -1.38E-01 5.43E-07 Yellow -0.086 -8.60E-08 -1.44E-01 5.97E-07 Red -0.101 -1.01E-07 -1.54E-01 6.56E-07 Figure 5: Spectral Image of 1000 lines per mm diffraction grating at a distance of 0.116 m from the wall. Figure 6: Relationship of the wavelength of the 1000 line per mm diffraction grating at a distance of 0.116 m from the wall.

Table 3: Recorded and Calculated Results of Diodes at L Distance 0.128 m. d= 0.000001 L= 0.128 Diode Colour Order, m Position, x (m) d*x m*sqrt(x^2+L^2) Wavelength, λ (m) Purple 1 0.061 6.10E-08 1.28E-01 4.77E-07 Blue 0.071 7.10E-08 1.28E-01 5.55E-07 Green 0.0815 8.15E-08 1.28E-01 6.37E-07 Yellow 0.093 9.30E-08 1.28E-01 7.27E-07 Red 0.107 1.07E-07 1.28E-01 8.36E-07 Purple -1 -0.056 -5.60E-08 -1.28E-01 4.38E-07 Blue -0.066 -6.60E-08 -1.28E-01 5.16E-07 Green -0.0775 -7.75E-08 -1.28E-01 6.05E-07 Yellow -0.091 -9.10E-08 -1.28E-01 7.11E-07 Red -0.1055 -1.06E-07 -1.28E-01 8.28E-07 Figure 7: Spectral Image of 1000 lines per mm diffraction grating at a distance of 0.128 m from the wall.

3.) Given the equation , the angular position can be found as . Therefore, ??𝑖?θ = ?λ ?𝑖?θ = ?λ ? taking the third distance L as 0.116 m and the calculated wavelengths then the angular positions of each colour diode are represented in the table below. Table 5: Angular Position Predictions of 500 lines/mm grating. Diode Colour Order, m Wavelength, λ (m) Angular Position, θ (rad) Purple 1 4.46E-07 2.23E-01 Blue 4.96E-07 2.48E-01 Green 5.47E-07 2.74E-01 Yellow 6.03E-07 3.02E-01 Red 6.60E-07 3.30E-01 Purple -1 4.14E-07 -2.07E-01 Blue 4.81E-07 -2.41E-01 Green 5.43E-07 -2.72E-01 Yellow 5.97E-07 -2.99E-01 Red 6.56E-07 -3.28E-01 Figure 9: Spectral Image of 500 lines per mm diffraction grating at a distance of 0.116 m from the wall.

Table 6: Experimental Results of Angular Positions of 500 lines/mm grating. Diode Colour Position, x (mm) L (mm) d*x m*sqrt(x^2+L^2) Wavelength, λ (m) Angular Position (rad) Purple 31 1.16E+02 6.20E-05 1.20E+02 5.16E-07 2.58E-01 Blue 33.5 d (m) 6.70E-05 1.21E+02 5.55E-07 2.77E-01 Green 34.5 2.00E-06 6.90E-05 1.21E+02 5.70E-07 2.85E-01 Yellow 38.5 7.70E-05 1.22E+02 6.30E-07 3.15E-01 Red 42 8.40E-05 1.23E+02 6.81E-07 3.40E-01 Purple -26 -5.20E-05 -1.19E+02 4.37E-07 -2.19E-01 Blue -29 -5.80E-05 -1.20E+02 4.85E-07 -2.43E-01 Green -34.5 -6.90E-05 -1.21E+02 5.70E-07 -2.85E-01 Yellow -38 -7.60E-05 -1.22E+02 6.23E-07 -3.11E-01 Red -41.5 -8.30E-05 -1.23E+02 6.74E-07 -3.37E-01 To verify the prediction of the angular position in Table 5 the results are compared to the experimental values found in Table 6 by calculating the percent error between the values. The percent error is found by the equation . So the percent %????? = ?𝑥???𝑖????𝑎?−?𝑥?????? ?𝑥?????? | | | | * 100 errors found were as follows: Percent Errors 15.77622412 11.8769014 4.231393242 4.477687492 3.163964729 5.657708656 0.8464137365 4.999211976 4.290830753 2.698334874