## 4 Experiment Process
### Data Recording  
To minimize measurement errors when determining the minimum diffraction angle for green light [25], the following method is employed. Setting the Reference Point. Use the normal to the grating as a reference. When the incident light and diffracted light are on the same side of this reference, proceed to the next steps. Finding +1 Order Diffraction. Release and rotate the specimen stage until the +1 order green light diffraction angle is minimized. Fix the stage in this position and measure the coordinate of the +1 order green light spectrum angle at this point. Finding \(-1\) Order Diffraction. Release and rotate the specimen stage again, this time aligning the normal to the grating plane near the symmetrical position. Locate the position where the \(-1\) order green light diffraction angle is minimized. Fix the stage and record the coordinate of the \(-1\) order green light spectrum angle. Calculating Minimum Diffraction Angle. Calculate the minimum diffraction angle \(\varphi_{\text{min}}\) and the corresponding incident angle \(i_{\text{min}}\) for green light. Determine the grating constant \(d\) using the measured angles, As shown in Table 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(K\) = 1 Spectral Coordinates & \(K\) = \(-1\) Spectral Coordinates & \(\varphi_{\text{min}}\) & \(i_{\text{min}}\) \\ \hline
**Left \(\theta_{1}\)** & **Right \(\theta_{1}^{{}^{\prime}}\)** & **Left \(\theta_{-1}\)** & **Right \(\theta_{-1}^{{}^{\prime}}\)** & \\ \hline
284\({}^{\circ}\)56\({}^{\prime}\) & \(104^{\circ}\)56\({}^{\prime}\) & 322\({}^{\circ}\)37\({}^{\prime}\) & 142\({}^{\circ}\)38\({}^{\prime}\) & 18\({}^{\circ}\)51\({}^{\prime}\) & 9\({}^{\circ}\)25\({}^{\prime}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measurement of minimum deflection angle. Minimum diffraction angle  
\[\varphi_{\min}=\frac{1}{4}\big{(}|\theta_{1}-\theta_{-1}|+|\theta_{1}^{\prime}- \theta_{-1}^{\prime}|\big{)} \tag{5}\]  
Incident angle corresponding to the minimum deflection angle  
\[i_{\min}=\frac{\varphi_{\min}}{2} \tag{6}\]  
The formula includes the following parameters. \(\varphi_{min}\): minimum diffraction angle for green light. \(i_{min}\): incident angle corresponding to the minimum deviation angle. \(k\): order of the bright fringe (spectral line). \(\theta_{1}\): angle of the left cursor for the 1 st diffraction order of green light. \(\theta_{1}^{\prime}\): angle of the right cursor for the 1 st diffraction order of green light. \(\theta_{-1}\): angle of the left cursor for the \(-\)1 st diffraction order of green light. \(\theta_{-1}^{\prime}\): angle of the right cursor for the \(-\)1 st diffraction order of green light. Next, measuring the diffraction angles at different incident angles involves a sequence of steps [26]. Begin by rotating the telescope to align the central bright fringe with the vertical crosshair. Lock the telescope in place and release the stage's locking screw, allowing it to rotate until the green crosshair aligns vertically with the central bright fringe. Secure the stage and record the angle coordinates of the central bright fringe. Fix the telescope, release the stop screw of the graduated disc, and rotate the disc to introduce an angle \(i\) between the incident light and the normal. Lock the disc in place and read the angle coordinates of the central bright fringe. Finally, release the telescope and measure the angle coordinates of the \(\pm 1\) order green light. Finally, obtain \(\overline{\varphi_{+  
The formula includes the following variables. \(i(n)\): incidence angle with index \(n\). \(\theta_{0}(n)\): left cursor degree of the 0 th order diffraction of green light with index \(n\). \(\theta_{0}^{\prime}(n)\): right cursor degree of the 0 th order diffraction of green light with index \(n\). \(\theta_{1}(n)\): left cursor degree of the 1 st order diffraction of green light with index \(n\). \(\theta_{1}^{\prime}(n)\): right cursor degree of the 1 st order diffraction of green light with index \(n\).