# Reflection Propagation Law of Electromagnetic Waves in U-Shaped Roadway
## 3 U-Shaped Roadway Model and Reflection Path Validity
### Reflection Path Validity
#### 3.2.2 Five-Time Valid Reflection Paths  
Figure 7 shows the two-dimensional five-time valid reflection paths, where the combination of points T to P as a secondary reflection and points P to R as a tertiary reflection are used as an example.  
Figure 6: Two-dimensional diagram of four-time valid reflection paths.  
* The emitting point T is first mirrored with respect to plane \(m_{1}\) to obtain the first mirror point I\({}_{1}\).
* Set I\({}_{1}\) as the base point; T is mirrored in plane \(m_{2}\) to obtain the second mirror point I\({}_{12}\), which is connected to point P.
* The intersection of plane \(m_{2}\) is B\({}_{12}\); point B\({}_{12}\) is then connected to point I\({}_{1}\), and the intersection of plane \(m_{1}\) is B\({}_{1}\).
* By connecting the points T, B\({}_{1}\), and B\({}_{12}\) sequentially, a secondary valid reflection path was formed.
* Mirror relay node \(P\) with respect to plane \(m_{5}\) for one level and obtain the first-level mirror point I\({}_{5}\).
* Set I\({}_{5}\) as the base point, mirror it on plane \(m_{2}\) for two levels, and obtain the second-level mirror point I\({}_{52}\).
* I\({}_{52}\) is then used as the base point, mirroring it in plane \(m_{3}\) for three levels and obtaining the third-level mirror point I\({}_{523}\); connect point I\({}_{523}\) with point \(R\).
* The point of intersection in plane \(m_{3}\) is B\({}_{523}\); connect the point B\({}_{523}\) with to point I\({}_{52}\).
* Finally, connect the point B\({}_{52}\) with point I\({}_{5}\), and the intersection in plane \(m_{5}\) is B\({}_{5}\).
* Points B\({}_{523}\) and I\({}_{52}\) are connected to the point of intersection B\({}_{52}\) in the plane \(m_{2}\).
* Finally, B\({}_{52}\) and I\({}_{5}\) are connected in plane \(m_{5}\) intersection for B\({}_{5}\); sequentially connected points P, B\({}_{5}\), B\({}_{52}\), B\({}_{523}\), and R form a tertiary valid reflection path.  
From the above, it can be seen that the transmitting point T to relay node \(P\) theoretically has 30 secondary mirror points, that is, 30 reflection lines, and the relay node \(P\) to receiving point \(R\) theoretically has 150 tertiary mirror points, that is, 150 reflection lines. Therefore, there are 180 mirror points and 4500 reflection lines in this combination. Similarly, when the combination of the transmitting point T to relay node \(P\) is a tertiary reflection and the relay node \(P\) to receiving point \(R\) is a secondary reflection, there are theoretically 180 mirror points and 4500 reflection lines. For the combination where there is one reflection from the transmitting point T to the relay node \(P\) and four reflections from the relay node \(P\) to the receiving point \(R\), and the combination where there are four reflections from the transmitting point T to the relay node \(P\) and one reflection from the relay node \(P\) to the receiving point \(R\).  
Figure 7: Two-dimensional diagram of five-time valid reflection paths.  
the receiving point \(R\), there are theoretically 756 mirror points and 4500 reflection lines. Therefore, all combinations of the five-time reflection paths theoretically have a total of 1872 mirror points and 18,000 reflection lines.