## 3 Results  
With the selected algorithm, we study the distribution of the length of the tracks recorded on smartphone photos stored in the CREDO database, in order to determine whether it is consistent with the zenith angle distribution of the muon (\(\sim\)\(\cos^{2}(\Theta)\)). The degree of the expected accordance will show the confidence of using the smartphone cameras as cosmic particle detectors. We start detailed studies with the distribution of the track length as it is shown as the histogram in Figure 4.  
Figure 3: The observed distribution of \(\cos(\Theta)\) for camera sensitive layer depth \(h\) equal to 5 px for different track length determination procedures: (**a–f**) (see text for detaied explanation for subfigures). The dotted line represents the expected dependency of the form \(\cos^{2}(\Theta)\). Predictions assuming that we are dealing with the cosmic ray muons with the known zenith angle distribution are also shown. These distributions differ for different values of the camera photosensitive layer thickness \(h\). The thickness of the particular camera we used in this work is not known precisely, leaving the value of \(h\) to some extent a free parameter which can be constrained by the data itself. We present here results for 3 px, 5 px, 10 px, and 15 px and the predictions of the best fitted value of \(h\). Details of the fitting procedure are given below. In Figure 4, we see that the measured distribution is close to the predictions for a width (\(h\)) close to 5 px. However, it can be seen that this agreement is not perfect at both long track lengths, as well as for very short lengths. Regardless, the distribution of track length presented in Figure 4 can be converted to the zenith angle distribution (assuming we have captured cosmic ray particle traces). Zenith angle distribution is more suitable for studying cases of small angles (short trace lengths). In Figure 5, we present the comparison between the predictions obtained using different values of \(h\). The length of the track determined with the algorithm described above, if expressed in single pixel size (px), is, by definition, an integer number. For small values of \(h\), which are expected in modern smartphone cameras, the measured zenith angle, given by Equation (1), would have to be discrete numbers. The resolution for small angles, at which most particles arrive at, is very limited. For larger angles, longer tracks, where the resolution of a determined angle is superior, the flux is substantially smaller, thus the simple zenith angle is not the best variable to study. However, Figure 5 also suggests that for small angles, where most of the events occur, the matrix sensitive layer thickness is close to 5 px. While the short track discrepancy may be due to the measurement uncertainty, the discrepancy for large \(l\) values can be mitigated by selecting an appropriate value for the photosensitive layer thickness \(h\). The \(\chi^{2}\) minimization procedure was used on the \(\cos(\Theta)\) distribution shown in Figure 6 where results are obtained for different assumptions about the thickness of the photosensi  
Figure 4: Measured track length distribution. Lines are shown for comparison with the predictions calculated for various values of smartphone camera matrix sensitive layer thickness (\(h\)) measured using individual pixel size (px): 3 px—dotted line, 5 px—thin continuous line, 10 px—dashed line, and 15 px—dot-dashed line. The thick solid line represents the result of our best fitted \(h\) (details in the text). On the abscissa, the value of the trace length measured, again, in the pixels size (px) is shown. All distributions are normalized at one point (\(l=5\) px). tive layer parameter \(h\). We have compared it with the expected power-law spectrum with a slope corresponding to the distribution of cosmic ray muons. This slope is given by the thick line in Figure 6.  
The distribution of the variable \(\cos(\Theta)\) illustrates very nicely the behavior of the long and very long (about horizontal) tracks.