Real derivation for time dilation. This is how time dilation was presented to me at the university. It's taken straight from the text book. The problem is that the derivation includes the lines "Mavis measures", and "Stanley measures." Well, neither Mavis nor Stanley has the means to make a measurement regarding the light in the model. I'm sure this is just an oversight. Can you augment the model to make the derivation logical. Pic related is my annotations and the derivation is at the link pages 7 and 8.

https://www.sydney.edu.au/science/physics/pdfs/schools_community/Special-Relativity-STW2014.pdf