Derive Phase difference between clocks with distance

1. The problem statement, all variables and given/known data



Derive Phase difference between clocks with distance



2. Relevant equations



I honestly don't understand how this equation ΔT = vD/c² is derived/figured out.



3. The attempt at a solution



We haven't covered Lorentz Transformations yet so is there a way to explain this to me without using it? I understand the concept of simultaneity, time dilation, and length contraction. This problem deals with the first two. The situation is a rectangular box with two detectors on either end marked with the left as A and the right as B. The box is centered along vertical axis where a flash of light in the center of the box flashes, and the light moves towards left and right towards the detectors. Now the box is moving at a constant velocity to the right.



A picture is attached because it's hard to explain. L is the length of the box, D is the distance between panel 2 and panel 3. T_r is the time it takes for the light to travel to the left detector (Event 1) and T_f is the time it takes for the light to travel to the right detector (Event 2).



I have equations from panel 1 to panel 2: cT_r = L/2 - vT_r

And from panel 1 to 3: cT_f = L/2 + vT_f



I just don't understand how to get to the phase difference between them with these equations.