In the following situation there is a train with an uniform movement and velocity v2. There are two observers. One of them is inside the train and the second one is outside the train. Suddenly a bulb is lighted inside the train and its lights go down. The green observer will see that the light arrives to the lower part of the window in the point A in t1, whereas the blue observer will see that the light touches the lower part of the window in the point B in t2. So the light travels a larger distance for the blue observer. The segment AB is the distance travelled by the train between the instants t1 and t2.
Applying the Pitagoras Theorem:
According to the second postulate of the special relativity, each observer must measure the same velocity of light, so c=c1=c2
This result is known as Lorentz transformation for time when one observer is at rest (there are another equations for the spatial coordinates).
For example, if the velocity of the train were half of speed of light, t2 would be 1.15 times t1, so time pass slower for the green observer. In fact, for the green observer the light travels a distance shorter than for the blue observer, so his time will have to pass slower in order to the velocity of light is the same for the two observers. This phenomenon is called time contraction.