Is the Distance Traveled by Light Affected by Time Dilation?

[cragar]

When you derive the time dilation equation, and you see the light move straight down in one frame and in the other frame you see it move on a diagonal because the object is moving.
My question is in the moving frame when you use the horizontal distance to derive the distance that the light travels using Pythagorean theorem. It seems that the horizontal distance would be length contracted , or unless the ruler used to measure that distance is also length contracted. But isn't the length contraction formula derived using time dilation?

 

[Doc Al]

In the light clock thought experiment, which is what I assume you are talking about, the horizontal distance is the distance the light clock traveled as measured by the other frame. No length contraction needed.

 

[cragar]

yes I am talking about the light clock, okay so it would be the observed distance traveled in the other frame, so you I guess it wouldn't matter.
thanks for your answer