Question on special relativity derivation

[prajor]

This might be silly or a gap in understading, pl. help. In the classic derivation of special relativity - Lorentz transformations we see the diagram (say from HRW )


Frame S' (moving with velocity v in direction x w.r.t S)

http://en.wikipedia.org/wiki/File:Time-dilation-001.svg
Frame S

http://en.wikipedia.org/wiki/File:Time-dilation-002.svg

1. Derivation is based on postulate that speed of light is constant in any direction and is not affected by the speed of the source or the observer. Now, isnt it true that in the second diagram (frame S) we have just constructed D with angle Theta - which means the light is affected by the moving source when looked at from frame S ?

2. If starting event was a emission of a single photon in Y direction, (and light is not affected as the postulate says ) would it reach the mirror ?

What is wrong in the arguments ? pl. help.

[sravanskarri]

You can think of it this way, light takes a little more time to reach the mirror when the observer sees it in REF frame S as S' is moving w.r.t S since the velocity of the light as assumed, cannot change in S, leading to the time dilation. Thait is the motion of Ref frame S' to is actually causing the target ( mirror) to move a little bit to the right while c remains constant.

Is that what you are asking ?

[prajor]

You can think of it this way, light takes a little more time to reach the mirror when the observer sees it in REF frame S as S' is moving w.r.t S since the velocity of the light as assumed, cannot change in S, leading to the time dilation. Thait is the motion of Ref frame S' to is actually causing the target ( mirror) to move a little bit to the right while c remains constant.

Is that what you are asking ?

Not really, my question is why should we give a horizontal component to the speed of light (perpendicular to its direction) while we are not giving any in the direction of propagation.

[sravanskarri]

Oh i see, Light is an electomagnetic wave in which energy propagates along the direction of propagation...and speed of light is the speed at which the energy propagates so it should not be treated as a vector.

[prajor]

Well, poynting vector just does that.

anyway, how do we answer that from the second question perspective :

2. If starting event was a emission of a single photon in Y direction, (and light is not affected as the postulate says ) would it reach the mirror ?

[sravanskarri]

>>Well, poynting vector just does that.
so what, postulate talks about spped of light and not Poynting vector.