I'm a little confused on this. If you're travelling at, say, 10% of the speed of light then light is travelling at 3x10^8 ms^(-1) relative to you. If you're moving at 80% of the speed of light and light is also travelling at 3x10^8 ms^(-1). For the second case, wouldnt light have to accelerate and move at a greater velocity in order to maintain the 3x10^8 ms^(-1) speed...? Then that means the actual speed of light relative to a stationary observer would be greater than 3x10^8 ms^(-1) . I might have confused myself even more here...

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    $\begingroup$ It's not a bad thing to be confused at first by this since, essentially, everyone is initially confused by this. However, this very well might be the most frequently asked question of all the frequently asked questions about special relativity. In other words, please take the time to do just a bit more research on this most frequently asked question. $\endgroup$ Commented Oct 20, 2014 at 21:45
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/2230/2451 and links therein. $\endgroup$
    – Qmechanic
    Commented Oct 20, 2014 at 21:47
  • $\begingroup$ @user58953 -- I started an answer with a numerical example before the question was closed, but I saw there was no answer with a similar numerical example to the earlier similar question, so I added my answer there--if you think such an example would be helpful, go here. $\endgroup$
    – Hypnosifl
    Commented Oct 20, 2014 at 22:27