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RE: Intuitive Special Relativity - Why You Can't Go Faster Than The Speed of Light
Check this out
As the ship goes faster and faster the light will redshift because it is receding from the stationary laser.
The ship is moving away from the stationary light source which in the example is blue.
It is essentially 'running away' from the light and will see the peaks and troughs of the light at a slower rate.
This is equivalent to reducing its frequency.
The faster you away from the source go the lower the frequency. It will go to green, then yellow, then orange, then red, then infrared and so on and so forth.
Also look up Doppler Shift.
Hope this helps.