Suggest you read-up on this - the predictions are all very weird but many have been experimentally confirmed.
Wikipedia's Special Relativity is reasonable as is Time dilation
If you are on a craft at near c the light you measure ( from the TV or otherwise) will be measured as traveling at c - that's the cornerstone of SR - the observer will always measure light - ANY light - as traveling at c. To reconcile the problems that brings up other measurement s have to give way - in particular time varies.
This may all sound silly but experiments all agree. Sub-atomic particles with a known short lifetime last longer at high speed and do so by exactly the amount that SR predicts.
Further down this topic someone mentions that IF a craft could reach close to c the traveler inside could tour the galaxy in a short time by their measure although thousands of years might have passed on Earth
Incidently GR also predicts time changes due to gravity, the closer to a large mass the slower time runs - these effects are also measured as predicted.
It's a weird universe.