I'm not sure what meaning the Danish phrase is meant to convey, but I assume what's being discussed is the television broadcast. If the father is indeed physically present and sitting on the television, then the translation stands as it is, i.e. "My father is on the television." However, if the father is featured in the broadcast, then it would sound better to say, "My father is on television." Although....now, I'm second-guessing myself. I suppose, depending on the context, it could be both. Maybe somebody can weigh in...
I'm not really sure what you're asking about, but I'll try to shed some light.
Both fjernsyn and tv can refer to both the TV box and the medium. The difficult point here is that they can use different prepositions:
- i fjernsynet - på tv = on TV, being broadcast (the most common usage)
- på fjernsynet - på tv'et = on the TV box
- (inde) i fjernsynet - i tv'et = in(side) the TV box
The problem is that "i fjernsynet" is pretty much never interpreted as "inside the device". "Der er transistorer i fjernsynet", maybe, but not "min far".
It would be kind of like saying "We're traveling to Greece this fall" and then waiting for someone to jump off a cliff for that vacation to happen.