There is a separation standard to be applied- check your Manual.
How that separation standard is accomplished is based on numerous factors which will determine the "runway occupany time" of the departing aircraft.
- the aircraft types concerned (speed down final and departing clias
- aircraft weight (long haul etc)
- the weather conditions (headwind, cloud base, visibility)
Taking all these into account, not only is the prescribed separation standard required at the moment of takeoff/landing of the two aircraft but the ADC must ensure that, in the event of a go around, a separation standard can be applied
eg firing a C182 with a lear on a 3 mile final might be OK in VMC because, not only will you have the prescribed standard when the Lear touches down but the C182 should be far enough out that in the event of the Lear going around instuctions can be issued to maintain visual separation. Try this in IMC and immediately the Lear has nowhere to go and the controller can't maintain separation ie
- can't maintain visual separation
- won't have 3nm radar separation (or may have but very quickly won't have)
- in a non radar environment the C182 won't be through a level which would give you an IMC assignable level to the Lear
In a nutshell then you can clear the departing aircraft for takeoff any time you like- there is no absolute cut-off. What comes with training is the judgement to know, taking into account the factors above, that the departing aircraft will land with the appropriate runway separation standard and that, in the event of a go-around, you'll be able to apply another standard between the two.
I might be teaching people how to suck eggs here, just that the original question seems to be fairly basic and I'm trying to give a fairly basic answer.