I've a question about the oil warning light on the dash; at what level does it come on?

I was filling the oil the other day and I accidently drove the car with low oil before I realised it, i.e.: the oil was slightly less than half way between the high and low marks on the stick.

But there was no warning light on the dash. How low does the level have to get before the light would come on? Is the warning light a reliable indicator of too low oil pressure?