PieterP:
Or you could just use a monostable 555 timer, no need for an Arduino.Pieter
I guess you could but I don't think we have the full story here where the exercise may specify an Arduino and anyway, for practical purposes, there has also to be an LDR or similar light sensitive device to ensure the light does not come on during daylight.
Not only that, if you need two or more PIR sensors to control a light or other load, some of the cheaper ones are prone to re-trigger each other through electrical noise caused when switching the load off. You then need programming logic to ignore the triggers which occur within X ms of the load switch. I know all this because I spent some considerable time stabilising an application which has 3 PIR sensors like this.