My personal design for an Automatic Light with PIR Motion Sensor.
Replace the "Push Button" with PIR in real build. The PIR signal will send 3volt signal high when it detect human movement which is simulated by pressing the "Push Button".
The 3volt signal will trigger the transistor (I'll plan to use TIP120 Darlington Transistor) and will activate the 555 Timer in Monostable mode.
The LED will light up in roughly 10 seconds. You can adjust the length of LED illumination by experimenting with the 100nF capacitor value.
The only thing that i'm concerned of is the 555 circuit take up so much current in idle mode (2.80mA) which is inefficient for low power operation IMHO.