I want to supplement chuckeys excellent explanation in a single regard. If the LEDs are white, as the schematic suggests, then the forward voltage can be rather expected around 3.5 V. So the LED current achieved with an 1 uF capacitor will be slightly smaller. Basically, you have to check the allowed current for your LED type (also considering self heating of the enclosure) and determine an appropriate capacitor. With white LEDs and the planned current level, I assume that nightlight will be sufficient for a large hallway!