light system for stairs
I'd avoid retroreflective IR sensors.  In my experience they can be fickle, and sensing range depends on the reflectivity of the target (shoe).  To make matters worse, you'd need predictable foot placement to meet your objective with just a single retroreflective sensor.

Consider a few opposed pairs of IR LED/sensors, such that the beams cross the full width of the stair tread.  You might get it to work with a single pair, located right near the edge.  Your circuit would need to detect when the beam was interrupted by a shoe, then illuminate the corresponding step.  

Something like this should prove helpful.  I also found a discussion of a similar project also using opposed beam sensors.

The current draw of each IR LED can be as low as a few mA (though it will make it harder to aim/align properly), so battery power is viable.   To reduce power consumption, the IR LEDs can be strobed (i.e. on for 10ms every 250ms), though the detector circuit design will become more complex as a result, and you may face latency issues (time from breaking the beam to next stair illumination coming on).