Very Low Cost Linear Position Sensor

[janoc]

Yeah the laser rangefinder is a bit of an overkill for your needs also.

Another idea that may work is simply installing an IR diode and a phototransistor and measuring the intensity of the reflection. It is not super accurate and likely won't work for more than 50cm distance but for a drawer that is likely plenty enough already. I have seen this used for some novelty MIDI instruments in the past and it works reasonably OK.