dc42:
What I think you are missing is the saturation voltage - Vce(sat) - of the PN2222A. The PN2222A (like the 2N2222A) is a rather poor transistor for medium-current switching because of its high Vce(sat). This is the voltage drop between collector and emitter when the transistor is turned on. More modern transistors such as BC327 or (even better) ZTX851 have lower Vce(sat).You need to subtract the Vce(sat) from the supply voltage (along with the IR diode voltage drop) when calculating the current through the series resistor.
Also bear in mind that Vce(sat) is usually measured with the base current being 10% of the collector current, and with a 330 ohm base resistor, you are not driving it that hard.
dc42:
822mV is within the expected range under these conditions. What matters more is the voltage between collector and emitter when the LEDs are on.
Sorry, I'm not that familiar with transistors. I'm starting to read the book The Art of Electronics 2nd Ed, but am not there yet. I'm not in school, this is just a hobby.
So the Vce(sat) is 1V, correct? So I need to push the current on the base to be 10mA to drive 100mA thru the collector/emitter?