Proper pull up resistors for optical limits

Wondering if anyone could give me advice on the correct pull up
resistor for my optical limit/home switches. I'm placing slotted
optical switches on the + side of my X,Y,Z axis to use as limit and
home. My servos are WorldServo SST1500s and the manual suggests
using optical switches on the + axis side. There is a diagram in
the manual that shows connecting them to +5V (which is supplied by
the servo through the limit switch plug). They show a resistor
between the +5V and the optical interrupter switch but do not give a
value on the resistor. I assume this is a pullup resistor (I know
very little about this) and I'm wondering if anyone can help me with
determining which size resistor to use???? The optical switches are
transistor output type, Min Output 0.5 IC @ 20 mA IF. Another type
I may use are the same except Min Output 1.8 IC @ 20 mA IF.

Thanks,

Frank