Electronic – Alter Solenoid Stroke

DC solenoids are hard to do at larger distances because the magnetic field decays with the square of distance. At 50 cm, you'd need a ridiculous amount of current. Such a solenoid is not impossible, but it is impractical.

The cheapest way to do linear motion (which, given your lack of speed and power constraints, is probably your primary motivating factor) is generally to use a stepper motor to move a belt or chain. 50 cm is actually quite a lot for linear motion, and this solution frees you from expensive long machined parts, like cylinder bores, pistons, threaded rods, and gear racks.

Something like this McMaster timing belt mated with a pair of these pulleys and with the (or whatever you're displaying) clamped to the middle of the belt should do the trick. Add a standard stepper motor, and be careful with your programming to avoid over-extending your belt.

If it says the stroke length is .05 inches, then you have to assume the stroke length is .05 inches (50 mils). There is nothing ambiguous here.

The nominal versus maximum stroke is less clear. It appears they are rating the solenoid for pulling in the nominal amount, but are saying that it can actually start further out. That will likely mean significantly less starting force, though. They are saying that this solenoid is meant to be used so that it is held the nominal distance out, but that it can mechanically go further. However, it's hard to trust what they say when the starting force is labeled in Ohms. Huh? I'd seriously wonder what else is wrong with that datasheet. I'd find a different solenoid, preferably from a different manufacturer.