In the double-slit experiment why does the light hitting the back screen not result in a measurement? How far away from the slit can the measurement take place and still cause a wave collapse and is there a consequence to moving the measurement further away from the slits)? What qualifies as a measurement?
In the double-slit experiment why does the light hitting the back screen not result in a measurement?
Light hitting the back screen does result in a measurement, which is why the photon only makes a single localized spot on the screen. The interference pattern becomes evident only after multiple photons have hit the screen, so we can see the distribution of spots.
...is there a consequence to moving the measurement further away from the slits...?
If the back screen is moved closer and closer to the slits, the distribution of spots accumulated at that new screen-position will look less like an interference pattern and more like an image of the two slits, depending on how close the screen is to the slits.
What qualifies as a measurement?
This is a very broad but important question. In a nutshell: any time the quantity-of-interest (the location of a photon, in this case) influences its surroundings in a prolific and practically irreversible way, as long as the effect is sensitive to the value of that quantity, then that quantity has effectively been measured.
(This principle doesn't solve the infamous "measurement problem", because it doesn't tell us how to calculate the distribution of outcomes. We still need Born's rule for that. But for all practical purposes, this principle does tell us when we can safely apply Born's rule.)
In the case of the double-slit experiment, the effect on the interference pattern depends on how far downstream we measure the (transverse) location of the photon, because the farther downstream the measurement is, the less sensitive it is to which slit the photon may have gone through.
The measurement is occurring in your eye and that is where collapse happens. You continue to see the screen because the light source is continuous. So if a 1000 photons go thru the slit maybe you observe 100 and your buddy sees 100 and the blackboard sees 500 and 300 slip out the window into outer space ( they don't collapse ! ).
Observation is a measurement.