For reference, astronomer William Miller is shown at prime focus with a photographic plate in this late 1940s-era image from the Google LIFE image archive.
Sky & Telescope magazine reported on the milestone in the News Notes of their February, 1990 issue. The exposure marked the end of nearly 40 years of such work. S&T described the passing of photographic emulsions like this:
So, after a century of faithful service to astronomers, it appears that plates will soon be things of the past at professional observatories, just like oil lamps, pendulum clocks, and slide rules.
Photographic plates have been entirely replaced by CCDs, which were first used at Palomar in 1976. Glass plates were used on the 48-inch Samuel Oschin Telescope up until 2000. While we no longer expose new plates they aren't entirely a thing of the past as we are still storing a great many glass plates on site and get requests from time to time from researchers who need to see a particular image.