I've looked at the design of the James Webb Space Telescope and I got curious about something, some years ago, it seems that the international space station was hit by micro-meteorites. I'm wondering if the same couldn't happen in the James Webb Space Telescope.
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No. Not too unprotected, as you put it. There are several misconceptions that I find common about the JWST, that need to be addressed:
JWST primary mirror elements are not made of glass and do not shatter on impact
It's primary hexagon mirror elements are made out of Beryllium powder pressed into blocks, that were later cut in half to create two mirror blanks and had most of their back side cut away leaving reinforcing rib structures and thin and light front mirror surfaces. Those front surfaces were later precisely shaped to their specification at JWST operational temperature (-400°F, -240°C) and polished to a mirror finish. Beryllium was specifically chosen due to its lightness, strength and ability to maintain shape at mentioned cryogenic temperatures. Read more about this process on JWST - The Primary Mirror (includes images and videos).
Unlikely impacts with micrometeorites (see below) would result in bullet holes, not fractures and shattered mirror surfaces, and those punctures are something that can be established during mirror calibration mode and corrected for with image post-processing. No large mirror is free from slight defects throughout their lifetime, and this is something astronomers are well used to dealing with. The important thing is that the primary mirrors still maintain their shape, together with secondary mirror maintain focus, and most of their joint surface doesn't distort end image too much with any such imperfections. Smaller problem areas can be corrected for in software, or otherwise adjusted to in hardware.
JSWT target halo orbit around Sun-Earth Lagrange point 2 is not littered with debris
Sun-Earth Lagrange point 2, or SEL2 for short, the point around which JWST will be stationkeeping in a halo orbital regime (its own orbital plane around SEL2 is perpendicular to the Sun-Earth plane), is one of the least gravitationally attractive points in the near-Earth space, roughly 1.5 million km more distant to the Sun than the Earth, and with the same orbital period as Earth itself. Think of this point either as the top of a hill, or perhaps better yet (since it's not really a "hill" per se, that would require negative gravitational attraction, or anti-gravitational point), as a nearly flat surface with increasingly steep slope towards its parent massive bodies, in our case the Sun and the Earth. In another analogy, where is the safest place to stand if you're at risk of being swept by an avalanche? At the flat top of otherwise a steep hill, of course.
This is a lot different to orbiting around the Earth in LEO (Low Earth Orbit), where the International Space Station (ISS) is;
JWST is not defenseless against collisions with debris and micrometeorites
Still, even with all said, collision with objects in transit through the SEL2 region are not excluded, so there are a few defense mechanisms that JWST will have available to it and its mirrors;
And there are other risk management options available to JWST, including preparing conjunction analysis for potential collisions with other satellites stationkeeping in SEL2 or intersecting it (won't be many, but it'll still be done, no question about it), planning its stationkeeping and attitude maneuvers to avoid hazards and protect its most sensitive parts against debris, interplanetary dust, micrometeorites, solar and cosmic events, and other detected threats, when, where, and as needed. But in a general sense, SEL2 is a relatively safe place to be compared to near-Earth orbits, as far as orbital debris and micrometeorite impacts go, as per your question.