Keilim, Chapter 14, Mishnah 6. This chapter continues to sort out which metal objects count as a keli that can receive tumah, and our mishnah takes up a case where one object quietly acquires a second job.
To follow it, we need a principle we have already established: the cover of a keli does not become tameh. Tumah attaches only to an item that stands on its own and carries its own name. Something whose entire identity is borrowed, an item known simply as "the cover of such and such," is not a keli in its own right, and so it remains outside the laws of tumah. That rule sweeps in every sort of cover, including the cover of a teni, a large metal basket.
When the cover is polished into a mirror
Picture the owner taking that metal lid, rubbing and polishing it until the surface gleams and throws back an image. It has not stopped being a lid, yet it now performs a second service as well. The mishnah presents the case: "Kisui teni shel matechet", the metal lid of a teni, "she'asah bo mar'ah", in which its owner fashioned a mirror. And on this the ruling is given, "Rebbi Yehuda metaher": Rebbi Yehuda holds it remains tahor.
Nobody questions that a mirror standing on its own is subject to tumah. Rebbi Yehuda, however, weighs what this slab of metal fundamentally is. Its principal service is sealing up the teni, that oversized basket of metal, while the reflecting function is merely an extra that the owner grafted onto it. Because the object is still defined by the job of covering, it carries no name of its own, and it therefore stays beyond the reach of tumah.
"Vachachamim metam'in." The Chachamim disagree and hold that it can become tameh. In their view, once an object genuinely serves a purpose, even a secondary purpose, that is enough to give it the status of a keli and to bring it into the laws of tumah. The reflecting surface is a real use, and a real use makes a keli.
A mirror that broke
The mishnah ends with a ruling about mirrors themselves: "Mar'ah shenishberah", a mirror that broke apart, "im einah mar'ah", if it no longer shows "et rov hapanim", the greater part of the face, then "tehorah", it is tahor. We take up the shards and test what they can still show; should the surviving pieces be too small to give back most of a person's features, the mirror is pure.
The reasoning is straightforward and it teaches us how the Mishnah measures usefulness. A sliver that shows only a fraction of one's face serves no one; it is simply too small to function. Such a fragment is no longer a mirror at all, and what is not a keli cannot receive tumah. A keli lives or dies by its usefulness, and once the use is gone, so is its status.