Delicate
Faint, Indistinct, Dim
な adjective
The kanji means delicate, and so does this word. Something that's delicate is probably also faint and indistinct. So use 微か to describe things like faint sounds, delicate breezes, and indistinct memories.
You should should speak in a delicate and faint voice when you cuss (かす). So delicate that the cuss words are indistinct to other people, even. It's the only acceptable way to cuss.
あきらめないで。まだ微かな望みが残っているよ。
Don't give up. We still have a faint hope.
シンと静まり返った雪山に、微かな音が響くのが聞こえました。
A faint sound could be heard echoing through the silent snowy mountains.
コウイチはロウソクの微かな明かりで日本語を勉強してたせいで目が悪くなってメガネを掛けているらしいですよ。
I heard that Koichi studied Japanese by the dim light of a candle, which worsened his eyesight, so that's why he's wearing glasses.