die Wimper
eyelash
One of the fine hairs that grow on the upper and lower edges of the eyelids and protect the eye from dirt and foreign objects.
Pass auf, du hast da eine Wimper im Auge.
Careful, you have an eyelash in your eye.

eyelash
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eyelash
One of the fine hairs that grow on the upper and lower edges of the eyelids and protect the eye from dirt and foreign objects.
Pass auf, du hast da eine Wimper im Auge.
Careful, you have an eyelash in your eye.

You can easily recognize the meaning from the context. If people are talking about eyes, beauty, or cosmetics, it means the hair. If the exact expression 'ohne mit der Wimper zu zucken' (without batting an eyelash) appears, the idiom is meant.
Sie tuscht sich jeden Morgen die Wimpern.
She puts mascara on her eyelashes every morning.
In a cosmetics context, typical collocations are 'die Wimpern tuschen' (to put mascara on one's eyelashes), 'sich die Wimpern färben' (to dye one's eyelashes), or talking about 'langen' (long) and 'dichten' (thick/full) eyelashes.
Für den Abend trug sie künstliche Wimpern.
For the evening, she wore false eyelashes.
Normally, people talk about 'den Wimpern' (the eyelashes) in the plural, since you have many of them. The singular 'die Wimper' (the eyelash) is usually only used when talking about one single, specific hair, for example if it has fallen out.
Ich glaube, ich habe eine Wimper im Auge.
I think I have an eyelash in my eye.
The expression 'ohne mit der Wimper zu zucken' (without batting an eyelash) is a fixed idiom. The form does not change and means that someone remains completely unimpressed and calm in a surprising or stressful situation.
Die Angeklagte hörte sich das Urteil an, ohne mit der Wimper zu zucken.
The defendant listened to the verdict without batting an eyelash.
hair
'das Haar' and 'die Wimper' both have to do with fine hairs on the body. 'Haar' is the general term: it can mean the hair on someone's head or a single hair on a person or animal. 'Wimper' is much more specific and refers only to the small hairs along the edges of the eyelids. So you can think of an eyelash as a special kind of hair, but not every hair is an eyelash. The words can be confused because eyelashes are also hairs. If it is about the head or body hair in general, 'Haar' fits. If it is directly about the eye, 'Wimper' is correct.

Eine Wimper ist mir ins Auge gefallen.
An eyelash got in my eye.
Nach dem Friseurtermin war ihr Haar deutlich kürzer.
After the hair appointment, her hair was much shorter.