The feminine form of the definite article is “hin”. Lets take two examples:

• “Bók” is a feminine noun. We add “hin” to the end of it and we get “bók + hin”. We don’t care about the “h” and we’re left with “bókin” (the book).
• “Kona” is also a feminine noun. To add a definite article to it, we create “kona + hin”. We don’t care about the “h” and so we’re left with “kona + in”. The vowel in the noun is much more important than the vowel in the definite article, so we’re left with “kona + n”. The result is “konan” (the woman).