The short (and funny-sounding) Norwegian word øy is a cognate to the English word island and both have the same meaning. These two are also cognates to the German (also kinda funny-sounding) Aue, with the meaning of water meadow. Let’s take a look at how these words are related to each other.
The English Island is obviously a compound word- and while the second part of island is very obviously related to the word land, the first component is not so easy to identify.
This first bit, the is–, pronounced /aɪ̯/, is what we are going to talk about today, since we can link it to the Norwegian øy, pronounced /œy̯/, and to the German Aue, pronounced /aʊ̯ə/.
As I explained in Isle & Island: A Coincidence over Time, the English island was once written as yland. This was later changed due to the similarities in meaning with the word isle, which, weirdly enough, is not related to island and øy at all, eventhough it bears the same meaning. Isle is also not a cognate to the German Aue.
Yland originates from the Old English iegland. The ieg– part, that is now written as is-, already meant island and can be traced back to a Proto-Germanic ancestor *awjo, a thing on water.
The same *awjo would have given us the Old Norse ey, word for island, and the Old High German ouwa, meaning floodplain, meadow or island. These would later evolve into the Norwegian øy and the German Aue, respectively.
And this makes these three words, that at first glance may appear completely unrelated to each other, cognates.
These are also cognates to the Latin aqua, water, but that is something I already explained previously.