"第一眼"是用 by the first sight 还是用 at first sight

后者

at the first sight
我们常说的一见钟情,就是用这个

后面的

fell in love with sb. at first sight.一见钟情
一般不用by the first sight.
eg.At the first sight Paul and Anna changed eyes.
保罗和安娜初次见面就互送秋波。

at first sight
一见钟情就是fall in love at first sight

第一眼 at first sight

我第一眼见到她就爱上了她。
I fell in love with her at first sight
第一眼我就爱上了它。
I fell in love with it at first sight

也有 " the first moment of see "这种表示

自从看见她的第一眼起我就讨厌她。
I have disliked her from the first moment of seeing her