What is the nature of the intensity of Rosalind and Orlando's love in Shakespeare's As You Like It?
Shakespeare certainly does portray many different types of love in As You Like It with varying types of intensity. Rosalind and Orlando's love for each other certainly is one example of intense love at first sight. However, interestingly, due to a warning Celia gives her, Rosalind decides to test the strength and depth of Orlando's love by maintaining her disguise as Ganymede.
We witness Rosalind develop feelings of love for Orlando at first sight the first time she meets him the moment he fights with Charles the court wrestler. However, Rosalind's feelings of love seem to stem from more than just Orlando's looks and his display of strength and valor. One of the first things Orlando says to her is that he is the youngest son of Sir Rowland de Boys, a name that means a great deal to Rosalind. Rosalind is well aware that her father, usurped and exiled by Duke Frederick, very much loved and admired Sir Rowland and so did her father's entire court. Hence, when she sees Orlando, Rosalind is also seeing her own father as well as the character traits her father admired in Sir Rowland, showing us that, even if her love is intense and at first sight, it is grounded on what she believes to be Orlando's character. Nevertheless, Celia later counsels Rosalind very wisely when she warns Rosalind that just because Rosalind's father loved Orlando's father and that Sir Rowland was full of good qualities, it does not necessarily logically follow that Orlando is also full of the same good qualities and equally deserving of Rosalind's love as Sir Rowland was, as we see in Celia's lines:
Doth it therefore ensue that you should love his son dearly? By this kind of chase, I should hate him, for my father hated his father dearly; yet I hate note Orlando. (I.iii.31-34)
In other words Celia is warning Rosalind to be more cautious, to not let her emotions run away with her, and to carefully consider Orlando's worthiness. We know that Rosalind takes her advice because next we see her decide to play a trick on Orlando by pretending to be Ganymede. In her disguise, she gets him to confide in her about his deepest feelings for her as Rosalind, confidences that she could not so easily have tricked him into saying had she approached him as a woman for the simple fact that men confide in fellow men much more easily than they confide in women. Furthermore, she does not disclose her true identity until she hears him proclaim that he would rather die than continue to be without Rosalind, which confirms exactly what she was hoping to confirm, that his feelings for her certainly are deep and sincere.
Hence, while both Rosalind and Orlando do fall in love at first sight, Rosalind also decides to govern her feelings with reason and be patient in deciding if the relationship is truly right for her.