So, when drawing cartoon eyes, we can use both of these ideas—how the eye works and how to communicate this concept with the viewer. In fact, we can take these ideas and further use them to communicate things like emotions or even general character traits.
Here are some examples. The only difference between the two is the eyes. However, notice how the first example looks rather sad and innocent, while the second looks stern. Elements of art like scale and shape can help visually communicate concepts like this.