I want to get close to my teacher?

So, a few years ago my friend died from cancer. I wrote an essay about her and read it to my English teacher to see what she thought of it, and I noticed as soon as I even mentioned the word cancer, she was crying. Her sister passed away from the same kind of cancer not long ago. Is it normal that I liked seeing her cry and would do it again if I could? Not because I like seeing her upset, but because I felt such a bond when I realized she trusted me enough to allow me to see her softer side. (She's generally a pretty tough lady.) I wish the two of us could bond over this mutual sadness. It made me feel more normal. Is this whole situation acceptable? I mean, I don't mean anything inappropriate by it,and we're both women, but the whole teacher-student thing makes it questionable..

Is it ok that I have such a desire to bond with my teacher?
Thank you for your input.