is there a way to find out...?

Question

when your friend opens/read the mail you've sent her??!!!

Answer 1

you can request return receipt.

If the user on the other side allows or accepts sending return receipts, then you will receive an email letting you know the email was opened.

This of course is not 100%.

Answer 2

If you are familiar with HTML mail, how about implementing image tag like bellow?



Then you can find this URL in your apache log with time and date which is the time when your friend opens your e-mail.