How do you observe mitochondria under a microscope?
In order to view mitochondria under a microscope, you will need a high powered microscope such as a transmission electron microscope, which blasts the section that you are attempting to get a picture of and then the electrons bounce back and forth, which creates a sort of “vibration” which is able to ping the details of the picture, in this case, a mitochondria in a cell and produces an image.
http://sciencelearn.org.nz/Contexts/Exploring-with-Microscopes/Sci-Media/Images/Mitochondria-under-the-microscope
The reason as to why you would need a TEM is because even though you can see cells through your typical compound microscope, mitochondria are small, and are inside of the cell, making them too small to make out detailed outlines of the actual mitochondria.