It's odd. My PhD supervisor went the other way. He had an undergrad in mech eng and did his grad work in physics.
It depends how much math and experiment you did in your undergrad. Get the calendar for the universities you are considering and see if you have the correct classes. You should be able to at least request these on line, possibly even receive electronic copies. Google will help you here. Find the web sites for the universities and look in their physics department sections and see what you can find.
Also, look for direct contacts with the departments you are interested in. Send them an email and ask for the information you need. Be sure to include the following:
- Where you did your undergrad, and what program it was.
- What program you are specifically interested in.
- Ask specifically what subjects you need to have taken, and what the requirement is for entry.
If you can find candidate profs to be your graduate adviser, send them an email also. Same basic information. If you can find something about their research program, and find a way for you to contribute to that, that would be very helpful. It might even get your foot in the door.
It may be that you already have nearly everything you need. The biggest differences are likely to be:
- Engineers do more and different kinds of labs.
- Depending on the kind of engineering they may have a lab project requirement for fourth year.
- Engineers do ethics classes and economics classes. Most physics degrees don't.
- Engineers may have industry work requirements, depending on the university and degree.
I have no experience with online universities. Again, Google should help you there.