It is interesting that you have a degree in ECE and you wish to change to Physics.
Engineering physics is different. You will learn physics but that will be enough to do engineering with it. You can get an Mtech from IIT Bombay as they are really good in that field.
In case you want to do research in physics, as micromass suggested, the only way out is to get a degree in physics.
Not to be discouraging but it is a very difficult field to be in. I feel that the most critical thing there is to get the right mentor to help you get a good hang of how to think when you become a physics researcher. These days, there is a lot of competition and it is very hard to get good guidance for research.
Also, this is the age when you feel like doing research and all that. After crossing 30, you will feel the need to get married and have a family. As a physics major, it takes a long time to get settled and then the salary won't be that good if you take up teaching. Women like men who earn decently and if they have options, they usually pick men who earn more.
These are some practical aspects and I have seen it happen. Please think carefully before changing fields. You have already invested time getting an engineering degree. Be very careful when it comes to changing fields at this point in your life.
I am sure other people have different views. Situation is different for different people. I am an Indian and I know exactly how it works in India. A big factor for Indian men is that beyond 30, it is tough to get a woman to get married to as men are considered too old. With factors like this and the ones related to low salary, you really have to ask yourself if it is worth all the sacrifice. In the west, you can afford to take that risk of going into pure science as the salary is modest for a professor here. The situation is very different if you are in India.