As we have learned, a minyan is a gathering of ten Jewish males who are of sound mind. In order for them to join as a minyan, they must be together in one place. If nine of them are in the synagogue and one is outside or in an adjacent room, they are not considered a minyan. If the person outside the synagogue is standing next to the door or window, and his face is visible, according to most poskim he can be counted as part of the minyan, because their eye contact unites them. It is not necessary for everyone to see him, rather it is sufficient for only some to see him. Nevertheless, there are poskim who maintain that eye contact cannot be used to link a person to a minyan, and only if he inserts his head into the window will he be considered present with them and thus be counted in the minyan. L’chatchilah, we are to be stringent about this, but in extenuating circumstances, when he cannot come inside and join them, we may rely on most poskim who are lenient and count him as long as his face is visible.
Someone whose face is not visible to those praying inside the synagogue, but is in the ancillary room of the synagogue, does not complete the minyan. Even so, if a minyan already exists without him, when he prays with them he is considered to be praying in a minyan.
Ten people who are standing in a field, as long as they can see and hear one another, are considered a minyan (Minchat Yitzchak 2:44).
When there is a minyan of ten inside the synagogue, anyone who hears the chazan may respond. For instance, a sick person who is bedridden and hears the congregation’s prayers from his house, though he is not regarded as one who is praying in a minyan, he may answer Amen, since not even a steel barrier can separate a Jew from the Shechinah that dwells with the minyan (Shulchan Aruch 55:20). Similarly, if he hears the sound of the shofar blowing or the megillah reading from the synagogue, he can have kavanah to fulfill the mitzvah by hearing it.
A person who hears a chazan via a live broadcast on the radio or television may answer Amen after him. However, he cannot fulfill his obligation by listening to the megillah reading on the radio or television, because he is not hearing the actual voice of the chazan himself.
In summary, there are four levels of joining together for matters of sanctity: 1. When a person is situated in the same place as the people praying or he is visible to them (according to most poskim) he can complete a minyan. 2. A person who is in the ancillary room of the synagogue but is not visible to the people praying cannot complete the minyan. If, however, there is a minyan without him, he is considered to be praying in a minyan. 3. One who is in a different room or outside the synagogue is not considered praying in a minyan, but may fulfill his obligation by hearing the chazan. 4. One who hears the chazan on the radio may answer Amen, but cannot fulfill his obligation by hearing him.