How are the -3dB point and the pole of an op-amp related?
Because a typical op-amp is dominant pole compensated, it has a single pole in the open-loop transfer function at low frequency, and a -20 dB/decade roll off.
This leads to the concept of &quot;gain-bandwidth&quot;.  The open loop gain times the open loop pole frequency will be the &quot;gain-bandwidth product&quot;.  From that you can calculate the new pole position (bandwidth) of the op-amp by just dividing the GBW product by the noise gain (gain as seen from the non-inverting input).
As an example, the old 741 op-amps had a GBW product of 1 MHz.  So if I set up my op-amp with a non-inverting gain of 2, my amplifier would have a bandwidth of 500 kHz, and the open loop pole at 10 Hz would shift to a closed loop pole at 500 kHz.
The math works out such that the magnitude of the transfer function at the pole is 0.707 of the low frequency magnitude, which is -3 dB, so a single pole at a given frequency marks the 3 dB point.