Ok, I think that sounds good to me.
Greater magnification is a somewhat problematic phrase as well, but I think we can work with it. There are two factors in play here, focal length, and aperture. Aperture is normally measured as the ratio of the lens opening to the focal length. So, if when we increase the focal length, we normally decrease the aperture. The answer to your question is, it depends.
Greater magnification is associated with longer focal lengths. When imaging the sky, this simply means that we're placing less of the area of the sky onto the sensor.
If you double the focal length (increasing magnification) while keeping aperture the same (for example, for from a 300mm f/2.8 lens to a 600mm f/2.8 lens), several things occur:
- less of the sky is imaged on to the sensor, 1/4 as much, to be exact.
- the size of the lens opening has doubled, which means the area of that opening has quadrupled, which means the light-gathering power has quadrupled.
The effect is that the apparent brightness of the stars will indeed quadruple. This is why building a bigger telescope is actually a helpful thing to do. Stars not previously visible are now visible, if you can build a telescope with a bigger hole for light to pass through, with more light gathering capability.
If you double the focal length but do not change the light gathering power of the system (for instance, inserting elements into a telescope system to increase the magnification) you will effectively cut the aperture in half. The will also have some effects:
- less of the sky is imaged on the sensor, 1/4 as much. Same as last time.
- the size of the lens opening is the SAME, the light gathering power is the SAME. The infinitesimal points which are the images of stars will remain at the same brightness.
This is why, in order to see deeper into the night sky, you cannot simply add elements on to the viewing end of the telescope. You must build a bigger telescope, with more light gathering power -- with a larger physical aperture through which light can pass.