Visual Limiting Magnitude For Pinpoint Objects


The limiting magnitude increases with higher magnification for pinpoint objects. The reason for this is that the object itself will noy appear larger despite the higher magnification. It's light is thus still concentrated in a point. The amount of light is determined by the aperture and is independant of the magnification. The amount of background you see depends on the magnification. The 'surface' brightness of the background is constant. Thus the amount of background light decreases with higher magnifications.

The upshot is that for higher magnifications you receive the same amount of light from the (pinpoint) object, but the brightness of the surrounding area gets lower. The contrast is therefore higher for higher magnifications.

The above is ofcourse purely theoretical, and assumes that the pinpoint object stay's a pinpoint. Unfortunately this is not true. The infamous airy disk spoils our praxis. As long as the magnification is so 'low' that one cannot discern the airy disk, the above holds true. However as soon as you start seeing the airy disk, you have reached the case where the 'pinpoint' object is no longer a pinpoint. And you should refer to the theory of optimum detection magnification.