Why can we see distant bright stars but not dim ones?

[joeb1990]

Ok so I was at the Hayden Planetarium and a plaque was describing a star billions of light years away that we can see because it is so much brighter. I was puzzled thinking about this. If the speed of light is constant there is no reason the intensity of it's light should affect how far away we can see it right? I mean if something is 13 billion light years away it will take 13 billion years to reach us regardless of intensity. Shouldn't we be able to see anything in this time frame as long as the light has been traveling long enough? Is it something to do with the sensitivity of the equipment? Thanks!

 

[mathman]

The light is not in one direction. Since it spreads out in all directions, the intensity in any specific direction decreases by an inverse square law with distance.