As far as I understand it, a light bulb irradiance (and illuminance) fall off following the inverse square law with distance, however radiance does not.

I wondered why we (and cameras) do not see objects as dimmer as we get farther away from them. Searching around I’ve found two possible explanations:

  1. The object’s light (irradiance) does get dimmer, but with perspective the object appears smaller so the two effects cancel out, and the perceived brightness is the same.

  2. The eyes/camera measure radiance which does not change with distance.

Radiance seems to have nothing to do with perspective so they kind of contradict. If the latter is correct, then why use lenses to “convey” more rays in one point as radiance remains the same? (Only irradiance inside the eye/ image film is higher.)


1 Answer 1


You are on the right track. Consider a piece of white paper at 10 feet away. If it is moved to 20 feet away, the light reflected from the paper entering your eye is decreased. That is, the irradiance at the entrance to your eye goes down. But - and this is what is often not realized - the image of that piece of paper on your retina is now smaller. The effects cancel, and the paper appears the same brightness when it is 10 or 20 feet away.

However, this is not true for a point source, which is a source that is too small for your optical system to resolve. For these, the size of the image on the retina is determined by the blur spot of the system, not the size of the object. For a point that is not resolved by the system, moving the point source further away will cause less light to reach the entrance pupil of your system. The image now stays the same size (whether on your retina or on a camera film plane) and so the apparent brightness decreases. For example, consider a candle at 1 mile away or 2 miles away. At 2 miles, the candle will appear less bright. This is also the case with stars, which are effectively point sources. The star and the piece of paper are two distinctly different cases.

  • $\begingroup$ Thank you, so the first one was right after all. As I understand it, eyes/cameras detect irradiance rather than radiance, radiance is just useful to calculate how much that will end up being. (Same radiance != same irradiance, as that will depend on the actual pupil solid angle and projected area considered) $\endgroup$
    – yggdrasil
    Apr 25, 2019 at 2:25

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