Hi everyone,
in the stream yesterday (#96), Casey underlined "illumination is constant along a line", which is correct of a 1d world (like a wave tube) , but for 2d and 3d worlds, illumination is decreasing because of conservation of energy,see here http://en.wikipedia.org/wiki/Inverse-square_law. you can say that for a perfect ray it doesn't matter, but it does matter for a finite sized ray, and also for understanding.
Casey answered in stream about a 2 mirror system, and he said that the diminishing effect of the higher order reflection is because the mirrrors aren't perfect. in the real world, a mirror returns about 97% i think of the light, so it really does has an effect, but the effect of the propagation of light is much more noticeable, diminishing light in a non linear way. i won't go into details because of the format of the posts, but the second reflection is about 25% of the original, the third 11%, and so on.
Thanks for reading.

edit: i watched till the end now, and i saw that what he called brightness is not intensity. he went into it at the end, but he talked about something like brightness=intensity/area of something,sorry about it.

Yeah, it is an unfortunately common mistake for people to think that the apparent brightness of light itself diminishes based on distance, but the truth is that it is only the brightness per unit area that diminishes, so only diffuse reflections diminish in apparent brightness. Direct reflections do not, they simply get smaller. Both "obey" the inverse square law, but in different ways (one in brightness, one in area), so it is very important not to confuse this.

If you think about it, it is actually very easy to understand, because if light actually got darker because of the inverse square law, things would get noticeably darker as you walked away from them. But as we all know from experience, they look the same, they just look smaller. And that is because brightness is constant along a line: their apparent size gets smaller in your field of view, but it does not get darker. Again, this is because the projected image on your retina is 1/d^2 brightness total, sure, but it is also 1/d^2 size, so the apparent brightness remains the same. If light actually got 1/d^2 brightness itself along a line, then the image would be both 1/d^2 apparent brightness and 1/d^2 size, a sort of "inverse fourth power law" :)

Make sense?

- Casey

Yeah, absolutely. I was coming from thinking about stuff like stars where you can't assess the beam width, so it just looks like the light diminishes with 1/r^2. for something like room light your reasoning is more correct.

Yes, there is a limit! Once you get to the point where the size of the projected image on your retina takes up less than one whole rod/cone, then it actually does diminish in brightness. It is effectively "sub pixel rendering" onto your retina :P

- Casey

e1211
Yeah, absolutely. I was coming from thinking about stuff like stars where you can't assess the beam width, so it just looks like the light diminishes with 1/r^2. for something like room light your reasoning is more correct.

What happens with a star is that (neglecting redshift, effects due to participating media such as the atmosphere, and the fact that stars are oblate spheroids and not discs oriented towards the viewer) you are indeed perceiving it at the same "brightness" as you would if you were standing next to the star, but you're viewing it with an extremely narrow field of view.

Let's take Sirius as an example. Sirius is 2.4e6km in diameter, but it's 8.1e13km away, which means that its apparent diameter is about 6 milliseconds of arc, or around 1/600,000th of a degree.

If you were standing near to Sirius and stared straight at it, you'd probably be blinded just as fast as you would if you stared at the Sun (probably faster, in fact). However, if you narrowed your field of view to 1/600,000th of a degree, you'd probably be okay.

(Disclaimer: I do not accept responsibility for any injuries sustained in the course of conducting this experiment. Please seek professional guidance if you're planning to take up close-proximity stellar astronomy as a hobby.)