How Far Must Someone Fall in a Cylinder to See the Entrance as a Dot of Light?

[John Connors]

Draw a cylinder, with diameter D and length/height infinity, mark the top point Y and the bottom point Z

Now Say a person falls into this cylinder/hole. (there are equal sources of light emitting into each end of the tube)

From the falling person's perspective the point Z looks like an infinitesimal dot of light that the human eye cannot distinguish. At what height/length in the cylinder/hole does the person view the same thing from the point Y?

What I want to know is how far does the person have to fall for the person can only see a dot of light at entrance Y.

This is not some problem someone has given me, this is a genuine problem That I came up with.

Also if there are any conditions that I am missing please take your own and If you have an answer for this please post what values you took for those parameters.

Thank you.

 

[Andy Resnick]

Are you asking for the resolution limit for human vision?

If so, the answer is rather complicated and depends on many factors- color (obviously), but also if the spot is steady or flickering, steady or moving, the relative contrast between spot and background, where in the visual field it falls, etc.

As a rule of thumb, the limit is about 1 arcsecond, IIRC. Objects subtending an angle less than this can still be detected if the contrast is high enough. There is no definitive definition of 'smallest visible object' in optics.

 

[mgb_phys]

Did you mean 1 arcmin?

 

[cesiumfrog]

Draw a cylinder, with diameter D and length/height infinity, mark the top point Y and the bottom point Z [...] At what height/length in the cylinder/hole does the person view the same thing from the point Y [as Z]?

Are you asking, what is infinity divided by two? (To wit, your answers are "never" and "half way down".)

If the cylinder has infinite height, it just isn't possible for it to have both a top end and a bottom end. (finite bounds and Euclidean space)

 

[Andy Resnick]

Did you mean 1 arcmin?

yep- thanks.

 

[mikeph]

should the unit not be a solid angle? Or are arcmin also units of solid angle?

 

[Andy Resnick]

I guess it could be arcmin^2, but since the eye is (reasonably) rotationally symmetric, the convention is to use plane angles (as in most of optics).