On an object's size vs distance relation

[davidge]

It's pretty easy to explain why objects appear small as the distance from them increases, if we use ray theory: as the distance increases, the angle become smaler. But I know the ray theory is far from being a accurate theory of light. My question is then, How can we explain the phenomenon of size/distance relation by using the next best theory of light that we have? I.e. using Maxwell theory

Just to say, I was driven to this question after reading about the Solar Eclipse that will occur later on this month.

 

[CWatters]

Why stop at Maxwell? Einstein's general theory of relativity explains gravitational lensing which changes the apparent size of very distant objects...

https://en.wikipedia.org/wiki/Gravitational_lens

 

[davidge]

Say I want to explain the apparent size of objects that are some hundreds of meters away from me. In that case, I guess using Einstein's Relativity would be too hard as we are on a planet (Earth) with plenty of matter around us, etc... It would be definitely more easy to go with Maxwell's electromagnetism. The question then is, How do we proceed?

 

[jbriggs444]

Say I want to explain the apparent size of objects that are some hundreds of meters away from me. In that case, I guess using Einstein's Relativity would be too hard as we are on a planet (Earth) with plenty of matter around us, etc... It would be definitely more easy to go with Maxwell's electromagnetism. The question then is, How do we proceed?

Find a wave solution to Maxwell's equations. Then use wavelet theory to see how waves propagate in straight lines. Then realize that ray optics is still a tool that gives correct answers.

 

[davidge]

Find a wave solution to Maxwell's equations. Then use wavelet theory to see how waves propagate in straight lines. Then realize that ray optics is still a tool that gives correct answers.

Ok, that's great, but my goal on this thread is to find a way of explaining the given phenomenon independently of ray theory

 

[Ibix]

Google for Huygens' Principle. It's basically step 2 in jbriggs444's plan.

 

[russ_watters]

Ok, that's great, but my goal on this thread is to find a way of explaining the given phenomenon independently of ray theory

That is indeed what @jbriggs444 outlined. The "problem" is that the answer is inherrently geometric so pretty much any valid method will end up giving approximately the same result and looking a lot like ray theory.

It's like what happens when you apply General Relativity to low speed or static situations: it automatically simplifies to Newton's law of gravity whether you ask it to or not.

 

[davidge]

Oh, ok. Thank you all. I will read something on the subject.