The area inside the blue is the .02 degrees

That is the unresolvable area

Kinda hard to show something you cant see

The cone does reverse inside the eye.
Light is projected on to the retina. We don't see things directly.
It goes through the lens is projected and inverted. https://cdn.discordapp.com/attachments/379214321907007488/466469361562026015/kan_ch26_f001.png https://cdn.discordapp.com/attachments/379214321907007488/466469513500688384/retinaimage.png Those images are right for a single point of light. This is part of another misconception. https://cdn.discordapp.com/attachments/379214321907007488/468563187713835020/unknown.png This illustrate how we would see a SINGLE point of light. Say a single photon reflecting off the molecule of a wall
Take notice how it emanates in a sphere. Now what we see is the light reflecting from EVERY molecule spherical , and traveling out. The important thing is this. The airy disks I started with.
That is what EACH point is.
Trillions (probably more) of points of light. We don't see each point. We can only differentiate points to the angular resolution limit.
So a trillion points in a 4 ft space at 3 miles looks like a point. Think of the horizon as a bunch of points of light, and not as a building , a boat or mountain.
Then equate an entire object to a point of light. As far as the angle goes. The angular size on an object has the same angular size when projected onto the retina.

Let's work from the center of vision out to the edges , Up (sky) Down (ground) So this image https://cdn.discordapp.com/attachments/379214321907007488/468559885718519848/unknown.png Below the blue you can only see ground
Above sky.
Now how do we bring the max viewing distance into focus?
max viewing distance of the ground
that is... We can only use the bottom half of our vision.
The central part is unresolvable.
The upper part is looking for the sky. The angle between B and C is fixed. We will say the same as the eye .02 degrees. So we are seeing above and below the blue cone but not the cone itself. Like seeing the horizon...the horizon is unresolvable...but the ground leading to it and the sky above it we can see. Question: So what happens when line A to C gets parallel to the ground? Answer: Whatever is in the cone is gone, the cone turns to a line. Exactly and what's in that cone. Anything in a line extending from A to C to infinity will never intersect the ground . But the cone is the area between B and C. So the ground stops at B , anything above point C can only see sky. So the cone in the drawing is the unresolvable part of the camera lens or our vision.

Look , these are the same distances. Obviously the angles are not the same. https://cdn.discordapp.com/attachments/379214321907007488/468569265574903818/unknown.png I can make it even more extreme... https://cdn.discordapp.com/attachments/379214321907007488/468569771735253012/unknown.png But guess what....the top of the building will get cut off. When the entire situation is reverse.
Image looking up with your chest up to the world trade center. You wouldn't see the top because the angle would be too shallow. https://cdn.discordapp.com/attachments/379214321907007488/468570710344728576/unknown.png Look what happens when you are closer to the vertical than the horizontal, the reverse. https://cdn.discordapp.com/attachments/379214321907007488/468570964817608715/unknown.png Here are some questions you can ask yourself. Where is the plane of the eye? What is the relative angle between the surface of target and the plane of the eye? Give that angle , what is the angular separation of the points of light on that target? https://cdn.discordapp.com/attachments/379214321907007488/468574743637786645/unknown.png The relative angle to the plane of the eye and the optical tilt of the target determine the angular separation
If I rotate the green block until it is vertical all the angle will grow. If I rotate it counter clockwise all the angles will shrink. If It was more to scale the angle difference would be more dramatic. https://cdn.discordapp.com/attachments/379214321907007488/468578052302176266/IMG_3195_one_world_trade_center_nyc2015_aagdolla-1038x576.jpg https://cdn.discordapp.com/attachments/379214321907007488/468578348789006336/502382332.jpg Now imagine the building is 3 miles tall and not 1776ft.

https://youtu.be/vSAlVua7T4g

Ok I get it geez

Watch the video

It is best

So in this case C would be the top of the object and B would be the bottom of it, right?

Basically

Its the center of our vision

Ok

And if the angle BAC is less than 0.02 it's unresolvable, right?

B is the ocean and c is the bottom of the boat

Yes

If it hits .02 degrees then its gone

Ok I understand it now

So the further you get away from the object the more the angle will change

Mmhmm makes sense

Nite =)

Ok

I think I have what I need to disprove it now

You cant disprove it

Its the way it works

<:lul:484994724118134784>

Ok then let's do the math

The given information is two separate facts that you have given thus far

First, the angle between the top of the object and the bottom needs to be less than 0.02 degrees in order for it to be unresolvable

No it is .02 degrees

Second, objects disappear from view at a distance of three miles

I said objects 5 feet high disappear

That's fine

Equal or less than

A 6 foot man at 3 miles you would still see his head

Mmhmm

His legs and body would blend in with the horizon

Gibson_1952_The_perceived_slant_of_visual_surfaces--optical_and_geographical.pdf

Fair enough

Gibson_1952_The_perceived_slant_of_visual_surfaces--optical_and_geographical.pdf