Why do we never use binoculars or telescopes to spot the object when it gets away

You can go try it

https://youtu.be/5-Law8Cw9kE

Z what would you say the distance is when we see no further
Like at what distance the object disappears and our eyes reach vanishing point

5 foot tall object will be mostly gone with human eye at around 3 mile

Okay

And it doesn't need to obstructed by anything? Our vision just reaches it limit?

Our vision has a limit yes

Globe model says its earth obstructing

Flat model says its our vision and the way light works

Ok

Cameras work the same as our eyes

They have limits also

The further an object (i.e. boat, building mountain) gets away from the lens, the angular separation will continue to close until the light blurs together and eventually becomes a line or point or edge"

Eventually the points of light all merge and appear as just a line on the horizon

I'm back

One more clarification hun

Yes?

By 0.02 degrees you mean the difference in angle between the top of the object and the surface of the sea, right?

I mean the angle at which the photons are traveling to the eye

So you look at your feet then look to horizon ehatever you dont see is because of that angle of light

Yeah but the eye can't differentiate between photons that hit at an angle that is has less than 0.02 degrees of difference?

That's why things merge together?

No if its at .02 degrees then the eye has lost it

What

Little rods and cones in the back of the eye

Cant see anything at the resolution

I'm not following

This is how angular resolution works physically in the eye.
https://cdn.discordapp.com/attachments/379214321907007488/459802853524111361/1_EN.png
Cameras work the same way.
The cones of the retina is a zoom in of the eye. If the angular size of the target is not enough to activate more than a single cones/sensor the object is unresolvable.
There are 3 ways to decrease angular separation.
1. Move the two separate targets further or closer together.
2.Increase the distance.
3. Change the angle of view.
https://cdn.discordapp.com/attachments/379214321907007488/459805458644074511/angseperation.jpg

First here is a demonstration of how angle of view changes the angular separation of 2 targets. https://cdn.discordapp.com/attachments/379214321907007488/459806914331541504/unknown.png

For example in this image, as the stop sign's angular size shrinks from distance or angle, the image that prjected onto the retina also shrinks. Eventually it will reach such as small size the eye can not physically detect the light. https://cdn.discordapp.com/attachments/379214321907007488/459808085436006410/refraction_cornea.png
A geometric analogy would be closing a pair of scissors. When the scissor tips are closer together than the spacing between the rods and cones of the eye then you get to see the target. The point where the tips cross from too close to normal vision is the angular resolution.
https://cdn.discordapp.com/attachments/379214321907007488/459817803038326784/unknown.png

https://cdn.discordapp.com/attachments/379214321907007488/459818062858682368/65116694_resized550bbc_sg_g4_eye.png
When the angle of view becomes to much it pretty much goes parallel, but you lose sight of the ground before that. It's the same on the globe too but even worse because the angle of view is increasing quicker because of the curving away of the ball surface.

These next images show someone how the angle stays the same but the area that you are actually observing increases. You can see the 5th image how the bottom of a building would disappear.

https://cdn.discordapp.com/attachments/379214321907007488/459819761644077057/unknown.png

https://cdn.discordapp.com/attachments/379214321907007488/459813762132869126/ang1.png

https://cdn.discordapp.com/attachments/379214321907007488/459813783464968206/ang2.png

https://cdn.discordapp.com/attachments/379214321907007488/459813767576813578/ang4.png

https://cdn.discordapp.com/attachments/379214321907007488/459813769548267542/ang5.png

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

This guy was a globe earther im pretty sure but knew how optics worked

Hold on bud I'm not finished yet

You have to debunk james gibson

So we would have something like this?

Not me

With 15840 feet equal to three miles

And the eye level of the observer at 6 ft

I dunno what you are trying to work out

Observer 5 feet

Fine I'll change it

Observer 5 feet. 15000 feet..5 feet gone

Ok but this is the information that was given, yea?

Thats with 20/20 vision

🤔

The object would be gone from view at three miles away

We good so far?

Thats what it seems to be when tested at the beach

Ok I'll keep going then

At about 3 miles 5 foot objects are gone

K keep goin. Dont forget to read James gibson

Gnite

Ok just a sec I'm doing the math

Tired nite

This is what the angle would be using the height of the observer and the distance of three miles

Which part ?