The basis for most optics based conclusions I have reached. [[Optics Angular Resolution or Earth Curve]] [[The Horizon]] All images taken from this video: # Angular Resolution and Our World <iframe title="Angular Resolution and Our World" src="https://www.youtube.com/embed/aVAWQGlXRWg?feature=oembed" height="113" width="200" allowfullscreen="" allow="fullscreen" style="aspect-ratio: 1.76991 / 1; width: 100%; height: 100%;"></iframe> ![[Attachments/Pasted image 20240908144024.png]] This effect is due to the limitations of angular resolution, causing the bottom to become indistinguishable before the top. as objects move further away on a flat surface, the bottom becomes invisible first due to the limits of angular resolution. The angle from the observer's eye to the bottom of the object becomes too shallow to resolve, making it disappear before the top. the eye's minimum angular resolution of 0.02°. This means that details smaller than this angle cannot be distinguished. As objects recede, the angle to the bottom becomes smaller, making it harder to resolve compared to the top. with a fixed angular resolution of 2.1°, distant points visually merge. The ground between points becomes unresolvable, causing the bottom of objects to disappear first.  the angle to the bottom of an object is shallower than the angle to the top. As distance increases, the bottom angle becomes too small to detect, while the top remains visible longer. 1. **Angular Resolution**: - Defined as the smallest angle between two points that can be distinguished by the observer. - In the first image, the angular resolution is fixed at 2.1°. As the distance increases, points D and E visually merge because the angle between them becomes smaller than the resolution limit. 2. **Visual Merging**: - When objects are far away, they may appear to merge due to limited angular resolution. This results in unresolvable ground between points, making it difficult to distinguish separate objects. 3. **Angle of View**: - The second and third images show how the angle of view to the top of an object decreases with distance. This reduction gives the appearance of the object getting lower in height. 4. **Perception of Sinking**: - The combination of decreased angle of view and merging of distant points creates a visual effect where objects appear to sink into the ground as they move further away. 5. **Orthographic View**: 1. **Geometric Proof of Visibility Limit**: - This image suggests that objects become invisible from the bottom up on a flat surface due to angular resolution limits. As distance increases, the bottom of objects may disappear first because the angle of view becomes too shallow to resolve them. 2. **Angular Resolution of the Eye**: - This image explains that the human eye has a minimum angular resolution of 0.02°. This means that two points must be separated by at least this angle to be distinguished as separate. The table provides visual acuity limits for various properties, emphasizing the eye's resolution capabilities. 3. **Fixed Angular Resolution**: - Here, angular resolution is set at 2.1°. As distance increases, points D and E visually merge, demonstrating that nothing is viewable between them. This illustrates how limited resolution leads to merging of distant points, making them indistinguishable. 4. **Angle and Distance Perception**: - This image shows that the angle to the bottom of an object is shallower than the angle to the top. As distance increases, the top of an object appears further away than the bottom, contributing to the perception of the bottom disappearing first. ### Analysis - **Angular Resolution Impact**: These images collectively demonstrate how angular resolution affects our ability to perceive objects at a distance. The bottom-up disappearance of objects is a result of the eye's limitations in resolving shallow angles. - **Practical Implications**: Understanding these concepts is crucial in fields like optics, photography, and visual design, where precise perception is necessary for accurate interpretation of visual information. <iframe title="Bottom Up Obstruction" src="https://www.youtube.com/embed/6pU0pKQh23E?feature=oembed" height="113" width="200" allowfullscreen="" allow="fullscreen" style="aspect-ratio: 1.76991 / 1; width: 100%; height: 100%;"></iframe> ![[Attachments/vlcsnap-00506.png]] ![[Attachments/vlcsnap-00507.png]] ![[Attachments/vlcsnap-00508.png]] ![[Attachments/vlcsnap-00509.png]] ![[Attachments/vlcsnap-00510.png]] ![[Attachments/vlcsnap-00511.png]] ![[Attachments/vlcsnap-00512.png]] ![[Attachments/vlcsnap-00513.png]] ![[Attachments/vlcsnap-00514.png]] ![[Attachments/vlcsnap-00515.png]] ![[Attachments/vlcsnap-00516.png]] ![[Attachments/vlcsnap-00517.png]] 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