I came across a video by Youtube author p-brane which seems to bring up a lot of good points, showing that the diagrams which are routinely paraded as examples for why the sun cannot set do not accurately demonstrate perspective.
First of all, I just want to say that the guy in the video is flat out wrong. He has absolutely no idea what he is talking about. A big hint is that he doesn't try to show the
correct way to calculate the angle (because he has no idea what the correct way is). I know you won't take my word on this, so....
Let's test who is right! We have the technology!
Proposed experiment: Supplies: 3 Thumbtacks. A role of string. A protractor. A camera. A tape measure. Two straws. Sticky tac.
Steps:1. Stick the thumbtacks in the wall like so: (Try to make the angle A relatively small so it will easily fit in the FOV of a camera.)
C *
B * * A
2. Tie the string between thumbtacks B and A, and C and A. Make sure the string is tight and straight.
3. Measure the angle between A-B and A-C as seen from the side using two different methods:
a. Use a protractor to measure the angle between the pieces of string leaving point A.
b. Use trigonometry to measure the angle based on the distances between each point. If you don't have a perfectly right angle at point B, then you can use the
law of cosines.
4. Measure the angle from the perspective of A using two methods:
a. Take a picture of B and C from the perspective of point A with a camera. Make sure you know the field of view of the camera. Make sure the camera has minimal barrel distortion. Measure the distance between the points in the picture, and convert it to an angle based on the camera's FOV.
b. Spot point B from point A with one eye through a straw. Once you have it spotted, carefully fix it to the wall with sticky tac (or tape, or something). Do the same with point C. Measure the angle between the straws with a protractor.
Interpretation:The angles measured in step 3 represent the angle from the "side view" diagram.
The angles measured in step 4 represent the "perspective" angle, which is supposedly different from the side view.
If I am correct, the angles measured in steps 3 and 4 will all be the SAME.
If Tom Bishop and the video are correct, the angles measured in steps 3 and 4 will be DIFFERENT.
Any takers?