Field of view vs. range of angles

[ScienceNostalgia101]

So this parody of an old video game portrays a (fictional!) oil explosion on an island from a distance; and the resulting duration of silence before the noise. Obviously, if we were directly given the angle to one end of the island and angle to another we could use geometry to estimate this fictional island's length. But here we're only given the distance to the island (via sound delay) and the fraction the island takes up of the field of view.

 

This got me wondering whether or not "field of view" can be used to estimate "range of angles" between the point of observation and the object being observed. For instance, is there a function relating what fraction of a field of view an object takes up to the difference, in angle, between a bearing to the left side of the object and a bearing to the right side of the object? Does it depend on what these angles are, or only on the difference between them?

[swansont]

You would need to know the magnification to know the angles. The angle between the two points is approximately the length of the island divided by the distance to it. (The exact equation would use the arc length)

[Sensei]

 

13 minutes ago, ScienceNostalgia101 said:

So this parody of an old video game portrays a (fictional!) oil explosion on an island from a distance; and the resulting duration of silence before the noise. 

Surprising attention to the details by movie makers..

13 minutes ago, ScienceNostalgia101 said:

Obviously, if we were directly given the angle to one end of the island and angle to another we could use geometry to estimate this fictional island's length. But here we're only given the distance to the island (via sound delay) and the fraction the island takes up of the field of view.

Parallax is widely used to measure distance to stars in this galaxy..

https://en.m.wikipedia.org/wiki/Parallax

[Trurl]

If you know your exact position and magnitude of explosion (how long the sound took to reach you) the direction you were looking at the explosion, you may be able to determine the location based on arc length.

 

You are at the tangent of that arc length. But the arc length is unique to you who measured it. Different magnitudes would have different arc lengths.

 

I need someone to verify this. But I believe if you have your exact position you may be able to tell.

 

It would be like finding the trajectory of someone shooting at you. The shot is a straight line and the angle. Reverse those and the arc lengths along the tangent to you is where the shooter is. The distance from you to the shooter would depend of the magnitude of the bullet. But to keep the same tangent the shooter would have to move along the same angle. If he shot with greater magnitude and a different field of vision it would be an entirely different arc.

 

I believe what you are trying to say and a question I will asks is:

With different positions having different arcs, do you have enough information to determine the location (knowing your current location) to solve the shortest distance you are from that arc? If you used that magnitude to measure from you to the original explosion?

 

I hope this makes sense. Correct me if am wrong. But it seems you are asking can you find the distance without enough known.

[ScienceNostalgia101]

On 1/5/2020 at 3:52 PM, swansont said:

You would need to know the magnification to know the angles. The angle between the two points is approximately the length of the island divided by the distance to it. (The exact equation would use the arc length)

Magnification... as in camera magnification, or is there an equivalent for "field of view" in the context of eyesight?

[swansont]

10 hours ago, ScienceNostalgia101 said:

Magnification... as in camera magnification, or is there an equivalent for "field of view" in the context of eyesight?

Yes, there is an angular magnification when you use a telescope/periscope. It makes objects look bigger and narrows the field of view, as compared to naked-eye vision. But presumably the object is smaller than the limits of the field of view. If the regular horizontal field of view is 2 radians (for humans it's a little bigger than that) and you have a 10x angular magnification, then the FOV in your device is 0.2 radians.