Most of these answers are assuming you’re asking about a situation that isn’t concerned with light source or direction, and that you are _only_ concerned with whether you can see through the _density_ of fog.
Let’s say the fog covers 5km^2 with whatever density is needed to make your hand nearly hidden at 2ft. That’s a lot of fog. Now, does it matter if that fog is 10km^2 instead? How about 2km^2? If you are 1km in and thus 1km closer to the edge, is that shortened distance to the end of the fog enough to make a difference in whether you can see your hand? No, not really.
Now let’s get closer to the answer to the question I think you’re asking. Let’s say _you_ are not in the fog; your eyes are 1ft outside the boundary, but your hand is 1ft inside the boundary. Let’s also assume this is during the day with the sun overhead. What will happen? More than likely, you won’t see your hand at all. But why? You could sort of see it when you were _in_ the fog, but now there is the distance of 1ft of fog between your hand and eyes and you can’t see your hand at all.
You’re experiencing, in part, [refraction](https://en.m.wikipedia.org/wiki/Refraction) and [reflection](https://en.m.wikipedia.org/wiki/Reflection_(physics)). This means a few things are occurring:
* The light coming from the sun is reflecting off the fog boundary into your eyes
* The light is not penetrating deeply enough into the fog because of refraction, which means less light is bounced off your hand
* The light that does make it to your hand is also refracted on its way back out toward your eyes
The first point is key. Essentially, when you are outside the fog, the light coming into your eyes from the fog boundary is brighter than anything else in the fog, so that’s what you end up seeing. When you’re in the fog, you don’t have that reflection off the boundary, so the scattered and refracted light is more visible to your eyes. This is also why it’s a bad idea to turn on your car’s brights when you’re in fog, as it so happens.
Visibility in fog is constant, wherever you are relative to it. Let’s assume there’s fog with 50ft of visibility.
* If you are 500 feet away from the fog, you can see 550 feet before things become fully obfuscated. You therefore can see thru only 50ft of the fog.
* If you are 500 feet into the fog, you can see 50ft in all directions. This means there’s now able to see 100ft diameter of fog, which is effectively twice as much things to see than while standing outside of the fog.
* If you are 40 feet from the edge of the fog looking out, you can effectively see everything outside of it (albeit partially obfuscated), so your visibility is technically infinity.
So if you’re “looking in”, you’re almost guaranteed eventually stop seeing things. But if you are “looking within”, or “looking out”, it feels like you can see more.
Imagine the particles suspended in air, vertical sheets or layers. Every layer blocks some part of the vision. Suppose these are the layers:
L1: .. . . .
L2: . . … .
L3: . . . . ..
L4: . . …
So now someone standing at L1 (facing L4) can partly see L2 (because of the gaps in L1), even less of L3 and none of L4.
So when you are ‘in’ the fog, you can see things close to you because there are not enough ‘layers’ or suspended particles covering the things up close (say at L2), but you can’t see ahead of you because the ‘layers’ stack up (say at L4).
I hope 5 year olds can get this.
You don’t actually see better in the fog. How well you see depends both on how much distance is between you and something else as well as how much fog is between you and the thing.
Say there is a house in the fog. You stand a good bit outside the fog and can barely see it. Now you walk into the fog and can see it much better. Not because you’re in the fog but because you’re much closer to the house now.
You can see through only so much fog, in it or out of it. Let’s say it’s a fog so dense you can see for 3 feet. In it or out of it, you can still see 3 feet into it. If you’re in the fog, you see through 3 feet of it in all directions, if you’re outside of it, it’s impenetrable only after the first 3 feet of haziness. Someone standing in the first 3 feet of this theoretical fog bank, while you were outside of the fog bank, would be as visible to you as if you were standing next to them in the same fog.
You could get the same idea with panes of tinted glass.
Put a piece of tinted glass (hypothetically) a foot from your face. Then another a foot behind it, then another and another. Say you’ve now got 10 panes of glass a foot apart and you looking through all of them at a flashlight at the other end. Even if they’re all quite lightly tinted, by the time the light gets through all of them to your eyes it might be extremely faint or not visible at all.
Now move your head in 5 panes. The light is brighter. It didn’t get brighter, there are just less panes between you and the light.
Same with fog. It’s blocking light at a certain “percent” like the tint and the more of it you’re looking through the less light you’re seeing.
So like when you moved up 5 panes and got closer to the light. You could see it better. Imagine instead of moving up you just put the 5 panes behind the flashlight. That’s fog. There is still 10 panes, but now there is only 5 between you and what you’re seeing. You can’t see anything beyond 10 panes, but anything that moves within 5 panes of your eye becomes visible.
It’s more about where the *source* of light is, and less about where the observer is.
Imagine you are in a clearing in a forrest, and there is a campfire hidden in the dense trees. All the light from the campfire gets blocked by the trees and can’t reach your eyes. It isn’t until you walk into the trees, and have fewer trees blocking your view from the fire, that you can clearly see where the fire is.
Now, if you put a fire in the clearing, and hide a flashlight in the trees, the light from the fire makes all the trees on the edge of the forrest brighter around you, preventing you from finding the flashlight. You would have to walk into the trees and have the light from outside blocked to have any hope of finding the flashlight in the forrest.
In this analogy, the water droplets in the air act like very many tiny trees, blocking your view of the light coming from inside the fog. You have to put some of the fog behind you to be able to see things inside it, simply because there is fog blocking the light from getting to your eyes. In addition, all the light around you outside the fog gets reflected on the edge of the fog, completely overwhelming the light coming from inside the fog. You have to block out the light outside the fog by going inside, to have any chance of seeing a weaker light inside the fog.
Ok, let’s do an experiment.
Take a piece of paper and a magic marker. Write a number between 0-9 that is 7” tall on the paper.
Take that paper, pin it to your wall. Then get your kitchen colander and hang it in front of the paper.
Walk 15 feet away and look back at the wall. The paper is completely obscured. You have no chance to read that paper behind it.
Now walk back to the wall, collect your colander, go back to your previous position and hold the colander up to your nose.
Now you can see through the holes and clearly make out the writing on the paper!
The reason is the obscuring object is closer to your eyes so the gaps between them make up a larger part of your field of vision. The further the object is away, the less it takes up your field of vision. This is also true of the gaps.
It is trivial to see through 5 feet of fog, because the gaps between the water droplets in the air are relatively close to your eyes. Visibility has to do with the thickness of the fog, not the placement.
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