Yes
But those who interact with it are allowed a Will Save. So if you cast right in front of your allies, you can tell them that it's an illusion and they can touch it and gain a will save, those 50 feet away are not allowed a will save until they interact with the illusion in some way, such as shooting an arrow at it.
Silent Image is a figment:
Figment: A figment spell creates a false sensation. Those who perceive the figment perceive the same thing, not their own slightly different versions of the figment. It is not a personalized mental impression. Figments cannot make something seem to be something else. A figment that includes audible effects cannot duplicate intelligible speech unless the spell description specifically says it can. If intelligible speech is possible, it must be in a language you can speak. If you try to duplicate a language you cannot speak, the figment produces gibberish. Likewise, you cannot make a visual copy of something unless you know what it looks like (or copy another sense exactly unless you have experienced it).
Because figments and glamers are unreal, they cannot produce real effects the way that other types of illusions can. Figments and glamers cannot cause damage to objects or creatures, support weight, provide nutrition, or provide protection from the elements. Consequently, these spells are useful for confounding foes, but useless for attacking them directly.
Also, the spell says it does not create texture, so if they touch the wall with their bare hands, they will most likely automatically know it's not real (no will save required) and can walk right through the illusion, but will not see it as a translucent image unless they pass their save.
The illusion does not create sound, smell, texture, or temperature.
If someone (ie: the caster) tells them that it's an illusion, they gain a +4 bonus to their will saves:
If any viewer successfully disbelieves an illusion and communicates this fact to others, each such viewer gains a saving throw with a +4 bonus.
The thing is, if wether you know it's an illusion or not does not automatically make your brain believe it. That's the point of illusions, tricking the senses. Though i do agree that it's the magic school that sees the most table variation in the game. Even if you know it's a silent image, like identifying it as it's being cast, someone told you what it is and what it does, the image is there and looking very real to you. Knowing what the spell does will allow you to walk right through without analyzing it, but it does look like a real wall to your character.
What counts as interaction is normally up to your GM, as the rules do not clarify that, but that will depend on what is the illusion and how people could interact with a real version of that illusion. The Ultimate Intrigue defines this interaction as spending at least one move or standard action with the illusion, but whether or not your table uses that rule is the GM's decision.
What is interacting with a wall? Touching it, trying to climb it, hitting it with a hammer, shooting something at it, etc.
What is not interacting with a wall: Looking at it, talking to it, waving at it, yelling at it, etc. Note that some of those examples could work against other types of illusions, such as an illusory dog or bear, and would probably allow a will save, but not against an illusory wall.
It is not possible with minor illusion, as with that
You create a sound or an image of an object (PHB 260)
and neither vacuum, nor air is usually considered an object. (There are discussions about this, looking them up is left to the reader.)
Nor could you use mirage arcane, as that explicitly states, that
The spell doesn't disguise, conceal, or add creatures. (PHB 260)
With silent image and major image there is a hint of possibility:
You create the image of an object, a creature, or some other visible
phenomenon (PHB 276, 258)
It comes down to whether that the space inside the illusion is filled with air is a phenomenon. Even if we accept that it is, this illusion has to change relative to the viewer, which would require precise calculations from the caster and would be essentially impossible against more than one observer.
My personal ruling would be that this is an abuse of the spell and not allowed. It is much more streamlined and easier to handle this way. If a PC wants to be invisible, there is already a spell for it and not even that high level.
Best Answer
The answer to your question is - there is more than one kind of illusion.
Glamers and figments change your senses, so they can't hold up weight. Characters trying to stand on them will fall through (and immediately disbelieve, since they have proof the illusion was a fake).
Shadows can hold up weight just fine.
However, some shadow spells can be partially disbelieved, in which case there is a % chance that the object doesn't "work" and the creature falls through. See shadow conjuration:
Patterns and phantasms affect the mind directly. These illusions can make someone believe they are standing on the floor, while in reality they have fallen down a pit.
For any non-instantaneous spell, the effect disappears once the duration ends. Regardless of what kind of spell was creating the bridge (illusion, conjuration, evocation, what have you) the creature standing on it will fall in the hole.