Convex lens with object at the focus When the object is at the focus, the image will be formed at infinity.
What exactly does this mean? What will it look like if you hold the entire apparatus at arms length? Will it be extremely blurry? Is it possible for it to act as an 'invisibility cloak'?
If you can add any pictures please do. I don't have a lens handy.
 A: It is easier to think about this in reverse - i.e. what does it mean for light to be approaching from infinity? When we reference light from an object at infinity, we mean that the object is so far away that all light rays (strictly speaking in terms of geometric optics) from the object appear as if they are parallel and traveling in the same direction. When these parallel rays approach the convex lens, they get focused to the focal point of the lens.
In optics, the direction of light travel does not matter, thus when an object is placed at the focal point of the lens, the light rays will become such that they are perfectly parallel and traveling in the same direction. This is usually called "collimated" light. 
Collimated Light
This method of collimating a light source (or object) is generally used in various imaging techniques such as shadowgraph and Schlieren. 
Now what will happen if you place your hand in the optical path of the light? Well, theoretically, you should see nothing since no image is formed from parallel light. But in reality the light will never be perfectly collimated so you may see a very blurry version of whatever your object is. As soon as you place another focusing element in its path though, all those light rays will be focused at its focal point and you will (theoretically) have a perfectly formed image of your object.
A: When a real image forms, all the rays from a single point of the object would 'want' to converge into a single point in the image plane (this is not entirely true in the real world, but for the sake of simplicity, let pretend it is:). If the image plain is at infinity, this means that the rays from said point would converge at infinity, or in other words: will never converge. Rays which never converge are parallel rays. This is also called collimated rays.
This mean that the image would be forever blurry - BUT!! if you would look at a collimated image, you would see it at any length from the lens, because the lens of you eye would focus the parallel rays onto your retina perfectly, regardless of your distance from the lens (because the rays are parallel).
