A 532 nm laser probe with a 5 mm lens tube means, the laser can be focused at 5 mm distance from the lens tube. Similarly what I can infer from the -20 mm lens tube?
I’m confused by your use of the word “tube”. A lens tube is not a lens. It is a tube into which lenses may be mounted to make a lens system. I can’t imagine what it would mean for a tube to have a negative length.
Lenses themselves, on the other hand, can be positive or negative and are characterized by their real or virtual focal lengths.
I think you may have fallen victim to a quirk of English where it isn’t clear which word an adjective describes. You might have a negative lens with a -20 mm focal length. You might refer to it as a -20 mm lens. You may mount that -20 mm lens in a lens tube. You may want to refer to the tube you are using to hold that -20 mm lens as the “-20 mm lens tube”. In this case it may seem like the “-20 mm“ is describing the tube, but it’s not. The tube is being described by referring to the lens it is holding. It is the tube that is holding the -20 mm lens. It is the {-20 mm lens} tube. When we write words out we have a solution for this problem. The words that go together are connected by hyphens. So, if you write “the minus-twenty-millimeter-lens tube” then it is clear that -20 mm describes the lens, not the tube. However, we don’t do that with numbers. (It would be particularly strange with the minus sign!) Instead, we figure it out by context. A -20 mm lens makes sense. A -20 mm tube does not. Thus, a “-20 mm lens tube” is a tube which is being used to hold a concave lens which has a -20 mm virtual focal length.
Thanks a lot Mike Albert for the correction. I am rephrasing my question with explanation. Yes I am referring a lens that is mounted on a tube. The 5 mm lens is a Plano convex where -20 mm is Plano concave lens. Both are mounted on a tube. Now is it clear ?
Ah. Ok. So the meaning of the focal length of a positive lens is clear, right? Parallel rays coming from the left are bent by the lens towards the axis and all meet at a point to the right of the lens called the focus. The distance between the lens and the focus is the focal length. You can think of that focal point as a “real image“. Those parallel rays from the left are from some distant point source. Those rays coming together at the focus are like a new point source. If you continue to they right it would appear to anybody to the right of the focus that all the light is coming from that focus. In fact, if the distant object is not a point source, but something big enough to resolve (say, the sun for example), there will be an image of the object formed at the focus, and, again to anyone to the right of the focus it will appear as if the light is coming from an object (for example a tiny sun) located at the focus.
With a diverging lens the rays are bent away from the axis and they never come together at a real focus. However, if you trace the rays backwards, it looks as though all the rays are coming from a point to the left of the lens. The distance between the lens and this virtual source point is the focal length.
In either case, someone looking from further to the right will see the light as coming from a source located at the focal point. In the positive lens case the light will seem to originate (and actually will originate) from a point to the right of the lens. In the negative lens case the light will seem to originate from a point to the left of the lens. If we take the lens axis to be a spatial axis with the lens at zero and the downstream direction (to the right in my example) as positive, then a positive lens makes a real image on the positive side of the lens and the negative lens makes a virtual image on the negative side of the lens.