Constructing a periscope/telescope - trouble with lenses Not sure if this is the best place for this, maybe physics would be a better fit, but I'm trying to build a periscope and am running into an issue. 

Traditional mirror periscopes work well, but when I look into the one end of the periscope, I see the reflected image at the end of a long tube. I figure that using some combination of lenses, you should be able to make it look as if the position of your eye/head was actually at the top of the tube looking out at the world rather than looking through a tube. 

My thinking here is that when you look through binoculars or a telescope, you don't see the inside of the tube, just the enlarged image. So shouldn't you be able to do the same thing but without the magnification?

I purchased some lenses from Amazon with focal lengths of 200mm and -100mm and based on some optics simulators assumed(incorrectly apparently) that I could arrange them 10cm apart and then another set reversed on the other side like so:

`````()````````````````)(```````````)(``````````````()
200mm````````-100mm``-100mm```````200mm

() = convex lens
)( = concave lens

The thinking here was that one set would condense the image down so that the walls of the tube were no longer visible within that viewing angle, and then the other reversed set would reverse that and the image would be back at normal size to my eye, it would just look as though my eye were actually at the opposite end of the tube. 

This didn't work. The image is close to life size, but the tube looks even longer: a foot long tube has turned into a 3 foot long tube, and the circle I can see the world through is very small.

Is this a pipe dream? I feel like it must be possible if they used periscope in military applications for years before electronics and fiber-optic cables were invented. 

Where did I go wrong? Any guidance would be hugely appreciated.

Edit: some follow up questions

Am I stuck having a small field of view out of the end? Or would using a lower focal point(wide angle) lens allow me to see a wider angle?

Also, is there any way to have a variable length tube? For instance if I'm looking around a wall, is there a way to install the lenses so that the tube could be "telescoped" out to look around a thicker wall?
You're close!  What you built is a back-to-back set of Galilean telescopes (with an overall magnification of 1:1).  The reason you're getting a smaller circle, but with a life-size image, is that the light bundles in the middle are diverging faster, and so you lose the edges if the Galilean assemblies are too far apart.

Military perisopes use optical relays to get the image down the tube without blocking out any of the view.  In simple terms, they have one relatively short-focusing  group of achromatic/apochromatic lenses (called an Objective) to focus the light to a crosshair, like in a rifle scope.  From there, the image is picked up by another long-focusing lens group called a relay.  The relay re-collimates the light (but at low angles).  The light is focused and collimated several times through the tube, until it reaches a final image plane, which is then looked at with an eyepiece (like you might have in a telescope).  

Overall, you can think of a periscope as a telescope/monocular/riflescope with relatively low magnification with several pairs of relays in between.  A point of note, you need an even number of image planes (0, 2, etc) to avoid having an 
upside-down image.  I can go into a lot more detail or provide some resources, but I think this most directly answers your question.  Please let me know if there's any other questions on this.

Source: I design optics for periscopes for naval applications.

Edit for additional questions:
First, the most comprehensive resource I found in my lazy search is this page: http://taylortechassoc.com/?page_id=97, which is actually written by a previous engineer at my company.  There's a ton of information there, mostly intended for people who already know about optical design, but there's probably a good amount you can get from it as well.

To the question in your comment: in your preliminary design, the positive and negative lenses are taking collimated light input, and outputting collimated light.  However, since they are acting as a telescope with magnification power, the angle of the rays coming out is wider than the angle going in (by a factor equal to your magnification).  The trick to a relay lens design (used in periscopes and some kinds of endoscopes, as well as other applications) is to get the collimated spaces short enough that you don't lose that light before it spreads out.  Or more accurately, that you get the angles of the collimated light to be small enough that you can spread out your lenses quite a bit while still maintaining this condition.

Regarding field of view: you're absolutely not stuck with a small FOV.  That depends entirely on the focal length of your objective.  A short focal length lens as your objective will give you a wider field of view (so long as your light isn't clipped by your top mirror).  You could also have an objective that changes focal length (a zoom lens) to change your field of view as desired.  For your application, an SLR camera lens could work quite well for this.

Regarding tube length: You could vary the spacing in the sections where the light is collimated.  This will impact how much light is being lost from it spreading out too much (typically limited by whichever section is longest).  The result will be a dropoff in the relative illumination (how bright the edge of the FOV is compared to the center).  This is an effect known as vignetting, and can be mitigated, but not without tradeoffs.