How to connect two cylinders with a third one connecting the two? I am trying to make a sketch of an optical setup.
Currently I am using long cylinders as beampaths. (if anyone has better suggestions, those are also very welcome)

My problem is that I want to connect my beampaths, such that each one of them makes a full path (just like the light in the real setup) which seems to be astonishingly hard in blender. I would like to simply enter start and end point of the line, then create a cylinder along that, but could not yet find a way to do something like that and rather have to work with Euler angles.

The image shows the setup I have this far. Between the two lenses I want to show the four beams from the left being focused and exiting the lens setup, connecting to the right four paths.
If I understand you correctly, you are looking for a curve with a bevel object.

When you are in objectmode, i would recommend to start with a bezier curve. go to the curve properties and there you can give it "thinckness" with a so called bevel object(has to be also a curve object). 



I assume that you need a circle for the cilindrical shape of the ray.

you can also change the diameter by adjusting the size of the bevel object. 



for getting sharp angles in your curve you also have to change the handle type of the curves vertices to  vector (Shortcut: V). 
therefore you have to be in editmode:



If you want to connect multiple objects together, select every object you want to join and then press CTRL+J. 

BUT 

It is not possible to "weld" multiple curves together, because a curve vertex can only connect to two curve segments. 



The only way is, to convert the curves to meshes (ALT + C)
and then you are able to connect the parts via mesh modeling.