Why do light rays going to infinity form a real image? My physics textbook tells me that when an extended object is placed at the focus of a concave mirror, the light rays reflect and go parallely towards infinity. Same happens when refraction occurs in a convex lens, when the object is placed at the focus of the lens. The book goes on to tell that a real, inverted and highly enlarged image is formed in the given situation. 
 So my question is : 

If the light rays, after getting reflected from a concave mirror (or after getting refracted from a convex lens), go parallely towards infinity, then how do they form a real and inverted image? (Because parallel lines do not intersect).

 Because to form real images, actual intersection of light rays must occur. But in this case, that doesn't happen. How can an image, if any, be formed in such a situation?
 A: Saying that something is at infinity is a convenient way of saying that the distance involved is much, much greater than the focal length.    
So when the object is placed in the focal plane of the lens/mirror it is convenient to say that the image is formed at infinity.  
In fact, in theory, the image is actually in two places.
On a screen as a real inverted image a long way away from the lens and on the opposite side of the lens to the object.
A virtual upright image a long way away from the lens which can be seen by looking through the lens at the object.
How can one infer all this?
By having the object close to the focal plane but remote from the lens and observing the image formed on a screen as being real, inverted and magnified.
Then moving the object closer and closer to the focal plane, seeing what happens and then imagining what would happen if the object was in the focal plane.  
In the end all of this is theoretical because real lenses have defects and your analysis has dealt with ideal situations.
A: Other textbooks do not say this. As you surmise, they operate under the assumption that parallel lines do not meet. None of the textbooks I've used for my Physics curriculum, including AP, have spoken of images from idealized cases with objects at the focus.
However, if you search the web, you can find many questions of a mathmatical nature whether parallel lines meet at infinity. I guess the author of your text subscribes to one of the "yes versions" of this question. In my opinion, it's a non-functional assertion that adds little to understanding how optics work.
