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?

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    $\begingroup$ There are textbooks which state that no image is formed and there are textbooks which state that a real image is formed at infinity. I don't agree with the latter for the reasons you have mentioned. $\endgroup$ – Yashas Feb 27 '17 at 16:39

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.

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    $\begingroup$ But if we produce 2 parallel lines backwards, they would still remain parallel. So does that mean that one image will be real on the other side of the lens and virtual on the same side of the lens, and vice versa for concave mirror? $\endgroup$ – Saksham Feb 27 '17 at 17:11
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    $\begingroup$ @Saksham : In practical terms, an object can never by exactly at the focal point, just as an image can never be exactly at infinity. The object (or part of it) will be a very small distance in front of or behind the focal point. $\endgroup$ – sammy gerbil Feb 28 '17 at 2:39
  • $\begingroup$ @Saksham This might also help: Your eye isn't really a point: the photoreceptive area of your eye is (roughly) a disk, and thus, if you have your eye in the path of parallel light rays, different parts of your eyes are going to pick up slightly different "spots" on the reflected "image". If you were really far away from an object, the reflected light rays from it would be effectively parallel to each other by the time they reach you. So the further your get away from the mirror, the more the reflected image you see will match what the original image would look like at that distance. $\endgroup$ – mtraceur Apr 10 '17 at 3:31

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.


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