# What does it mean to say image is formed at infinity?

In case of a concave mirror, when the object is at the focus, my book states that the image is formed at infinity and is highly magnified, real and inverted. But the reflected rays are parallel and will never meet, so no image will ever be formed no matter the distance, right?

How can an image be formed at infinity?

• Your concern relates to the definition of infinity. The current "official" definition of infinity as an Extended Real Number is logically inconsistent despite the fact that many would argue to the contrary. Long story short, in your case infinity means very far, so far that increasing the distance any further would make no difference in your system. "Parallel" is a mathematical abstraction that in reality holds true only approximately (light is a wave). Parallel means parallel enough to not be able to detect any angle. So the practical infinity in optics is about 100,000 focal distances. – safesphere Aug 27 '17 at 20:07

The equations are symmetric with respect to "image position" and "object position": If we start with an object at position $X_o$ and the mirror creates an image at position $X_i$, the swapped positions $X_o \leftrightarrow X_i$ fulfills the equation as well.

Now, if we start with an image at $X_i = \infty$, the light rays, which fall onto the mirror, will be parallel. The mirror reflects these and forms an image at the focal point $X_i = f$. What happens, if we put the object at the focal point, $X_o = f$? Well, due to the symmetry, the image positions becomes the old object position, $X_i \rightarrow X_o$.

So, also the image is never really formed, we still say that "the image is formed at infinity" just to maintain the symmetry of the problem. However, since this can never be measured, the wording is only a convention, not an experimental fact.