Seeing the image as explained by Geometrical optics?

Question

I was thinking about how the human visual system perceives the position of an object. I assume it essentially does this by focussing the incoming rays onto the retina and then judging from the power of the lens required to focus and the size of the image, it guesses the position. Assuming this process to be present always, the net result is that we can assume that when a set of diverging rays from a point fall on the eye, it traces the position of the object to the point from where it appears to diverge. But then in two cases I fail to see what we will "see"!

1] when using a convex lens, as in simple microscope' the image is formed at "infinity" and the object is at focal point. Then the rays are parallel. But still we can see the image and what is more, there is even a high-school formula for the angular magnification in this case! But if the rays are parallel how can they be traced back to appear to be diverging from one point where the image of the object will be perceived?

2] What if the rays are converging, in case we poke our eye in the path of the rays coming from a object placed in front of the convex lens such that our eye is pushed in between the lens and the place where real image would have been formed? Then the rays are converging so can we still see the image or the object looked at through the lens becomes invisible?

And on a small side question, when we say that the object is at infinity, all we mean that the rays from each point are parallel to one another but not that the rays from different points are parallel, right?

Answer 1

A quick note on your assumption about the eye: this isn't how the eye judges distance. In fact the eye doesn't judge distance at all. The brain judges distance by comparing the images from the left and right eyes and using parallax to estimate the distance.

Anyhow, I remember being puzzled about the forming of images from objects at infinity. The point to remember is that any object at infinity, no matter how big, will appear infinity small so all rays from any part of the object will come from a single point and will therefore be parallel. Any object that has a finite angular width is not at infinity, even if it's as far away as the Andomeda galaxy! This does have the slightly paradoxical result that infinity, at least as far as your eye is concerned, is farther away for large objects than for small ones. As you note in your question, the best way to deal with this is to use the formula for angular magnification rather than use the distances.