# In an optical system with a single convex lens, where should the image area be placed in order to take pictures at infinite focus?

I'm trying to learn how camera lenses work, and have gotten stuck. Say that we have an optical system consisting of a single lens with focal length f, and we want to take pictures of objects which are infinitely far away. The light rays will in other words be parallel, and when these rays pass through the lens they will be focused at a single point at a distance f away from the lens. But, how can we then take pictures of such objects if all of their rays are focused at a single point?

I'm not questioning the laws of optics since obviously they work, but I can't figure out where the error in my thinking is. Could someone please shed some light on this (pun intended)?

EDIT: For those who are interested, this question is closely related (although not exactly the same).

Rays from the scene do not converge to a single point. Only rays coming from a single point in the "infinitely distant" scenery converge to a single point in the focal plane. Rays from a different point in the scenery converge to a different point in the focal plane. And all the different rays from all the different points in the scenery converge to their respective points in the focal plane, thus reconstructing the scenery in a 2-dimensional image.

The focal plane is generally curved, unless the lens is specifically designed. You can find some nice drawings of this here.

• This leads me to a second question: the focal plane behind the lens, would it need to be curved like the lens in order to retain the focus, or is it sufficient with a flat surface? – gablin Jul 15 '14 at 13:59
• @gablin Yes, the focal plane is generally curved. The lens can be designed in a special way to provide flat focal plane, but the simple usual lens provides curved field. I'm going to add this into my answer. – mpv Jul 15 '14 at 14:11
• Although Dr Chuck's answer has higher votes, I'm going to accept this one because of the image which was very helpful to me. – gablin Jul 16 '14 at 13:12

It is not the case that all the rays will focus at the same point. Rays with different directions will focus at different points. You are probably thinking about rays parallel the the optical axis all converging on axis, at a distance equal to the focal length from the lens.

• Just to be clear - with "rays with different directions", do you mean rays that hit the lens at different angle with respect to the normal of the lens? If so, is it then true that all rays which strike the lens exactly parallel to the normal (that is, at 90 degrees from the axis of the lens) will be focused to a single point behind the lens? – gablin Jul 15 '14 at 13:56
• @gablin Yes, all rays that are parallel with the lens axis will arrive to a single point. But rays from different locations in the scene do not enter the lens exactly parallel. They are coming from various directions and are focused to different points in the focal plane. – mpv Jul 15 '14 at 14:43
• @mpv - yes, you beat me to it (and as shown in the diagram in your earlier answer). – Dr Chuck Jul 15 '14 at 14:45

In the configuration you described (Infinite/focal plane conjugation) the lens acts as an angular position to linear position mapping system. Each parallel ray bundle at a given angle $\alpha$ with the optical axis converge to a position $y$ away from the optical axis in the focal plane and:

$y = \alpha.f$

where $f$ is the focal length of the lens. The size of your image (zoom) is then determined by the focal length.

• Of course! This explains why a shorter focal length gives a higher angle of view, since with a longer $f$ you need a smaller $\alpha$ in order to reach the same offset $y$! – gablin Jul 16 '14 at 13:10