Image of a Convex Lens Cut in Half Horizontally

[LovePhys]

Hello everyone,

A friend of mine came up with this question in class and I really do not have a good answer.

Suppose you have a convex lens that has been cut in half horizontally and the top half removed.

The question is: Will the bottom half of the lens still form an image?
I really have no idea of how approach this problem. Normally, suppose that an object is placed on the principal axis, then one of the three special rays is supposed to go through the optical center of the lens. But in this case, the top half has been removed, would that have an impact on the optical center?

Any help would be greatly appreciated.
Thank you,
LovePhys

 

[jtbell]

The image is formed by rays that pass through all parts of the lens. Cutting away half the lens (or equivalently, blocking half of it with a piece of cardboard) blocks half the rays, but the other half still go through and reach the image, at the same location.

The principal rays are special only for us humans, because they're easy to trace through the focal points so we can use them to locate the image quickly.

In the diagram below, the principal rays are in red. The other rays in black each contribute equally to the image.

 

[physwizard]

Thats right. Reducing the number of rays will only cause the image to dim.

 

[LovePhys]

@jtbell and physwizard: I understand it now. Thank you very much!

 

[Zag]

That's a nice way of thinking about the problem, jtbell! :)