Image of a Convex Lens Cut in Half Horizontally

AI Thread Summary
Cutting a convex lens in half horizontally and removing the top half does not prevent the bottom half from forming an image. The image is still produced by the rays that pass through the remaining part of the lens, although the overall brightness of the image may decrease due to fewer rays contributing. The principal rays, while useful for tracing the image location, are not the only rays that form the image; all rays passing through the lens contribute equally. Thus, the optical center remains unchanged, and the bottom half can still effectively focus light. The discussion clarifies that the image will still be formed, albeit dimmer.
LovePhys
Messages
57
Reaction score
0
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.
attachment.php?attachmentid=58939&stc=1&d=1369227004.png

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
 

Attachments

  • lens.png
    lens.png
    1.4 KB · Views: 1,656
Science news on Phys.org
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.

attachment.php?attachmentid=58941&stc=1&d=1369231578.gif
 

Attachments

  • rays.gif
    rays.gif
    21 KB · Views: 1,618
Last edited:
  • Like
Likes 1 person
Thats right. Reducing the number of rays will only cause the image to dim.
 
@jtbell and physwizard: I understand it now. Thank you very much!
 
That's a nice way of thinking about the problem, jtbell! :)
 
Back
Top