A symmetrical biconcave thin lens is cut into two identical halves, and they are placed as shown in the figure -

enter image description here

We are required to find the total number of images of the object, formed in the above particular case.

According to me, only 2 images should be formed - one after refraction through both lenses, and one after refraction through first lens (or second) only. However, the answer given says that a total of three images are formed, and I'm not able to locate where and how the third image is formed.

Am I missing something obvious? Please guide me in the right direction, and help me understand the above concept. I'm not able to understand why there should be a third image - only two seem obvious to me.

Thanks a lot.

  • $\begingroup$ first lens (or second) only is two lenses, so there are 3 different lenses in total, and 3 images. $\endgroup$ Jul 10, 2018 at 12:51
  • $\begingroup$ this exercice answer is poor. It's impossible for light to get to the bottom lens without either going through the top lens, or reflecting or passing through the flat side of either one of the lenses. Plus you are out of the Paraxial approximation.... On top of that you are totally out of the thin lens approximation $\endgroup$ Sep 18, 2018 at 11:50

1 Answer 1


You missed the fact that the object is on the optical axis (dotted line in diagram) of the left-hand concavo-plano lens, so the image from that half lens will be on the same optical axis, somewhat closer to the lens than the object. Lets call that distance, from lens to image, D

The same object is well above the optical axis of the right-hand plano-concave lens (not shown on diagram!), so the image from that half lens will be closer to the lens, at the same distance D, and proportionally closer to the unmarked optical axis.

Thus, the second image will be below the first image.


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