Finding Focus Length in Broken Double Convex Lens

[Prashasti]

Homework Statement

A thin double convex lens of focal length f is broken down into two halves at the axis. The two haves are then combined, as shown in the figure. What will be the focal length for the arrangements?

http://www.meritnation.com/app/webroot/img/shared/content_ck_images/images/Untitled(375).png

Homework Equations

The Attempt at a Solution

For (i), I think that the answer is infinite because any incident ray will either go undeviated or will be laterally displaced - but the combination will not be able to converge it.

Is it right?

And, about the second arrangement - I think it must be 2f, but in my book, f/2 has been given as the answer!

 

[Quantum Defect]

Your answers look good to me. I think you even realize that f/2 is the correct answer, based upon your drawing...

The combined lens will be more focusing -- i.e. shorter focal length. 2f is a focal length 2X as long. Can that possibly be right, given your picture?

 

[Prashasti]

Ahh! I got it!
Power is inversely related to focal length. Now, because the combination is "more" converging (more power), its focal length will be less.
I think it's correct now.
Thanks!