Finding Focus Length in Broken Double Convex Lens

AI Thread Summary
The discussion centers on determining the focal lengths of a broken double convex lens when its two halves are combined. One participant suggests that the focal length of the first arrangement is infinite, as incident rays do not converge. For the second arrangement, there is confusion regarding whether the focal length is 2f or f/2, with the consensus leaning towards f/2 as the correct answer. The relationship between lens power and focal length is highlighted, indicating that a more converging combination results in a shorter focal length. Ultimately, the participants reach an understanding of the correct focal lengths based on their analysis.
Prashasti
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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.
upload_2015-2-10_17-57-20.png

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!
upload_2015-2-10_18-2-55.png
 
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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?
 
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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. :headbang:
I think it's correct now.
Thanks!
:oldsmile:
 

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