Finding Focus Length in Broken Double Convex Lens

In summary, the conversation discusses a thin double convex lens that is broken down into two halves and then combined. The focal length for the combined lens is discussed, with one person initially thinking it is infinite and the other person stating that it is actually 2f. The concept of power being inversely related to focal length is also mentioned, leading to the realization that the combined lens will have a shorter focal length due to its increased power. The conversation ends with a thank you and smiley emoji.
  • #1
Prashasti
63
2

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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  • #2
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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Likes Prashasti
  • #3
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:
 

Related to Finding Focus Length in Broken Double Convex Lens

What is a double convex lens?

A double convex lens is a type of lens that has two outwardly curved surfaces, with the same radius of curvature. It is thicker in the middle and thinner at the edges, and is used to converge or focus light.

What is the significance of finding the focal length of a broken double convex lens?

The focal length of a lens is the distance between the lens and the point where light rays converge to form an image. In a broken double convex lens, the focal length may change due to the damage, and it is important to determine the new focal length in order to properly use the lens for its intended purpose.

How can I find the focal length of a broken double convex lens?

The most common method is to use the lensmaker's equation, which relates the focal length of a lens to its radius of curvature and refractive index. This equation can be rearranged to solve for the focal length, using measurements from the damaged lens.

What factors can affect the accuracy of determining the focal length of a broken double convex lens?

The accuracy of the measurement can be affected by the extent of the damage to the lens, the precision of the measurements taken, and any errors in the calculations used. Additionally, the material and shape of the lens can also impact its focal length.

Are there any alternative methods for finding the focal length of a broken double convex lens?

Yes, there are other methods such as using a laser to measure the focal length, or using a lensometer to directly measure the curvature of the lens. However, these methods may require specialized equipment and may not be as accurate as the lensmaker's equation method.

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