Calculating Focal Length of a Drop of Water

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Homework Help Overview

The problem involves calculating the focal length of a spherical drop of water with a specified radius and refractive index. Participants are discussing the appropriate equations and assumptions needed for this optical scenario.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply a formula for light rays coming from infinity but questions their result when it does not match the expected answer. Other participants suggest using the lensmaker's equation instead of the thin lens equation, raising concerns about the applicability of the latter in this context.

Discussion Status

Participants are exploring different approaches to the problem, with some suggesting that the original formula may not be suitable. There is a recognition of the need to consider the radius of curvature in the application of the equations, indicating a productive direction in the discussion.

Contextual Notes

There is a mention of the thin lens approximation potentially being misapplied, and the need to account for the negative radius of curvature for the far surface is highlighted. The original poster's assumption about light rays coming from infinity is also under scrutiny.

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Homework Statement



What is the focal length of a drop of water in the form of a sphere with radius 4mm given that the refractive index of water = 4/3

Homework Equations





The Attempt at a Solution



Here, i think i will need to assume that the light rays are coming from infinity, and using this formula

[tex]\frac{n_1}{u}+\frac{n_2}{v}=\frac{n_2-n_1}{r}[/tex]

n1/u is 0. Substituting n2=4/3 and n1=1,r=4, i got v=16 and for distant light rays, image distance equals the focal length.

But i am wrong, the answer given is 6mm.
 
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It is possible that the formula you used is not applicable to this situation. When I use the lensmaker's equation (which seems like a natural thing to use), I get an answer that is close but not quite equal to the answer you have been given.

http://en.wikipedia.org/wiki/Lens_(optics)#Lensmaker.27s_equation

If I use the thin lens equation (which is just below the lensmaker's equation in that article), I get the answer that you've been given in your solutions. HOWEVER, I do not think that the thin lens approximation applies here, so really you should be using the lensmaker's equation. It's possible that whoever made your solutions incorrectly applied the thin lens equation to this situation.

EDIT: In applying these formulae, keep in mind that the radius of curvature of the far surface should be negative.
 
A sphere is known as a ball lens in optics - it;s very useful for coupling light into fibres for example. http://www.edmundoptics.com/technical-support/optics/understanding-ball-lenses/

See http://spie.org/x34513.xml for a derivation
 
Last edited by a moderator:
cepheid said:
It is possible that the formula you used is not applicable to this situation. When I use the lensmaker's equation (which seems like a natural thing to use), I get an answer that is close but not quite equal to the answer you have been given.

http://en.wikipedia.org/wiki/Lens_(optics)#Lensmaker.27s_equation

If I use the thin lens equation (which is just below the lensmaker's equation in that article), I get the answer that you've been given in your solutions. HOWEVER, I do not think that the thin lens approximation applies here, so really you should be using the lensmaker's equation. It's possible that whoever made your solutions incorrectly applied the thin lens equation to this situation.

EDIT: In applying these formulae, keep in mind that the radius of curvature of the far surface should be negative.

Thank you.
 

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