Calculating Focal Length of a Drop of Water

[thereddevils]

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

$$\frac{n_1}{u}+\frac{n_2}{v}=\frac{n_2-n_1}{r}$$

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.

 

[cepheid]

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.

 

[NobodySpecial]

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

 

[thereddevils]

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.