Radius of curvature of the cornea

1. Nov 20, 2008

spaghed87

1. The problem statement, all variables and given/known data
The cornea, a boundary between the air and the aqueous humor, has a 3.0cm focal length when acting alone.

What is its radius of curvature?

2. Relevant equations
n(1)/s + n(2)/s' = (n(2)-n(1))/R

where, n is the index of refraction (unitless), s' is the img dist (cm). and s is the obj. dist (cm). R is the radius (cm).

also, 1/s + 1/s' = 1/f

where, f is the focal length.

also, n(1) is air having a index of refraction of 1.00
and n(2) is the aqueous humor having a index of refraction of 1.34

3. The attempt at a solution

So, I assumed since only f was given as 3.0cm that 1/s' + 1/s could be 1/6.0cm + 1/6.0cm = 1/3.0cm. Then that would give 1.00/6.0cm + 1.34/6.0cm = (1.34-1.00)/R giving R to be 0.87cm but it says that is wrong. Any ideas??? Also, I thought there was a equation editor for this website? I can't seem to see it... Is it only for the premium members?

Last edited: Nov 20, 2008
2. Nov 20, 2008

dimpledur

Radius of curvature is the distance from the cornea to the centre of curvature. If the focal length is half this distance, what do you think the answer is?

3. Nov 20, 2008

spaghed87

Are you implying that it is 2*f=R? 6.0cm is not the right answer if so. That only applies for mirrors right? They seem to be indicating the "air" and the "aqueous humor" in the problem... both of which have given index of refractions in the book. I believe the equation used to solve this problem will deal with the index of refraction... It is hinted in the problem statement pretty much. Thanks for the help though... let me know if you have any other thoughts.

4. Nov 21, 2008

LowlyPion

As for your Equation editing there is a Σ at the top of the message window that is an aid to inserting LaTex into messages. If you want to see how some equations are constructed just click on them and the underlying LaTex is revealed.

You can also take advantage of the X2 and X2 buttons for subscripting and superscripting.

n(1)/s + n(2)/s' = (n(2)-n(1))/R yields:

$$\frac{n_1}{s_1} + \frac{n_2}{s_2} = \frac{n_2 - n_1}{R}$$

Wouldn't the lens makers relationship be the way to approach it?

$$\frac{1}{f} = (n-1)*(\frac{1}{R} + \frac{1}{R})$$

5. Nov 22, 2008

spaghed87

I guess you could approach it from the lens makers... I don't see how though. I'm given only one radius... in your formula that needs to be a R subnot 1 and 2. Also, I'm dealing with two index of refraction values. With the amount of known values I have I cannot seem to piece them together into a formula that satisfies utalizing them all. Am I missing something? Am I supposed to use only one index of refraction and pull another radius out of the sky? hmm, thanks for the help anyways... always appreciated. i'm just frustrated... it is due tomorrow morn.

6. Nov 22, 2008

naresh

It is useful to think about the definition of focal length. How is focal length defined?

7. Nov 22, 2008

LowlyPion

What is the n of the cornea? Or is it perhaps the same as the lens? In which case there is no second radius and the only consideration is the outer radius so the f*(n-1) = R?

8. Nov 22, 2008

naresh

That formula will only apply if you are focusing into a medium with index 1. Therefore it applies well to lenses, but can get confusing with single interfaces. It is simpler to use the original equation and use the definition of focal length.

9. Nov 22, 2008

spaghed87

I did f*(n-1) = R even before you mentioned the equation in that form. Maybe the masteringphysics website is off. I derived that formula by taking s=f and s' being equal to inifinity for an answer of 1.02cm (we are on the same boat). Yes, it is focusing into a medium with an index of 1. This beats me. I'm down to two attempts left. I'll still pass this class just fine... I just hate not getting an answer.

10. Nov 22, 2008

naresh

Well, you're almost correct. What do s and s' refer to? Where is the light coming from, and where is it focusing (remember, we're talking about the eye, not an abstract mathematical equation )?

Last edited: Nov 22, 2008