How Does Spherical Aberration Affect Focal Length in Biconcave Lenses?

[Falken_47]

Homework Statement

Hi, I have a question regarding my physics lab assignment. Last week I performed an experiment on the focal length of a biconcave lens using different part (using the radius of the lens) of the lens. This is done by completely covering the lens with a cardboard except for that one spot which radius is to be tested upon

So that I obtain different values of focal length for different radius. From my observation it can be seen that the focal length decrease as the radius increase, which is the same as articles which discuss about spherical aberration. However, I'm having trouble finding the formula which relates the behavior or anything that can be inferred from my findings, as this is an open lab class (meaning you can do whatever you want)

Homework Equations

The Snell's Law: n₁sinθ₁ = n₂sinθ₂

The Attempt at a Solution

This is the part which really confuses me as my professor said to use the snell's law in order to solve this problem. Also, any advice on how to proceed with the problem?

Sorry if the above explanation is not clear as it is hard for me to describe the situation

Any help would be greatly appreciated!

 

[jbsteele]

The Snell's law is only applicable if the light is passing through a material with different refractive indices, which is not the case in your experiment. In your experiment, you are using a biconcave lens, so the behavior you are observing is due to the spherical aberration of the lens. The formula for this aberration is given by:1/f = (n-1) [1/R1 + 1/R2 - (n-1) d^2 / (R1R2)]where f is the focal length of the lens, n is the refractive index of the material of the lens, R1 and R2 are the radii of curvature of the two surfaces of the lens, and d is the thickness of the lens. From this equation, you can see that as the radius of the lens increases, the focal length decreases, which is exactly what you are observing.