How Can You Minimize Spherical Aberration in a Single Lens System?

[fantagero88]

Homework Statement

- single lens
- f=50cm
- refractive index n=1.53
- if object placed 70cm, find the radii of curvature for the two surfaces of the lens which would minimise spehrical aberration

Homework Equations

what i got from my notes

refraction at a spherical surface

(n1/so+n2/si)=((n2-n1)/R)+h²[(n1/2so)(1/so+1/R)²+(n2/2si)(1/R-1/si)²]

this is after using the third order theory

The Attempt at a Solution

i tried to make another equation for the other side of the refractive surface and then added them together,
and also, tried to use r= infinity because i read that plano-convex can reduce SA.

but still i could get it on what kind of value that could show me when SA is minimised. and also, i couldn't get rid value for h, which the value is not given.

is minimising SA is to get the complete thins lens equation from the third order theory??

thank you

 

[fantagero88]

i found the answer..
damn, i lost one piece of my note.. no wonder i was lost.

so, what i did i just used bending factor to get the radii.
i'll try to post up the answer then i got back home
thanks