# Homework Help: Optics of spherical surfaces expressed as functions of y

1. Jun 3, 2010

### razmataz

1. The problem statement, all variables and given/known data

Problem is: A maksutov camera, which is made from a refelector with a spherical surface s and a transparent corrector with two spherical surfaces s1 and s2. The radii of s, s1 and s2 are 2f, r1 and r2, respecitvely. Z=0 is the centre of all these spherical surfaces.

There is a diagram with y-z axis, with the 3 spherical surfaces as shown above centred on z axis.

(a) Express the profiles of the spherical surfaces in Figure 2 as functions of y and then expand these to the 4th power of y.

(b)Suppose the refractive index of the corrector is n and that r1 = f. Derive an expression for r2 that enables the corrector to correct the spherical aberration of the reflector.

2. Relevant equations

Not sure - hard topic with bad lecturer

3. The attempt at a solution

For (a) i know the equations of the surfaces when expanded to 4th power to be:

S = 2f - y^2/4f - y^4/(64f^3)

S1 = r1 - y^2/2r1 - y^4/(8r1^3)

S2 = r2 - y^2/2r2 - y^4/(8r2^3)

but i need to know the initial function of y before expansion?

Also for part (b)

I need help gettin from

(n-1)((1/r1^3)-(1/r2^3))(y^4/8) = (y^4/32f^3)

to the solution (below)

Question states r1 = f

Supposed to end up with

r2 = ((4n-4)/(4n-5))^(1/3)) * f

Can any one show me the steps?!