Derive the optical path length of the incident light

[kpl]

I have been asked to write down the taylor expansion for two concentric spherical surfaces with radii r1 and r2 of a lens and mirror combination which I think is called a Mangin Mirror.

It is supposed to be related to the x and y-axis positions.

Also, I have been asked to derive the optical path length of the incident light being reflected back to the surface of the lens with radius r1.

I don't know were to start for either question.

Any ideas would be much appreciated!

 

[Andy Resnick]

What is the application? Is this homework?

 

[jtbell]

I have been asked to write down the taylor expansion

Of what?

for two concentric spherical surfaces with radii r1 and r2 of a lens and mirror combination which I think is called a Mangin Mirror.

Is this like figure C-4 on the following page?

http://www.jmloptical.com/level2/ProductInfo/m_spherical_info.aspx

(found via a Google search for "Mangin mirror")

It is supposed to be related to the x and y-axis positions.

Again, of what?

 

[kpl]

Optics reply

Exactly like the C-4 diagram.
Let z1(y) and z2(y) be the expressions for the two surfaces of the lens in Figure 1 (see attachment) respectively. Write down the Taylor expansions of z1 and z2 to the fourth power of y.