Derive the optical path length of the incident light

In summary, the conversation discusses the task of writing down the Taylor expansion for two concentric spherical surfaces of a lens and mirror combination, specifically known as a Mangin Mirror. The conversation also mentions deriving the optical path length of incident light reflected back to the surface of the lens. The conversation also includes a link to a diagram for reference. Finally, the conversation asks for help with writing the Taylor expansions of the two surfaces.
  • #1
kpl
6
0
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!
 
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  • #3
kpl said:
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 [Broken]

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

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

Again, of what?
 
Last edited by a moderator:
  • #4
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.
 

Attachments

  • Optics.doc
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1. What is the optical path length of incident light?

The optical path length of incident light refers to the distance that light travels through a material in a straight line. It is a measure of the distance between the light source and the point where the light interacts with the material.

2. How is the optical path length of incident light calculated?

The optical path length of incident light can be calculated by multiplying the refractive index of the material by the physical distance the light travels through the material. This calculation takes into account the speed of light in the material and any changes in direction the light may experience.

3. What factors can affect the optical path length of incident light?

The optical path length of incident light can be influenced by several factors, including the refractive index and thickness of the material, the angle at which the light enters the material, and any changes in direction or reflection that occur within the material.

4. How does the optical path length of incident light impact the behavior of light in a material?

The optical path length of incident light plays a crucial role in determining the behavior of light in a material. It affects the speed and direction of light as it passes through the material, as well as its intensity and polarization. Understanding the optical path length is essential in many fields, including optics, materials science, and engineering.

5. Can the optical path length of incident light be changed?

Yes, the optical path length of incident light can be altered by changing the properties of the material it passes through. For example, the refractive index can be modified by changing the temperature or pressure of the material, or by adding dopants to alter its composition. The thickness and angle of the material can also be adjusted to change the optical path length.

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