Optical Path Length: Deriving Reflected Light on Lens Surface

In summary, the conversation involves deriving the optical length of incident light being reflected back to the surface of a lens with radius r1. The equation for the surfaces of the lens is assumed to be r^2 = y^2+z^2, with two surfaces of radii r1 and r2. The person attempting the problem has used Fermat's principle but is stuck on the derivation. Another person remembers doing the problem and suggests that the derivation is not simple. There is a discussion on whether to subtract the expression for r1 from r2 and representation of the reflected velocity.
  • #1
kpl
6
0

Homework Statement



Derive the optical length of the incident light being reflected back to the surface of the lens with radius r1.

Homework Equations



i have assumed that the surfaces can be given as r^2 = y^2+z^2
there are 2 surfaces of the lens with radii r1 and r2

The Attempt at a Solution



is it simply subtracting the expression for r1 from the expression for r2?
i have attemped using Fermats principle but cannot get very far
 
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  • #2
I think I remember doing this problem a while back - if I'm right, the derivation is not simple. If nobody replies, give me some time to recall my memory...
 
  • #3
I don't know if you've managed to do the problem but you were on the right track.

You asked whether or not you subtract the expression for r1 from r2 - that depends if you represented the reflected light ray's velocity as negative or if you've subtracted the entire reflected path. Either way should be fine, though I would probably stick with representing the reflected velocity as negative.
 

1. What is optical path length?

Optical path length refers to the distance a light ray travels through a medium, such as air or glass, before reaching a specific point. It is typically measured in meters or centimeters.

2. How is optical path length related to the reflected light on a lens surface?

The optical path length is directly related to the amount of light that is reflected off of a lens surface. The longer the path length, the more reflections that occur, resulting in a greater amount of light being reflected.

3. How is optical path length calculated?

Optical path length is calculated by multiplying the refractive index of the medium by the physical distance the light travels through that medium. This can be represented by the equation: Optical path length = refractive index x distance traveled.

4. Why is it important to consider optical path length when designing optical systems?

Optical path length is crucial in determining the performance and efficiency of an optical system. It can affect factors such as the amount of light that reaches a detector, the resolution of the system, and the quality of the image produced.

5. How can optical path length be optimized in an optical system?

One way to optimize optical path length is by using materials with a high refractive index, such as glass or plastic, to reduce the distance the light has to travel. Additionally, careful design and placement of lenses and mirrors can also minimize the path length and improve the performance of the system.

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