First, we need to find the angle deflection of light ray if it passes a convex lens.

Hence,

By using lens equation,

If the lenses are separated by angle of θ, then the total number of lenses is

If we want to trap a ray of light, we just need to have the light forms a (nearly) circle path. On one cycle of the path, the light passes N lenses, so the total deflection is

The total deflection must equal to 2π,

In order to get the longest focus length, variable h must be at its maximum value (i.e. aperture length, D)

That's my solution.

If you have any question, correction, or comment, please leave a comment below.

Thank you.

## 2 comments

The maximum value of h is D/2, so the final result is half the one given in the above solutin

If the angle of deviation becomes 2pi then how will the paraxial approximation hold true. If paraxial approximation fails then we cannot use the general lens equation 1/f = 1/V + 1/U.

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