System of N Thin Coaxial Lenses
M.I. Karimullah
Mohamed Imteaz Karimullah, Burlington, Ontario, Canada.
Manuscript received on 19 July 2024 | Revised Manuscript received on 27 July 2024 | Manuscript Accepted on 15 October 2024 | Manuscript published on 30 October 2024 | PP: 1-16 | Volume-4 Issue-2, October 2024 | Retrieval Number: 100.1/ijap.B105104021024 | DOI: 10.54105/ijap.B1051.04021024
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: In geometrical optics, in a system of two thin coaxial lenses, there are several standard formulas, including “𝟏/𝑭=𝟏/𝒇𝟏+𝟏/𝒇𝟐−𝒅/𝒇𝟏𝒇𝟐”. The purpose of this paper is to generalize these formulas to the case of a system of an arbitrary number of thin lenses. In particular, this paper proves that the focal length Fn of a system of n thin coaxial lenses is given by 𝟏/𝑭𝒏=Σ{(−𝟏)𝒎Π[(Σ𝟏/𝒇𝒓𝒔𝒂𝒔𝒓𝒔=𝒂𝒔−𝟏+𝟏 𝟎=𝒂𝟎<𝒂𝟏<⋯<𝑎𝒎<𝒂𝒎+𝟏=𝒏;𝒅𝒏=𝟏)𝒅𝒂𝒔]𝒎+𝟏𝒔=𝟏}𝒏−𝟏𝒎=𝟎, where, fr is the focal length of the rth lens, and dr is the distance between the rth lens and (r+1)th lens. For a fixed value of m, all combinations of values of the a’s (satisfying the condition “0 = a0 < a1 < … < am < am+1 = n”) are taken in the inner sum.
Keywords: Coaxial lens System, Focal Length, Gaussian lens Equation, Magnification Formula.
Scope of the Article: Optics and Spectroscopy