1 About this module

• Prerequisites:
• Objectives: This module explores the physics and math behind the modeling of a side (internal) focusing scope.

2 The basic math

The basic model is as follows:

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1{f}_2}$

In this equation, $f$ refers to the overall focal length of the system of lenses, while $f_1$ and $f_2$ refer to the focal lengths of the elemental lenses. $d$ is the distance between the elemental lenses.

For calibration purposes, there are $d_{L1}$, $d_{L2}$ and $d_{\infty }$. While the actual distances are not known, the relative differences are known. These are the distances between the elemental lenses to produce a sharp image at lengths $L1$, $L2$ and $\infty$ from the lens system.

The key is to compute $f_1$ and $f_2$ from all the known factors.

In general, we have the general equation as follows:

$\frac{1}{f\left(L\right)}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d\left(L\right)}{f_1{f}_2}=\frac{1}{f\left(\infty \right)}-\frac{1}{L}$