Optics Paraxial Geometrical Equation Formula Latex Code and Summary

Optics Paraxial Geometrical

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Equation

$$\frac{n_1}{v}-\frac{n_2}{b}=\frac{n_1-n_2}{R} \\ \frac{1}{f}=(n_{\rm l}-1)\left(\frac{1}{R_2}-\frac{1}{R_1}\right) \\ \frac{1}{f}=\frac{1}{v}-\frac{1}{b} \\ \frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1f_2}$$

Latex Code

                                 \frac{n_1}{v}-\frac{n_2}{b}=\frac{n_1-n_2}{R} \\
            \frac{1}{f}=(n_{\rm l}-1)\left(\frac{1}{R_2}-\frac{1}{R_1}\right) \\
            \frac{1}{f}=\frac{1}{v}-\frac{1}{b} \\
            \frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1f_2}

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Introduction

$\frac{n_1}{v}-\frac{n_2}{b}=\frac{n_1-n_2}{R} \\ \frac{1}{f}=(n_{\rm l}-1)\left(\frac{1}{R_2}-\frac{1}{R_1}\right) \\ \frac{1}{f}=\frac{1}{v}-\frac{1}{b} \\ \frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1f_2}$

Latex Code

            \frac{n_1}{v}-\frac{n_2}{b}=\frac{n_1-n_2}{R} \\
            \frac{1}{f}=(n_{\rm l}-1)\left(\frac{1}{R_2}-\frac{1}{R_1}\right) \\
            \frac{1}{f}=\frac{1}{v}-\frac{1}{b} \\
            \frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1f_2}

Explanation

Latex code for the Paraxial geometrical optics. I will briefly introduce the notations in this formulation.

$R$ : refraction at a spherical surface with radius R
$|v|$ : distance of the object
$|b|$ : distance of the image
$n_{1}$ : refractive index of the lens
$f$ : focal length
$R_{1}, R_{2}$ : curvature radii of both surfaces
$D:=1/f$ : dioptric power of a lens
$1/f=8(n-1)d/D^2$ : Approximation of focal length

Discussion

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I wish for the knowledge to pass this exam.

2023-12-08 00:00
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2023-04-03 00:00
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