Image formation and Newton's formula

Formation of image by cardinal points

Formation of image by cardinal points

A ray parallel to principal axis after refraction from the lens system passes through the focus F₂.
A ray passing through F₁ become parallel to the principal axis after emerging from optical system.
A ray meeting first principal plane at any height emerges through the second principal plane from the same height and on the same side of the optical system.
A ray directed towards a nodal point N₁, emerges through the other nodal point N₂ parallel to the previous ray.

Newton's formula

$https://latex.codecogs.com/svg.image?\frac{K_{1}H_{1}}{AB}=\frac{H_{1}F_{1}}{BF_{1}}$

$https://latex.codecogs.com/svg.image?\frac{A_{1}B_{1}}{AB}=\frac{H_{1}F_{1}}{BF_{1}}$

$https://latex.codecogs.com/svg.image?\frac{-y_{2}}{y_{1}}=\frac{-f_{1}}{-x_{1}}$

$https://latex.codecogs.com/svg.image?-\frac{y_{2}}{y_{1}}=\frac{f_{1}}{x_{1}}$ ....(1)

$https://latex.codecogs.com/svg.image?\frac{A_{1}B_{1}}{M_{2}H_{2}}=\frac{B_{1}F_{2}}{H_{2}F_{2}}$

$https://latex.codecogs.com/svg.image?\frac{A_{1}B_{1}}{AB}=\frac{B_{1}F_{2}}{H_{2}F_{2}}$

$https://latex.codecogs.com/svg.image?\frac{-y_{2}}{y_{1}}=\frac{x_{2}}{f_{2}}$

$https://latex.codecogs.com/svg.image?-\frac{y_{2}}{y_{1}}=\frac{x_{2}}{f_{2}}$ ....(2)

$https://latex.codecogs.com/svg.image?\frac{x_{2}}{f_{2}}=\frac{f_{1}}{x_{1}}$

$https://latex.codecogs.com/svg.image?{x_{1}}{x_{2}}={f_{1}}{f_{2}}$

$https://latex.codecogs.com/svg.image?{x_{1}}{x_{2}}=-f^{2}$
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