Image formation and Newton’s formula

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

• From ΔABF₁ and ΔF₁K₁H₁

• Since A₁B₁ = – y₂, AB = y₁, H₁F₁ = – f₁, and BF₁ = – x₁

                ….(1)

• From ΔA₁B₁F₂ and ΔM₂H₂F₂

• Since A₁B₁ = – y₂, AB = y₁, H₂F₂ = f₂, and B₁F₂ = x₂

                ….(2)

• From equations (1) and (2), we get

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