Abbe invariant of two optical environments is constant¶

The point \(S\) is located on the front of the optical axis, i.e. on the part that is outside the spherical lens (outside). The point \(S'\) is located on a part of the optical axis inside the lens The Abbe’s invariant connects the front and back segments \(S\) and \(S'\), allowing one of them to be determined if the second one is known

Conditions:

Abbe’s formula is valid only for paraxial rays;
Law is valid for one refractive surface
All rays emanating from point \(S\) and forming different but necessarily small angles with the axis will pass through point \(S'\) after refraction.

Links:

OptoWiki.

curvature_radius¶

radius_of_curvature.

Symbol:: r
Latex:: \(r\)
Dimension:: length

medium_refraction_index¶

relative_refractive_index of the medium.

Symbol:: n_0
Latex:: \(n_{0}\)
Dimension:: dimensionless

distance_from_object¶

euclidean_distance from lens to object.

Symbol:: d_o
Latex:: \(d_\text{o}\)
Dimension:: length

lens_refraction_index¶

relative_refractive_index of the lens material.

Symbol:: n
Latex:: \(n\)
Dimension:: dimensionless

distance_from_image¶

euclidean_distance from lens to image.

Symbol:: d_i
Latex:: \(d_\text{i}\)
Dimension:: length

law¶

n_0 * (1 / d_o - 1 / r) = n * (1 / d_i - 1 / r)

Latex:: \[n_{0} \left(\frac{1}{d_\text{o}} - \frac{1}{r}\right) = n \left(\frac{1}{d_\text{i}} - \frac{1}{r}\right)\]