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:

1. Abbe’s formula is valid only for paraxial rays;

2. Law is valid for one refractive surface

3. All rays emanating from point \(S\) and forming different but necessarily small angles with the axis will pass through point \(S'\) after refraction.

Links:

1. 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:

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