Abbe invariant of two optical environments is constant
======================================================

The point :math:`S` is located on the front of the optical axis,
i.e. on the part that is outside the spherical lens (outside).
The point :math:`S'` is located on a part of the optical axis inside the lens
The Abbe's invariant connects the front and back segments :math:`S` and :math:`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 :math:`S` and forming different but necessarily small angles with the
   axis will pass through point :math:`S'` after refraction.

**Links:**

#. `OptoWiki <https://www.optowiki.info/glossary/abbe-invariant/>`__.

.. py:currentmodule:: symplyphysics.laws.conservation.abbe_invariant_of_two_optical_environments_is_constant

.. py:data:: curvature_radius

    :attr:`~symplyphysics.symbols.basic.radius_of_curvature`.

Symbol:
    :code:`r`

Latex:
    :math:`r`

Dimension:
    :code:`length`


.. py:data:: medium_refraction_index

    :attr:`~symplyphysics.symbols.optics.relative_refractive_index` of the medium.

Symbol:
    :code:`n_0`

Latex:
    :math:`n_{0}`

Dimension:
    :code:`dimensionless`


.. py:data:: distance_from_object

    :attr:`~symplyphysics.symbols.classical_mechanics.euclidean_distance` from lens to object.

Symbol:
    :code:`d_o`

Latex:
    :math:`d_\text{o}`

Dimension:
    :code:`length`


.. py:data:: lens_refraction_index

    :attr:`~symplyphysics.symbols.optics.relative_refractive_index` of the lens material.

Symbol:
    :code:`n`

Latex:
    :math:`n`

Dimension:
    :code:`dimensionless`


.. py:data:: distance_from_image

    :attr:`~symplyphysics.symbols.classical_mechanics.euclidean_distance` from lens to image.

Symbol:
    :code:`d_i`

Latex:
    :math:`d_\text{i}`

Dimension:
    :code:`length`


.. py:data:: law

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


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