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plane parallel plate

A plane parallel plate in air or vacuum is made of two parallel surfaces separated by a transparent material with a refraction index n. The first surface is an interface between air or vacuum (as first medium) and plate material (as second medium). The second surface is an interface between plate material (as first medium) and air or vacuum (as second medium). It is assumed that longitudinal and transversal directions are respectively perpendicular and parrallel to the surfaces.
A light ray refracted by a plane parallel plate is parallel to the incident ray but is shifted.

Longitudinal shift induced by  a plane parallel glass plate

longitudinal shift induced by a plane parallel plate for small incidence angle

For an incident light ray in Gauss conditions ( with a small incidence angle ), the longitudinal shift dx of the transmitted light ray depends only on the refraction index n and the thicknes e of the plate. Consequently, for incident light rays all focusing on a point, transmitted light rays all focus on another point longitudinally shifted of a distance dx. This means that the two points are conjugated by the plane parallel plate.



shift induced by  a plane parallel plate in the general case

shift induced by a plane parallel refractive plate in the general case

In the general case, when Gauss conditions are not realized ( for large incidence angles ), a plane parallel plate generates aberrations, which means that the image of a point through it is not a point but a spot with non null dimensions. In consequence, the longitudinal shift dx depends not only on the refraction index n of the plate and its thickness e, but also on the incidence angle i of the light ray.
It is also possible to calculate transversal shift dy and perpendicular shift dr ( in a direction perpendicular to the light ray ) as functions of n, e and i.

References

"Optique Fondements et applications" - 2004 - author : José-Philippe Perez.

"Optique géométrique Imagerie et instruments" - 2007 - author : Bernard Balland.

"Optique géométrique paraxiale" - Institut d'optique théorique et appliquée - 1985 - author : Michel Cagnet.

"Formation des images Aberrations" - Institut d'optique théorique et appliquée - 1985 - author : Michel Cagnet.



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