Tutorial : miscellaneous - plane parrallel plate - ray shift vs angle of incidence

Rays refracted through a plane parallel plate are not deviated but only translated. The longitudinal shift of a ray is:

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i is the incidence angle, n is the refraction index and e is the thickness. The transversal shift is then :

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The shift in a plane perpendicular to the ray is :

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Therefore, all incident rays focused at a point A are shifted to the front after transmission through the plate at a distance dx from A depending only on the incidence angle i. This means that the plate generates spherical aberration ( see "spherical aberration" tutorial ).

For sufficiently small incidence angles ( in Gauss conditions ), the longitudinal shift dx calculated above can be approximated as follows :

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dx is no more depending on the incidence angle. Therefore, the conjugate of a point by a plane parallel plate is a point shifted by dx. Note that the magnification is +1.