Elements with spherical surfaces

1- Spherical mirror

Definition

It is a spherical surface capable of reflecting almost all the light. It has a center C, a radius of curvature SC=R , and a vertex S.

Geometric construction: Stigmatism

The normal is carried by a radius.

If we take parallel rays coming from infinity that strike a concave mirror, we obtain a convergence that does not occur at a single point, but over a small region.

Gauss relation ⇒ small angle of incidence
Therefore: S′≈SS'

 

It is the conjugation formula at the vertex

The conjugation formula at the center

Gauss relation ⇒ small angle of incidence
Therefore: S′≈SS'

2- The plane diopter

A plane diopter is formed by two transparent media with different refractive indices, separated by a flat surface.

Definition

It is an association of two plane diopters D1 and D2 parallel to each other, distant from e, having a refractive index n and immersed in a medium of index n

Geometric construction

The position of the image relative to the object:   

Lateral displacement d