Читать книгу Optical Engineering Science - Stephen Rolt - Страница 22

The location of the cardinal points has given us a complete description of a generalised optical system. Given that the function of an optical system might be to produce an image of an object located at a specific point, we might want to know the location of that image. Figure 1.11 shows the relationship between a generalised object and image.

Referring to Figure 1.11 and by using similar triangles it is possible to derive two separate relations for the magnification h₂/h₁:

Figure 1.11 Generalised object and image.

And:

(1.6)

The above equation is Newton's Equation and may be re-cast into a more familiar form using the definitions of object and image distances, u and v, as previously set out.

(1.7)

If f₁ = f₂ = f, we are left with the more familiar lens equation. However, Eq. (1.7) is generally applicable to all optical systems. Most importantly, Eq. (1.7) will give the locations of the object and image in systems of arbitrary complexity. Many readers might have encountered Eq. (1.7) in the context of a simple lens where object and image distances are obvious and easy to determine. For a more complex system, one has to know the location of the principal planes as well in order to determine the object and image distances.