Эротические рассказы

Optical Engineering Science. Stephen RoltЧитать онлайн книгу.

Optical Engineering Science - Stephen Rolt


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from the object by rotation alone. Conversely, if the optical system were to contain an even number of reflective surfaces, then the parity between the object and image geometries would be conserved.

      Another way in which a plane mirror is different from a plane refractive surface is that a plane mirror is the one (and perhaps only) example of a perfect imaging system. Regardless of any approximation with regard to small angles discussed previously, following reflection at a planar surface, all rays diverging from a single image point would, when projected as in Figure 1.15, be seen to emerge exactly from a single object point.

      1.4.6 Reflection from a Curved (Spherical) Surface

      The incident ray is at an angle, θ, with respect to the optical axis and the reflected ray is at an angle, ϕ to the optical axis. If we designate the incident angle as θ1 and the reflected angle as θ2 (with respect to the local surface normal), then the following apply, assuming all relevant angles are small:

equation Geometrical illustration of the reflection of a ray from a curved surface.

      As with the curved refractive surface, a curved mirror is image forming. It is therefore possible to set out the Cardinal Points, as before: Cardinal points for a spherical mirror

images images
images images
Both Principal Points: At vertex
Both Nodal Points: At centre of sphere

      The focal length of a curved mirror is half the base radius, with both focal points co-located. In fact, the two focal lengths are of opposite sign. Again, this fits in with the notion that reflective surfaces act as media with a refractive index of −1. Both nodal points are co-located at the centre of curvature and the principal points are also co-located at the surface vertex.

      Earlier, in order to make our lens and mirror calculations simple and tractable, we introduced the following approximation:

equation

      That is to say, all rays make a sufficiently small angle to the optical axis to make the above approximation acceptable in practice. When this approximation is applied more generally to an entire optical system, it is referred to as the paraxial approximation (i.e. ‘almost axial’). If the same consideration is applied to ray heights as well as angles, the paraxial approximations lead to a series of equations describing the transformation of ray heights and angles that are linear in both ray height and angle. This first order theory is generally referred to as Gaussian optics, named after Carl Friedrich Gauss.

      (1.19)equation

      (1.20)equation

      1.6.1


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