Читать книгу Optical Engineering Science - Stephen Rolt - Страница 25

The law governing refraction at a planar surface is universally attributed to Willebrord Snellius and referred to as Snell's law. This states that both incident and refracted rays lie in the same plane and their angles of incidence and refraction (with respect to surface normal) are given by:

(1.12)

This is illustrated in Figure 1.12.

The refractive indices of some optical materials (at 550 nm) are listed below:

 Glass (BK7): 1.52

 Plastic (Acrylic): 1.48

 Water: 1.33

 Air: 1.00027

Snell's law is, in fact, a direct consequence of Fermat's principle. The reader may wish to derive this through the application of differential calculus. In finding the optimum path from a point in one medium to a point in another medium, the ray will attempt, as far as possible, to minimise its path through the higher index medium. Snell's law thus represents the minimum optical path condition in this instance. Where the ray passes from a high index material to a low index material, there exists an angle of incidence where the angle of refraction is 90°. This angle is known as the critical angle and, for angles of incidence beyond this, the ray is totally internally reflected. The critical angle, θ_c, is given by:

Figure 1.12 Refraction at a plane surface.

(1.13)

A single refractive surface is an example of an afocal system, where both focal lengths are infinite. Although it does not bring a parallel beam of light to a focus, it does form an image that is a geometrically true representation of the object.