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Ih

) \—

Fig. 2.7. Telecentric aperture stop

Fig. 2.7. Telecentric aperture stop

Telecentric pupils are commonly used in mechanical measuring systems. For example, a graticule placed in the image at IIH will give measurements of the object size which are independent of focus error.

Before leaving the Gaussian properties of optical systems in general, we must consider the application of the general formula of Eq. (2.22) to the specific case of a refraction or reflection at a single surface. It is easily shown [2.3] that f = and f' = (2.32)

n — n n — n where n and n are the refractive indices in the object and image spaces, f and f the corresponding focal lengths and r = 1/c is the radius of curvature of the surface. Then Eq. (2.22) becomes n n n n n — n „

s s f f r again following the strict Cartesian system, measured from the refracting surface, for the distances s, s , f ,f and r. The radius r is therefore positive for a surface which is convex to the incident light from the left.

It can also be shown [2.3] that the general case of refraction, as expressed by Snell's law of Eq. (2.12), can be extended to reflection at a surface if we write n = —n and maintain the same strict Cartesian system of signs. This implies that distances, after reflection, to a succeeding refracting or reflecting surface are also reversed in sign because the light direction is reversed. The general formula for reflection at a surface with optical power, i.e. finite curvature c, is then obtained by inserting n = +n, n = —n (or equally n = —n, n = +n) in (2.33) giving n n n 2n s' s f' r

in which n becomes simply a uniform scaling factor reflecting the optical path laws expressed in Eqs. (2.11) and (2.20). Eq. (2.34) reduces, irrespective of the value of n, to the simple reflection equation

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