1. Lenses types and basic formulaes.         Depending on the shape of a surface, lenses can be devided into the following types: plano-convex lenses (Fig. 1)

plano-concave lenses (Fig. 2)

bi-convex lenses (Fig. 3)

bi-concave lenses (Fig. 4)

concave-convex lenses (positive or negative meniscus, Fig. 5 and 6         Depending on radius correlation, lenses can be devided into positive (converging) and negative (dispersing). Plano-convex, bi-convex and positive meniscus lenses are positive (converging).  Fig 5

Plano-concave lenses, bi-concave lenses and negative meniscus lenses are negative (dispersing). Fig 6

Positive lenses converge parallel to the axis pencil of light to the point on the axis, called focus (Fig. 1). Negative lenses disperse parallel to the axis pencil of light as if rays go out of the point, which is also called focus (Fig. 2).         The selection of lens type is defined by the exact optical scheme and allowable deformation of the wavefront (aberration). The most dependent on the lens type is spherical aberration that occurs because of central and edge pencil rays, incident on the lens, actually focus in different points on the axis, but not at the single focus point.          Generally we can say that meniscus lenses have minimum spherical aberration in comparison with that of plano-convex, plano-concave, bi-convex and biconcave lenses. However, if the requirements for an image quality or for a quantity of energy, converging to the point, are not so important, it is better to use lenses with plano surfaces, because they are technologically simplier and thus cheaper.           It should be also noted that minimum focal length at assigned material and lens diameter can be achieved when using bi-convex and bi-concave lenses.                 Basic geometric correlations for all types of lenses are illustrated by the figure 7. Fig 7

The course of rays traveling through the from the object h to the image h' is shown on this fiigure. The point F', which is located on the axis of optical system (lens) and in which rays, that were parallel before passing the lens, come together is called focal point. The distance between F' point and main P' point is called focal length of a lens. For a lens with central thickness CT, focal length can be calculated by the following formulae: where R1 and R2 are radiuses of a lens surfaces, n is refraction index of material of a lens.       For a thin lens CT can be assumed to be zero, main planes P and P' coincide. The formulae of a thin lens is as follows: Back focal length, BFL, i.e. the distance from the top of the last surface of a lens to the back focal plane, can be determined by using: The formulae for linear maglification V is given by: The sagital height of a lens surface is determined by:

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