8 Geo-Optics 2008

# 8 Geo-Optics 2008 - G.1 GEOMETRICAL OPTICS CON V ER G IN G...

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G.1 Hermann Wellenstein Spring 2008 GEOMETRICAL OPTICS CONVERGING AND DIVERGING LENSES, LOUPE, AND TELESCOPE A. INTRODUCTION: By geometrical optics we mean primarily ray-tracing. That is, we try to understand how systems of lenses and mirrors will behave by following individual "rays" of light through the instrument, usually graphically. This is simplified by knowing the very few special rules of how a light ray behaves as it goes through a lens or is reflected off a mirror. These rules are arrived at by elementary geometry, and you should read SZY in order to understand what follows.

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GEOMETRICAL OPTICS G.2 Hermann Wellenstein Spring 2008 We shall recapitulate some important points. The description of optical instruments in the terms of geometrical optics gives their main features, such as image location and size, brightness, and some information on distortion, quite satisfactorily. In this laboratory, you will examine some fundamentals of simple lenses, and construct two common instruments, the telescope and the microscope. There are two general types of lenses: converging and diverging lenses. The former type is thicker in the middle than at the edges (convex lens). Rays of light, in passing through such a lens converge more. The diverging lens is thinner in the middle than at the edges; light rays diverge more after passing through such a lens. The principal focus , F, of a lens is the point on the axis of the lens (in the case of a converging lens) through which all rays, originally parallel to the axis, pass (Figure 1a,), or (in the case of a diverging lens) appear to come from, when refracted by the lens (Figure 1b). The distance from the center of the lens to this point is called the focal length of the lens, f. A convergent lens has a positive, a divergent lens a negative focal length. Thus, algebraic signs must be carefully observed in the basic lens equations. By convention, an object distance is always positive when on the side of the incoming rays; an image distance is positive if the image is on the side of the outgoing rays. The rays of light used in ray-tracing are called principal rays and are shown in Figure 1. As mentioned above, a ray of light from the object parallel to the lens axis is bent to pass through the focal point on the outgoing ray side of the lens for a convex lens (Figure 1a), and is bent away from the axis for a diverging lens so that it appears to be coming from the focal point on the incoming ray side of the lens (Figure 1b). A ray that passes through the center of the (very thin!) lens is unbent as it is apparent from the symmetry of the lens about that point (Figure 1c, 1d). F F a) b) Figure 1 (a) (b).
GEOMETRICAL OPTICS G.3 Hermann Wellenstein Spring 2008 And finally, rays passing through the focal point on the incoming ray side of the converging lens (or heading toward the focal point in case of the diverging lens) come out of the parallel to the axis (Figures 1e, 1f). The point where

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8 Geo-Optics 2008 - G.1 GEOMETRICAL OPTICS CON V ER G IN G...

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