## 611. Conjugate Foci

Conjugate Foci. For every distance between lens and object, there is a certain corresponding distance between lens and image. These distances are termed "conjugate foci" (conjugate, yoked together, coupled); the distance between lens and object is the anterior or major conjugate, and the distance between lens and image is the posterior or minor conjugate (except in enlarging, when their positions are reversed). With the variation of distance, we also find that there is a variation in the size of the image. As the object approaches, the image recedes and becomes larger; as the object recedes, the image approaches nearer to the lens and becomes smaller.

## 612. Ratio Of Distance And Size

Ratio Of Distance And Size. A very simple mathematical rule governs both the relative distance of object and image from the "center" of the lens and also the relative size of object and image. The ratio of distance is also the ratio of size, for size of image compares to size of object as distance of image compares to distance of object. If the distance of the object is two, three or four times that of the image (the distance of the image then being one-half, one-third or one-fourth that of the object), the image is one-half, one-third or one-fourth the size of the object, and so on. Expressing the distances in multiples and fractions of focal length, we can formulate a very simple method of determining either distance or size. Fig. 18.

613. When object and image, 01 and I1 Fig. 18, are of the same size, they are equidistant from the center (c) of the lens, and the distance in either direction is twice the focal length or the distance from the center of the lens to the principal focus. Now let us measure off the focal length in either direction from the "center" when f will be the principal focus, and f1 its corresponding point in front of the lens. These points will be our starting points, the points from which we will measure. Let us call the focal length F (F thus being equal to cf and also equal to cf1, because either distance represents the focal length of the lens). "We then find the object, O1, 1 F beyond f1, and the image, I1, 1 F beyond f. Then let us move the object another focal length away and place it in the position of O2, 2F beyond f1. The image will then be in the position of I2, 1/2 F beyond f, and its size will be one-half the size of the object. Move the object another focal length away, to the position of O3. 3F beyond f1, and the image will be found at I3, 1/3F beyond f. Its size? Just one-third the size of the object. If the object is ten focal lengths beyond f1, the image is one-tenth of a focal length beyond f and is one-tenth the size of the object. A distance of 100 or 1000 focal lengths beyond f1 in one direction means 1-100 or 1-1000 of a focal length beyond f in the other direction, with corresponding proportions of image.