Dear Nikhitha

Image Formation by Thin Lenses

There are two alternative methods of locating the image formed by a thin lens. Just as for spherical mirrors, the first method is graphical, and the second analytical.

The graphical method of locating the image formed by a thin lens involves drawing light-rays emanating from key points on the object, and finding where these rays are brought to a focus by the lens. This task can be accomplished using a small number of simple rules.

Consider a converging lens. It is helpful to define two focal points for such a lens. The first, the so-called image focus, denoted , is defined as the point behind the lens to which all incident light-rays parallel to the optic axis converge after passing through the lens. This is the same as the focal point  defined previously. The second, the so-called object focus, denoted , is defined as the position in front of the lens for which rays emitted from a point source of light placed at that position would be refracted parallel to the optic axis after passing through the lens. It is easily demonstrated that the object focus  is as far in front of the optic centre  of the lens as the image focus  is behind . The distance from the optic centre to either focus is, of course, equal to the focal length  of the lens. The image produced by a converging lens can be located using just three simple rules:

1. An incident ray which is parallel to the optic axis is refracted through the image focus  of the lens.
2. An incident ray which passes through the object focus  of the lens is refracted parallel to the optic axis.
3. An incident ray which passes through the optic centre  of the lens is not refracted at all.

The last rule is only an approximation. It turns out that although a light-ray which passes through the optic centre of the lens does not change direction, it is displaced slightly to one side. However, this displacement is negligible for a thin lens.

Figure 80 illustrates how the image  of an object  placed in front of a converging lens is located using the above rules. In fact, the three rays, 1-3, emanating from the tip  of the object, are constructed using rules 1-3, respectively. Note that the image is real (since light-rays actually cross), inverted, and diminished.

Figure 80: Image formation by a converging lens.

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