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The Lens
A lens is an optical system with two refracting surfaces. The simplest lens has two spherical surfaces that are close enough together for the distance between them (the thickness of the lens) to be negligible. Such a lens is called thin lens.

The main quality of the lens is its ability to produce images of objects. The images can be erect or inverted, real or virtual.

The position of the image, as well as its type, can be established by graphical methods. To do this, use properties of the rays passing through the center of the lens or its focal points, as well as the rays that are parallel to the optic axis.

The position of an image can also be determined by using the thin lens equation. If the distance between an object and the lens is s and the distance between the lens and the image is s', the thin lens equation is

1/s + 1/s' = 1/f.

Focal length f is equal to the distance between the center of the lens and the focal point, i.e. the point where the rays that are parallel to the optic axis converge.

Lenses can be converging or diverging. The converging lens has a real focal point - upon its passage through the lens, a ray converges to the real point. A diverging lens has a virtual focal point.

The focal length of a converging lens is f > 0, while the focal length of a diverging lens is f < 0.

In regards to the distances s and s',

s > 0 and s' > 0 for real objects and images,

s < 0 and s' < 0 for virtual objects and images.

Depending on the position of the object with respect to the lens, the size of the image changes. The ratio of the linear size of the image h to the size of the object h' is called the lateral magnification:

m = h'/h = - s'/s.

The signs in the formula are such that for an erect image, m > 0, and for an inverted image, m < 0.

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