When light passes from air to glass, unless the light strikes the glass perpendicular to the glass' surface, the angle the light moves is changed. The angle light makes with the perpendicular is lessened within the lens. When light moves from glass to air, the situation is the opposite. Light increases its angle with the covering when it moves from glass to air. Most habitancy have observed this by viewing something like a stick partially submerged in water. The stick appears to be bent at the covering of the water. This bending of light is called refraction.

With a typical convex lens, one thicker in the center, the angles the light makes entering and exiting the lens differ on each side of the lens. The corollary is to bring the light together on the opposite side of the lens, allowing the image to be projected. In photography, it is the projected image that is recorded, regardless of the type of camera used.

Light from a point enters the lens in any place on the lens' surface, and is bent back to a point where it can focus. The length behind the lens where the light produces a focused image depends on the length the branch is in front of the camera, and on the focal length of the lens. The focal length is the length parallel rays of light that enter a lens would come together at a point.
The reciprocal of the length the branch is in front of the lens plus the reciprocal of the length the image is created past the lens equals the reciprocal of the focal length, for thin lenses. If the lens is thick, the light stays inside the lens longer, so a more involved formula is needed.
No converging lens can be used to image an object that is closer than the focal point. An object in such a position does not yield a real image.
Any object in the middle of the focal point and a length of twice the focal length produces an image larger than the subject. This may not be desired in photography.
Any object beyond twice the length of the focal length produces a reduced image. This is what is desired.
A lens also reverses the image, where the top becomes the bottom, and so on.
For a distant object, the reciprocal of its large length from the lens produces a very small number, so a camera can be designed with the image about the focal length beyond the lens. Shortening this length for near objects is needed for good results. It is the job of the photographer to adjust the camera so as to secure the top potential possible. Notice when manufacture these adjustments it is the lens that moves, altering the length to the projected image.
This report is provided by Henry M. Smith of Black Spaniel Gallery. Feel free to visit http://blackspanielgallery.8m.com which is the website for the author.
The importance of the Focal distance in Photography
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