# Topic 29. Camera Lenses, Part 1. Focusing on the Object

The lens of a camera must form a real image of the object that is being photographed – the rays of light from a point on the object must actually strike the film at a single point in order to trigger the chemical reaction that records the image. Although the lens of a camera is a complex multi-element design to minimize aberrations, its general properties are equivalent to a positive lens of comparable focal length. We can therefore understand the performance of a camera lens using the principles we have outlined in previous topics.  (See Topic 23. Thin Lenses, part 2. Ray tracing rules and Topic 24. Thin Lenses, part 3. Images using positive lenses.)

The ray-tracing rules we have established define a unique relationship between the focal length of the lens and the positions of the object and the image. In other words, when a lens of some focal length is placed at a given distance from the film plane then this distance and the focal length of the lens determine the distance to an object that is in sharp focus. In principle, objects at any other distance are not clearly focused. In order to bring an object at some other distance into clear focus, it is necessary either to move the lens or to change its focal length. Either of these changes is possible, and both are supported by more expensive cameras. Simpler and cheaper cameras usually have the ability to move the lens but not to change its focal length, while neither the focal length nor the lens position can be changed on the very simplest cameras.

In order to get a feeling for how much the lens must be moved to bring different objects into focus, the following table is computed using the algebraic form of the ray-tracing equations for a single positive lens. (See Appendix E, page 418 in the textbook, or just trust me.)

Distance of the object in front of the lens                          Position of the image behind the lens

in units of the focal length                                                in units of the focal length

10                                                                         1.11

100                                                                       1.01

1,000                                                                     1.001

10,000                                                                   1.0001

For example, suppose we are using a lens whose focal length is 50 mm, which is a typical value for the lens on a 35 mm camera. The first entry in the table above says that an object 500 mm (just under 20 inches) in front of the lens (10x50) is imaged 55.5 mm behind the lens (1.11x50). If this object is to be imaged on the film plane, the lens must be located 55.5 mm in front of the film. The next entry says that an object that is 5000 mm (5 m) in front of the lens (about 16 feet) will be imaged 50.5 mm behind the lens. The lens must therefore be moved closer to the film plane in order to focus on this more distant object. The same thing is true for the other entries – the lens must be moved closer to the film plane as the distance to the object increases. Note that the changes become smaller and smaller as the distance to the object increases. In order to bring objects from 20 inches to infinity into clear focus, this particular lens must be able to move about 5.5 mm – from 55.5 mm in front of the film to essentially 50 mm in front of the film plane.

The lens motion required to bring these objects into focus is surprisingly small, and it is not difficult to design a camera that allows the lenses to move by these amounts relative to the film plane.  On the other hand, the position of the image changes more and more rapidly as the objects gets closer to the lens, and most lenses cannot move far enough to focus on close-in objects for that reason. For example, an object that is 5 focal lengths in front of the lens has an image that is 1.25 focal lengths behind the lens, while an object that is 2 focal lengths in front of the lens has an image that is 2 focal lengths behind it. These motions cannot be accommodated by standard lens mounts, although there are special-purpose mounts that can do this.