In an earlier section, the basic concept of focal length was described as the dis- tance from the lens to the plane where light from parallel light rays will come to a point. It is traditionally measured in millimeters. All simple lenses have a fi xed focal length, which is a direct result of the way the lens was ground. It can be used to create images of objects over a wide range of distances, but the distances in conjunction with the focal length will determine the size of the image. The focal length will also determine the angle within which the object must sit in order to be in an image frame of a given size.
In a camera, the frame size and shape of the sensor are fi xed by the design of the camera. If it is a 35 mm fi lm camera, the frame is 36 by 24 mm. Digital cameras vary somewhat, but a nominal size might be 24 by 18 mm. These frames have diagonals of 43 mm and 30 mm, respectively. When the focal length of the lens is equal to the diagonal of the image frame, that lens is called a normal lens . It turns out that at this length the image will be close to that which a person would see if he or she were standing at the point of the camera. Humans can see across a rather large total angle of view, but only the central 50 degrees yield good detail and rendition. If you extend your arms and hold you hands out on either side of your head, and look straight ahead, you will be aware that something is on either side of you, up to an angle on the order of 170 degrees. But you will not be able to see any detail. For exam- ple, you will not be able to distinguish fi ngers or if anything is being held in the hands. As you swing your arms forward, you will reach a point at which you can see fi ngers and clutched items clearly. If you were to measure the angle formed by your arms, it would be approximately 50 degrees. Long ago it was noticed that when the focal length of a lens is about equal to the diagonal of the image frame, the fi eld of view is the same as that you would visually see. Hence it is called the normal lens. This is not a highly precise measure- ment, but it tends to work well over a reasonable range. Some 35 mm fi lm cameras are equipped with a 50 mm lens, which is called normal, and others with a 40 mm lens also called normal. Both work well enough.
If the focal length of a lens is longer than the normal length, then the lens is called a telephoto lens. If it is shorter than normal, it is called a wide- angle lens. Table 3.1 shows these relationships numerically, indicating the key lens relationships of focal length, focus, and magnifi cation. The table shows, for several image frame formats, a number of focal lengths and how those would be classifi ed. It also shows a column for relative magnifi cation. This is not absolute magnifi cation but the degree to which each lens will magnify objects compared to the normal lens. Bigger numbers indicate that an image of the same object at the same distance would be continually larger as the focal length is increased. Absolute magnifi cation is the size of the image divided by the size of the object. Longer (focal length) lenses magnify more and cover a smaller angle of view than shorter ones. Simplistically, it is a linear relationship: if the focal length is doubled, horizontal and vertical distances covered within the frame will each be cut in half, and the area cov- ered will be reduced by a factor of four.
In mechanical cameras, the image frame is fi xed and the assembly that holds the lens is fi xed relative to the plane of the image frame. If the key subject is to be brought into sharp focus, however, the distance between the lens and the image plane must increase as the key subject is placed closer to the camera. To accommodate a range of key subject distances, the mecha- nism holding the glass elements must be able to move relative to its mount- ing on the camera. When we change this location, we are adjusting the focus, or focusing the camera. Focusing the camera does not involve chang- ing the focal length!
Note that some of the items in the object are not in the same plane as the key subject. Some are between the key subject and the camera and oth- ers are beyond it. In general, some but not all of these items will be in good focus. The closer they are to the plane of the key subject, the more sharply they will be rendered. In general, there is a range of distances in front of (prefocal) and beyond (postfocal) the key subject at which items will be rela- tively well rendered. The range of relatively good focus is called the depth of fi eld , or depth of focus (technically these terms are different, but in common practice they are used interchangeably).
Most camera lenses are not simple lenses, but rather are compound lenses with several elements. It is important to note that the focal length of a compound lens is related to both the surface grind of the glass elements and the spacing between the elements. Figure 3.8 shows the basic relation- ships associated with a compound lens comprising only two elements. Note that the focal length is no longer controlled only by the way the glass ele- ments are ground, but is now also dependent on the distance between those two elements. If the device that holds the glass elements has the ability to move the glasses relative to each other, that mechanism can adjust the focal length of a mounted lens. This cannot be done with a simple lens. When a
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Table 3.1 Camera Lens Categories
Common Camera Formats
4 5 in 102 127 162.6 6 7 cm 60 70 92.2 35 mm 24 36 43.3 digital * 18 24 30.0 Format name Dimensions (mm) Diagonal (mm)