PHOTOGRAPHY IS NOTORIOUS for its many numbers that a photographer needs to know about. Focal length is one of those numbers.
Most inexpensive compact cameras have an easy-to-use zoom feature, and casual photographers can merely set the zoom to whatever they want without worrying about any confusing numbers. But confusion can occur if they use a camera with interchangeable lenses, for then they need to learn about focal length.
Fortunately for beginners, the kit lens that comes with most inexpensive interchangeable-lens cameras is adequate for most purposes. These cameras may even come with two lenses; for example, 18 to 55 millimeters and 70-200 mm. All you really need to know is that large numbers zoom onto distant objects, while smaller numbers capture ‘more of the scene’.
It's easy. If you want to get the whole scene in your photo, you set your lens to 18 millimeters. If you want to zoom in, you set your lens to 55 mm. But then a friend asks you to take a photo of her, using her camera. You stand about ten feet away, and taking note of the millimeter markings on her lens, you set it to 18 millimeters and then look through the viewfinder — and you are surprised that she appears smaller in the viewfinder than you would expect. She suggests that you zoom in a bit, using a setting of about 30 millimeters. So 18 mm on your camera is the same as 30 mm on her camera. As it so happens, a nearby photographer is taking a photo of the same scene: his camera is large and he tells you that he is using a 55mm lens — but he too is taking in the whole scene, for 55 millimeters is a wide-angle lens for his camera. You learn that focal length settings are not necessarily commensurate between cameras.
A pinhole lens
Light usually travels in a straight line through air, and so we can construct a very crude, but workable, lens just by making a small hole in an opaque surface. Light will travel in a straight line from an object, through this pinhole, where it reaches its destination, which may be light sensitive film or a digital camera sensor.
The focal length of the pinhole lens is merely the distance from your sensor to the pinhole. To illustrate the angle of view of this pinhole lens, draw a line which is the length of your sensor: say, 35 millimeters wide. Perpendicular and centered on this line, draw a dot, which represents your pinhole. Draw a straight line from the edges of the sensor through the dot: this shows the angle of view of your pinhole lens. If you bring the pinhole closer, the view gets wider; and draw it farther away, and the angle of view gets narrower. You should see that for any given focal length, a larger sensor will give you a wider angle of view. Using trigonometry, you can calculate the angle of view for any combination of sensor size and focal length. Suppose you have two cameras, one with a sensor twice as wide as the other: doubling the focal length of the pinhole lens on the larger camera will give you precisely the same angle of view as the smaller camera.
Now take a glass lens, and focus it on some object very, very far away, and note the size of the object projected on your sensor. Then take a pinhole lens, and move it closer or farther from the sensor until its projected image is precisely the same size as the image formed by the glass lens. The distance from the pinhole to the sensor is the effective focal length of the glass lens. An 18 millimeter glass lens projects the same size image as would a pinhole located 18 millimeters from the sensor.
But please note that this equivalence between a glass lens and pinhole lens only works when the distance from lens to the object is much greater than the distance from the lens to the sensor. A regular camera lens, after all, is not a tiny dot like our pinhole lens, but rather is made of multiple thick chunks of glass. If you focus a glass lens upon a subject very close by — like when using a macro lens to focus on a small insect — then its effective focal length will change considerably. Click here for more details.
Also note that this equivalence only works when a glass lens produces a rectilinear image — where straight lines in the scene translate to straight lines on the image. Fisheye lenses are a bit more complicated since they produce so much distortion.
Equivalent focal length
Serious photographers use seriously large cameras. This is for the simple reason that large camera sensors — either digital or film — naturally produce cleaner, sharper, more detailed images. Click here to see why. Now photojournalists also want good picture quality, but they also lug cameras around all day long, and so they need a camera that is a good compromise between weight and image quality. Photojournalists are typically the most commonly-seen type of professional photographer — and amateurs, in imitation, started using similar equipment, which included the 35mm film format. Vast numbers of amateur-grade, interchangeable-lens 35 millimeter film cameras were produced, most notably by the same manufacturers who made the photojournalist cameras.
People became quite used to the sizes of lenses for these cameras. For example, a 50mm lens produced an image that looked rather normal — not too zoomed in, and not too wide. Lenses in the range of say 105 millimeters or larger were good for portraits, while 30 millimeter or smaller focal lengths were good for architectural interiors. Now, please recall that these focal length sizes are for 35 mm film; a medium-format camera would use longer focal lengths for the same purposes, while an inexpensive consumer camera would use much shorter focal lengths.
Eventually the manufacturers of photojournalist cameras went digital; alas, however, due high cost, the digital sensor size was smaller than the beloved 35 millimeter film. Because people were so familiar with the focal lengths used by 35 millimeter cameras, manufacturers stated equivalent focal lengths. So an 18 mm lens used with the new digital sensor is said to be equivalent to (that is, provides the same angle of view) a 27 mm lens used on a 35 mm camera. A 35mm lens on these digitals is equivalent to a 50 mm lens on a 35 mm camera. Is this helpful, or confusing?
Because the 35mm format was rather standard, digital cameras with sensors smaller than 35 mm are often called cropped-sensor cameras, although this terminology can be rather confusing to beginners. I find that beginners often get hung up on the marketing term ‘crop factor’. A 20 mm lens on a camera with a crop factor of 1.5 will provide the same angle of view as a 20 mm x 1.5 = 30 mm lens on a 35 millimeter film camera. Now this terminology is likely only useful if you are very familiar with the old 35 millimeter cameras and their lenses, and is otherwise confusing.
If you are a beginner, I would suggest you forget all about equivalent focal lengths and crop factors. Instead, find out the size of your sensor, in millimeters. For example, many consumer digital SLR cameras have a sensor that is about 30 millimeters across on the diagonal. A wide-angle lens will have a value that is less than this measurement, while a telephoto lens will be much larger than this value. A normal lens — for this sensor — will be equal to this size or perhaps a bit larger.