# Talking about Focal Lengths in Photography

## Thin lens approximation

The focal length tells us the angle of view-how much of the scene will be captured-and the magnification-how large individual elements will be. The longer the focal length, the narrower the angle of view and the higher the magnification. The shorter the focal length, the wider the angle of view and the lower the magnification.

For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points) of the lens. For a converging lens (for example a convex lens), the focal length is positive, and is the distance at which a beam of collimated light will be focused to a single spot. For a diverging lens (for example a concave lens), the focal length is negative, and is the distance to the point from which a collimated beam appears to be diverging after passing through the lens.

The focal point F and focal length f of a positive (convex) lens, a negative (concave) lens, a concave mirror, and a convex mirror.The focal length of an optical system is a measure of how strongly it converges (focuses) or diverges (diffuses) light. A system with a shorter focal length has greater optical power than one with a long focal length.

### General optical systems

For a thick lens (one which has a non-negligible thickness), or an imaging system consisting of several lenses and/or mirrors (e.g., a photographic lens or a telescope), the focal length is often called the effective focal length (EFL), to distinguish it from other commonly-used parameters:

Front focal length (FFL) or Front focal distance (FFD) is the distance from the front focal point of the system to the vertex of the first optical surface. Back focal length (BFL) or Back focal distance (BFD) is the distance from the vertex of the last optical surface of the system to the rear focal point. For an optical system in air, the effective focal length gives the distance from the front and rear principal planes to the corresponding focal points. If the surrounding medium is not air, then the distance is multiplied by the refractive index of the medium. Some authors call this distance the front (rear) focal length, distinguishing it from the front (rear) focal distance, defined above.

In general, the focal length or EFL is the value that describes the ability of the optical system to focus light, and is the value used to calculate the magnification of the system. The other parameters are used in determining where an image will be formed for a given object position.

For the case of a lens of thickness d in air, and surfaces with radii of curvature R1 and R2, the effective focal length f is given by:

where n is the refractive index of the lens medium. The quantity 1/f is also known as the optical power of the lens.

The corresponding front focal distance is:

and the back focal distance:

In the sign convention used here, the value of R1 will be positive if the first lens surface is convex, and negative if it is concave. The value of R2 is positive if the second surface is concave, and negative if convex. Note that sign conventions vary between different authors, which results in different forms of these equations depending on the convention used.

For a spherically curved mirror in air, the magnitude of the focal length is equal to the radius of curvature of the mirror divided by two. The focal length is positive for a concave mirror, and negative for a convex mirror. In the sign convention used in optical design, a concave mirror has negative radius of curvature, so

, where R is the radius of curvature of the mirror's surface.

### In photography

How focal length affects photograph composition: adjusting the camera's distance from the main subject while changing focal length, the main subject can remain the same size, while the other at a different distance changes size. The dolly zoom is based on this effect.
When a photographic lens is set to "infinity", its rear nodal point is separated from the sensor or film, at the focal plane, by the lens's focal length. Objects far away from the camera then produce sharp images on the sensor or film, which is also at the image plane. Photographers sometimes refer to the image plane as the focal plane; these planes coincide when the object is at infinity, but for closer objects the focal plane is fixed, relative to the lens, and the image plane moves, by the standard optical definitions.

The focal length of a lens determines the magnification at which it images distant objects. The focal length of a lens is equal to the distance between the image plane and a pinhole (see pinhole camera model) that images distant small objects the same size as the lens in question. Combining this definition with an assumption of rectilinear imaging (that is, with no image distortion) leads to a simple geometric model the photographers use for computing the angle of view of a camera.

To render closer objects in sharp focus, the lens must be adjusted to increase the distance between the rear nodal point and the film, to put the film at the image plane. The focal length f, the distance from the front nodal point to the object to photograph S1, and the distance from the rear nodal point to the image plane S2 are then related by:

. As S1 is decreased, S2 must be increased. For example, consider a normal lens for a 35 mm camera with a focal length of f = 50 mm. To focus a distant object (), the rear nodal point of the lens must be located a distance S2 = 50 mm from the image plane. To focus an object 1 m away (S1 = 1000 mm), the lens must be moved 2.6 mm further away from the image plane, to S2 = 52.6 mm.

Note that some simple and usually inexpensive cameras have fixed focus lenses which cannot be adjusted.

Focal lengths are usually specified in millimetres (mm), but older lenses marked in centimetres (cm) and inches are still to be found. The angle of view depends on the ratio between the focal length and the film size.

A lens with a focal length about equal to the diagonal size of the film or sensor format is known as a normal lens; its angle of view is similar to the angle subtended by a large-enough print viewed at a typical viewing distance of the print diagonal, which therefore yields a normal perspective when viewing the print; this angle of view is about 53 degrees diagonally. For full-frame 35mm-format cameras, the diagonal is 43 mm and a typical "normal" lens has a 50 mm focal length. A lens with a focal length shorter than normal is often referred to as a wide-angle lens (typically 35 mm and less, for 35mm-format cameras), while a lens significantly longer than normal may be referred to as a telephoto lens (typically 85 mm and more, for 35mm-format cameras), though the use of the term is inaccurate as it implies specific optical design qualities that may or may not apply to a given lens.

Due to the popularity of the 35 mm standard, camera–lens combinations are often described in terms of their 35 mm equivalent focal length, that is, the focal length of a lens that would have the same angle of view, or field of view, if used on a full-frame 35 mm camera. Use of a 35 mm equivalent focal length is particularly common with digital cameras, which often use sensors smaller than 35 mm film, and so require correspondingly shorter focal lengths to achieve a given angle of view, by a factor known as the crop factor.

The focal length of your lens is it's main characteristic. It determines your angle of view, that is, how close or how far away you have to be from your photographic subject to capture it in a certain size. With a short focal length (wide-angle lens) you can stand close to somebody and still capture their full body size. With a long focal length (telephoto lens) you can stand far away and still get a close-up picture. Wide-angle lenses are considered good for landscapes and photojournalism since you can capture the whole scene in the same shot and the long telephoto lens is considered good for sport, wildlife and paparazzi photography, since you can be relatively far away from your subject, ideal if you don't want to disturb it or be noticed. The range of lenses and focal lengths available is listed along with the DX equivalent substitute lens here:

Range of lenses Lens range for
35mm Film Format
Equivalent Lens range
for Nikon DX Format
Fish-eye lenses: 8-14 mm 4-10 mm
Ultra wide-angle lenses: 15-20 mm 10-15 mm
Wide-angle lenses: 20-40 mm 14-30 mm
Normal lenses: 40-60 mm 28-40 mm
Portrait lenses 80-100 mm 50-75 mm
Moderate tele-photo lenses 90-150 mm 60-100 mm
Tele-photo lenses: 150-300 mm 100-200 mm
Extreme tele-photo lenses: 300-1000 mm + 200-100% mm +

The focal lengths listed here are the "35mm equivalent" scale. Newer pocket-size digital cameras use a different scale and you might see something like "focal length 2.8-9 mm" on one of these. This does not mean that everything is taken with an extreme wide-angle / fish-eye look. See to your camera manual to see how it converts into the 35 mm equivalent.

The big question is: what focal length is good to use and in which circumstances?

It is often said that the fish-eye and wide-angle lenses provide an exaggerated perspective and a large depth of field (depth of focus). This is not quite true since the perspective only depends on where you stand in relation to your subject and the depth of field only depends on what lens aperture you are using.

But these truisms, technically incorrect perhaps, are there for a reason. The thing about the exaggerated perspective comes about since, with a wide-angle lens you'll normally go closer to your subject in order to fill your frame. Taking a picture of a rose, for instance, with a 20 mm lens you'll need to be within one foot distance in order to render it in a decent size on your print. With a 200 mm lens however, you'll normally take a few steps back, thereby changing your perspective. So while the perspective strictly speaking isn't determined by the lens itself, for practical purposes it is.

In order to avoid the 'exaggerated perspective' a good rule of thumb states that you should be at a distance of at least 10 times the depth of your subject. Things like the size of your final print and the intended viewing distance also plays a role, but for simplicity's sake let's just follow the rule of thumb: If the rose is 4 inches across, you'll have to be at least 3 feet away from it to avoid exaggerating the perspective. Once you've decided on your distance and viewpoint, just zoom your lens to the focal length that fills the frame with a nice composition. No one says that you must have a 'correct' perspective, certainly I don't. But for some purposes it is more important than others. If you're taking a close-up photo of someone's face for instance, exaggerating the perspective and making their nose look huge can do bad things for your popularity. Again, determine the depth of the visible parts of your subject, in case of a human face straight-on, it will usually be about 6-7 inches from the tip of the nose to the back of the ear. Then multiply by 10 and move back until you are at least 5 feet away and zoom in to fill the frame. Your focal length will typically be in the area of 100 mm (75mm on a DX camera) which is incidentally referred to as a portrait lens.

In case of huge landscapes, long streets etc. It is next to impossible to be 10 times further away from it than the total depth of the entire scene. To capture such scenes from close to far away, you'll normally need a wide-angle lens and the perspective will as a result be 'exaggerated'. This has it's own charm though. It can result in a nice sense of depth in the photo.

With a long telephoto lens your perspective will often become flat since you'll be a bit far away and the relative distances from you to the subject and the background are not that much different. And As a result, the 'flat' perspective arises because the background objects aren't rendered that much smaller than objects a little closer to you.

About the depth of field that the lens provides, as I said before, it doesn't always depend on the lens focal length. But for practical purposes, it does! When you zoom in on something, making your focal length longer, you magnify that part of your image more and more, thereby increasing what's known as 'the circle of confusion'. It is exactly equivalent to cropping your short focal length photo and As a result, since it's basically the same image, it has the exact same depth of field. Confused? Don't let it keep you awake at night. When you look through your camera viewfinder or at the LCD screen, you'll see what's in focus and what isn't.

A more important thing to be aware of is that when you zoom in and use a long focal length, it becomes more important to keep your camera steady. A tripod is best, but it can be a pain to lug around all day. Instead, try to look around and see if you can put your camera down on a table, rock or fence somewhere, making it steady. If not, at least try to steady yourself by leaning slightly against a tree, wall or something else solid. And use a fast shutter speed. If you are using a focal length of, say, 300 mm, then use a shutter speed of no more than 1/300th of a second. You might want to make it even less, perhaps 1/500th of a second to be sure not to let your shaky hand blur the picture. Even ever so slight hand-shaking from your pulse can blur the image when using long lenses, so be sure to follow this rule of thumb. Many newer telephoto lenses have a stabilization mechanism build into them, which can greatly reduce hand-shake on the lens, allowing shutter speeds to be 4 to 8 times slower.