People always laugh when the math teacher says that you will use it later in life. The weird part is that artists tend to use more math than anyone outside the hard sciences if they want to become the best at what they do, and photographers are among the best.
While most photographers use a calculator some get so good at it that they can do even some of the more advanced math in their head; when you get used to calculating the best f-stop/ISO combination for a given illumination on a target at a particular range, it is a relatively simple process for a photographer.
When it comes to a good lens, focal length is easy.
Types Of Lenses
For our purposes, there are just two lenses: primary and zoom. A primary is a fixed lens; it cannot change its magnification.
A zoom lens, however, has an actual range of magnifications that can be selected by twisting the lens; while most photographers tend to use the extremes.
A good photographer knows how to use a variety of different settings. Most photographers have a number of different lenses for different purposes, such as primary for portraits, telephoto lens for long-range shots, and a fisheye lens for dramatic shots, for example.
The Upside And Downside Of Lenses
Each type of lens has its pluses and minuses that need to be considered, but only one that really needs consideration here.
The primary lens is lighter, generally less expensive by itself, is cheaper by itself, and is better for those who like to move around for the better shot.
The zoom lens, however, is better for those who cannot move around, but is cheaper by itself and is more portable than a group of primary lenses.
However, the primary lens only has one focal length making it easier to determine field of view while the field of view must be determined for each of its different focal lengths.
For each lens focal length is an important number. The focal length helps to determine f-stops, which help determine focus ratios and to determine the exact field of view.
While not enough can be said about f-stops there is also a lot that has been said about them.
The field of view, however, is something that most photographers do not worry enough. Simply put, the field of view is what your lens actually sees; the lens usually sees more than you do through the viewfinder.
While it is usually no problem to crop out what you do not need, it is not a bad idea to try to limit that wasted space a bit.
Eliminating that wasted space is where the ability to determine focal length comes in handy. It is actually not that hard for a digital camera; in general the focal length is the on the lens itself.
In essence, a 35mm lens has in effect a 35mm focal length; a zoom lens has a focal length equal to the current lens, whatever that may be.
It needs to be noted that this is an effective focal length; unlike an analog camera, a digital camera projects its image onto a sensor rather than film.
Now, if it were analog camera you would have all sorts of math to do at this point.
The Nature Of Digital Camera
That is sort of an interesting issue to keep in mind, however, as it will come up in discussions. A digital camera is all about the equivalencies rather than the actualities.
This is because of the electronic nature of digital photography; it needs to be noted that when you deal with different focal lengths odds are good that the sensors will create different fields of view for the focal lengths; this translates to the idea that while each of the different focal lengths of a zoom lens will have a different field of view.
But that just means that things only get interesting and so experience with the difference focal lengths can only hope.
In essence, there will be a lot of hedging, but it will come down to actually looking up the specifications of the camera and actually measuring.
This is not to say that there will not be some math, but that is because you need to determine the angle before you can determine the field of view.
The specifications should have the sensor width; if you have that then it is easy to determine angle of view in degrees, or radians if you prefer; the formula is (with X equal to pi or 180 degrees): Angle of View (in degree) = 2 * ArcTan ((Sensor Width/(focal length * 2)) * X
Once you have that number, you can convert that to how linear your field of view is in meters by using the following formula: Linear Field of View = 2 (Tan (angle of view/2) * distance to subject)
Oh, and one more term just because it will come up: The width of the sensor is also referred to the “crop view” as it determines how wide the angle of view is.
Wile you may have to experiment with the formulas a bit in order to make sure that it conforms, but they should conform.
An Alternative Way To Know The Sensor Length
If you do not have the sensor length, you can always look it up online if you need to, but it is usually not that hard to find. As noted it is great to know for those that like to be precise, and it can be a great way to show off to your friends.
For those that like to limit the amount of time that you spend manipulating the image, however, this can be a great way of speeding things up a bit.
Also, when you are in the field, it can make things a lot easier.
At the very least, you know how much the camera is seeing more than your viewfinder and can thus better estimate exactly how much of the picture you are actually getting when you take the picture.
This gives you some serious advantages on not only a tight shoot but also when you are working with crowds.
Going back to the zoom lens, odds are that each focal length may be attached to a different sensor, meaning that different focal lengths may have different fields of view.
This can make it interesting for a photographer to remember the different specs, especially if they are in the field.
Nonetheless, for a serious photographer, it can only help make things easier in the long run and allow for some precision in the field.
All in all, it is just a better way of knowing your camera and being able to really be creative with it.
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