When I adjust the focus of my camera, in general, does this affect the focal length? I have heard that it does.
In general: possibly yes.
You actually adjust focus of your lens, not your camera. It can be an advantage1 to design a lens in a way that it changes its focal length slightly when focusing. This is not very important if you take still images. This is different for video of course and one reason why cinema lenses are so expensive
But even if your lens is not guaranteed to have a constant focal length, it might still have it. Maybe it's just having that issue at certain focal distances and you'll be able to happily modify focus at other distances without seeing any change in focal length. To what extent a feature is partially existent on a product is something you will never see advertised or in a spec list. If a constant focal length is important to you, you should rent the lens and try it out if it is not explicitly labelled to have this feature.
1 advantage as in the lens designers do not have to worry about it. It costs money to make lens designers think about things. If a company decides that a feature of a lens is not important and the lens designers do not have to think about it, it can make the lens cheaper, which can be an advantage (if you don't care about the feature either)
I think Alan Marcus is saying that focusing on near objects requires moving the lens farther from the focal plane. You can see that for yourself with a simple lens like a hand-held magnifying glass. That is, the "length" required to focus diverging rays is longer than initially parallel rays.
And this actual length affects f/stop.
I was assuming the question referred to field-of-view and apparent magnification.
But from the essential physics, the "focal length" is different for each subject distance. The lens designer needs to add complexity to compensate for the visible effects of this change, such as f-stop labeling.
The focal length is a measurement taken when the camera is focused on a far distant object. By distant we are talking about a star. Opticians often make an artificial star target which is simply an illuminated pinhole. A far distant subject is said to be at an infinite distance (symbol ∞). Technically the object must be so far away that light rays from that object arrive at the camera lens as parallel rays. An object like a coin viewed from a distance of 3000 diameters meets these requirements. We are taking about a 1 inch disk (25.4mm) viewed from 3000 inches = 250 feet (72 meters). OK that establishes infinity ( ∞).
Now the job of the camera lens is to refract (Latin to bend back or deflect). What happens is: Light rays enter the lens their direction of travel is altered. The new path resembles an ice-cream cone. The image formed is at the apex (pointy end) of this cone of light. We focus our camera by moving the lens forward or backward. The idea is to cause the apex of the cone to just kiss the surface of film or digital imaging chip. If the distance is right a super tiny circle of light plays on the sensitized surface. If the distance is wrong, this circle of light is perceived as a circle and not as a point of light. The size of this circle of light is the key. It must be so tiny that the human eye cannot discern it. This will be 0.5mm viewed from normal reading distance. Because the modern camera produces a tiny image of the outside world, we must enlarge this image to make it useful. We enlarge when we view this image on our viewing devices or make a print. The circle size of 0.5mm holds so the circle size in the camera must be super minuscule so it can withstand the needed enlargement. Typically this value will be a diameter of about 1/1000 of the focal length. Super high end lenses might be 1/1500 the focal. Thus the typical 50mm lens will deliver a circle size of 0.050mm.
Now the lens has limited refractive power. As you focus on nearby objects, the light rays from these objects do not arrive parallel, they arrive diverging. Nevertheless the job of the lens is to converge these rays to an ice-cream cone shape. To accomplish we must move the lens further away from film or digital sensor. In other words, we provide greater distance so the lens can do its job and attain the tiny circle size. By the way, the circle is called the circle of confusion because under the microscope it is seen as a circle with scalloped edges.
Now you know why the lens is racked further from film or sensor when focusing close. This elongated distance is called back-focus distance. We do not call this the extended focus distance the focal length. That is reserved for an infinity set-up( ∞). However mathematically it plays its part just like the focal length distance. The f/numbers are computed by dividing the focal length by the working aperture diameter. The result of this math is the focal ratio or f/number. These values engraved on the lens are only valid for the infinity set-up. At close distances the elongated back focus cases an error. This error is called “bellows factor”. At super close distances like unity (life-size or 1:1), the error is 2 f/stops. The back focus at magnification 1 is 2x the focal length. In other words at "unity" life-size a 50mm will be 100mm from the film or sensor. When doing close-up work the danger is under exposure due to bellows factor. This is mitigated in the micro lens design and in the modern cameras that measures exposure thru the lens.
More gobbledygook from Alan Marcus