Focal Length Definition in a Camera

Question

I am having trouble understanding the meaning of focal length. I thought focal length was the distance between the lens and image sensor. These sources validate that definition: http://ksimek.github.io/2013/08/13/intrinsic/ http://imaging.nikon.com/lineup/dslr/basics/19/01.htm

However, I'm not sure how this works with the Lensmaker's Equation:

The lensmaker's equation calculates focal length as a function of the lens geometry and refractive index.

I'm wondering if refocusing a camera will change the focal length. By definition 1, if we move the lens closer to the sensor to focus, it will change the focal length. But by definition 2, the focal length is intrinsic to the lens and will never change.

How do these two definitions relate? Even if we assume the camera lens is thin, the thin lens approximation is still a function of the lens geometry, not the distance from the lens to the sensor.

Answer 1

The focal length of a lens doesn't change - it is a function of the lens material, shape and (for a complex lens) the spacing between the elements.

For an object at infinity placing a sensor at one focal length behind the principle plane will give you an in-focus image. You can focus on a closer object by moving the lens away from the image plane.

There is a small effect of focal length change with focus because not all rays entering the lens at all angles are focussed perfectly. This effect is called 'breathing' and you try and avoid it in high quality cinema lenses. In still image lenses it isn't usually a concern.

Answer 2

If you want to take an in-focus image of an subject that is infinitely far away, you put the sensor at the focal point of the lens. If you want to take an in-focus image of something closer, then the incoming light rays are not parallel, but are diverging. The sensor needs to be moved back, increasing the distance between lens and sensor, to accommodate the "extra bending" the rays need to do.

Answer 3

Focal length is a peoperty that is independent of the position of object. It is taken for object at infinity so that the rays incident on the lens are parallel. Your formula will give the focal length that is the image position with object at infinity. I hope this clears the confusion.

Answer 4

Focal length is constant for each lens and is the plane distanced from the lens such that to parallel rays coming from an object at infinity on one side will bend and converge at that plane on the other side of the lens.

This happens because the refraction of the lens has bent the rays of light in. If you hold a 3d object at some distance to the lens, its image as smaller 3d projection will form at a distance on the other side farther than focal length.

As you move this object closer to lens its projection gets farther away from lens focal plane and also a bit bigger, till you hold the object at the focal length of lens in front side. Then its image will project to infinity on th back side!