How can the focal length of a lens be many times greater than the lens's physical length?

Question

I bought a Tamron 16-300. Question is: how can it have a focal length 0f 300 mm when it is only about 30 mm long? Doesn't the lens have to be 300 mm from the sensing element?

Answer 1

According to a related discussion on dpreview:

A lens can be made physically shorter than its focal length by the use of additional lens elements called a telephoto group.

According to the Wikipedia page for Telephoto lens:

The basic construction of a telephoto lens consists of front lens elements that, as a group, have a positive focus. The focal length of this group is shorter than the effective focal length of the lens. The converging rays from this group are intercepted by the rear lens group, sometimes called the "telephoto group," which has a negative focus.

Answer 2

There are several approaches to getting a lens system with a long focal such that it is closer to the media than its focal length. The most common of these is the 'telephoto' lens

^{From Wikipedia: https://commons.wikimedia.org/wiki/File:Lens_telephoto_1.svg}

What this does is it that the outer lens element (at the front of the lens system) has a positse focus and is bending the light more significantly than a simple lens of some focal length would. Then the second element group (with a negative focus) refocus the light again so that the light appears to have come from a much greater focal length. This allows for a shorter lens system than the focal length would be otherwise.

Another approach is to 'fold' the lens with mirrors.

This is a 500mm lens that is only 109mm long.

The light path itself does have some glass in it, but it is bounced around a bit:

^{From Wikipiedia: https://en.wikipedia.org/wiki/File:MinoltaRFRokkorX250f56text.svg}

You will note that the light comes in, is adjusted a little bit, bounces off the back (and adjusted), bounces off the front (and adjusted) and then goes through a few more pieces of glass. The light path is folded through the lens to get a much longer focal length in a smaller distance.

Answer 3

Making a lens shorter than a simple lens is exactly what the term telephoto means. Telephoto groupings basically act kind of like a magnifying glass, making the field of view close faster than would happen with a simple lens system.

Traditional telephoto lenses still required a fair bit of space and lots of lenses to operate, but newer things like diffractive optics can condense this down even further to make very short telephoto lenses without sacrificing a whole lot in terms of image quality.