The old adage that you don’t get something for nothing applies here. Teleconverters are short lens extensions that attach between the lens and the camera body. They multiply the focal length, usually by a factor of 1.4 or 2.0, thereby magnifying the image. Since the aperture is a function of the focal length, it multiplies the aperture by the same factor. The result is that you lose light. You also lose image quality.
So why would you want to use something that seems so deleterious to your images? You can still get decent image quality if you understand the shortcomings of teleconverters and when you should and should not use them. It is also worth mentioning from the start that any teleconverter that can be had for under $150 is probably not worth using at all. A good teleconverter will cost you almost as much as a decent lens. The Canon ones are right at $430.
It is always best to put a high quality teleconverter behind the highest quality lens you can get. This usually means a fast, prime lens, i.e. one that’s f4 or f2.8 and has a fixed focal length. Putting an inexpensive, off-brand teleconverter behind a $400 zoom lens will probably yield images that would not be suitable for even web-based display, especially if you are used to enjoying sharp images.
A technical advantage of using a lens with a teleconverter rather than a longer lens is twofold. One, you get the added flexibility of being able to remove it should your subject move closer to you and two, with a teleconverter, you retain your close focusing distance. So whereas a 400mm lens may only focus as close as 15 feet, a 200mm lens that normally focuses down to 9 feet, will still have the same ability to focus down to 9 feet with a 2x teleconverter installed. In this way you can do macro photography with a long lens, something usually reserved for short lenses.
I often couple my 500mm f4 lens with a 2x teleconverter for a resulting system of 1000mm at f8. This is a powerful combination but it is quite slow. I would never consider hand holding this. For one, it is quite heavy, but because of the extreme magnification (think narrow angle of view), very small movements will induce blur into the image. So since I’m always using a tripod and a gimbal mount and this lens has good image stabilization, I can easily shoot even in reduced light at this aperture.
One way to get around the aperture loss is to mount a long lens on a cropped sensor camera body. In this way you get the effect of a 1.6X teleconverter but you don’t get the aperture loss. You do however get a loss due to sensor noise, especially at higher ISO values. I purchased a cropped sensor camera body just for this setup. I use it for almost all of my long lens shots. In fact, the images seen on this page were shot with that body, where the effective focal length (as compared to a full frame sensor) is 1600mm!
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