sports photographers often use large aperture, long focal length lenses. what limitations do these lenses impose on the photographs?

The depth of focus achievable with those lenses is small.

Explanation:

A larger aperture makes it much harder to focus on more than one object. When using a telephoto lens (the ones the question is referring to), the depth of focus is very small. For example, using a telephoto lens to take a photo of a runner might get the runner in focus, but certainly not the track, or the audience behind them. If you look at photos, especially older photos, of Olympians in almost any sport you can see this.

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