I know it has been asked before, but I'm still not sure if I understand the focal length issues of EF-lenses on APSC cameras in Canon system. I already have the EF-S 55-250 IS STM and I'd like to buy a longer telephoto - if I get the EF 70-200 will it give me effectively more range than EF-S 55-250 (200 x 1.6 = 320 mm)?
Answer
No, a 70-200mm lens will give you less range than a 55-250mm lens on both ends of the focal lengths. In order to understand the comparative fields of view yielded by an EF-S and an EF lens on an APS-C camera body in terms of the same field of view on a full frame/35mm camera, you must multiply the focal length of both lenses by the 1.6X crop factor.
Your EF-S 55-250mm f/4-5.6 IS lens gives an FoV equivalent to an 88-400mm lens on a FF camera.
An EF 70-200mm f/4 (or any other 70-200mm lens) mounted on your Canon APS-C camera gives an FoV equivalent to a 112-320mm lens mounted on a FF camera. What the 70-200mm "L" Series lenses give you is significantly better image quality and wider, constant apertures. The faster speed of a wide aperture telephoto lens is vital when shooting action or sports under challenging lighting.
A 70-300mm telephoto lens mounted on your Canon APS-C camera would give you an equivalent FoV of a 112-480mm lens mounted on a FF camera. But most 70-300mm lenses are not much, if any, better optically than the 55-250mm lens you already have. They also usually have the same f/4-5.6 slower variable aperture.
For more, please see Why do Full Frame lenses and crop body lenses exhibit the same crop factor when used on a crop body camera?
For more on the optical differences between the EF 55-250mm f/4-5.6 IS II, the EF 70-300mm f/4-5.6 IS, and the Canon 70-200mm "L" series lenses,please see this answer to What improvements I could expect upgrading from Canon EF 55-250mm IS to a Canon 70 - 300mm? (Hint: Not a whole lot)
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