There are few lenses that work as well with extenders as the Canon EF 300mm f/2.8 L IS II USM Lens. This shot was taken with a Canon EF Extender 2x III mounted for a 600mm focal length. The results are remarkable. 600mm f/5.6 1/2000s ISO 320 Horse Jumping. For some, this is the ultimate thrill.
An f/2.8 lens can take a 2x TC and still be only an f/5.6 aperture, so it will still AF on any Canon body. These are certainly more expensive than the $1800 100-400 L, but older used ones can often be found on eBay and Craigs List for around $3000 to $3500 (original non-IS versions), and starting around $3500 to as much as $6000 (IS versions).
2.8" / 72 mm. 11.5 oz / 325 g. Buy Canon Extender EF 2X III featuring EF Mount Teleconverter, 2.0x Magnification Factor, Microcomputer Controlled, Communication Between Lens & Camera, Spectra Coating Reduces Ghosting/ Flare, Protective Fluorine Coating, Dust and Water Resistant, Compatible with Select EF Mount Lenses. Review Canon null.
The lens you describe, the EF 75-300mm f/4-5.6 III which often comes in a kit with the EOS Rebel T7, is not compatible with either EF extender. The EF Extenders can only work with the lenses which have clearance in the back to allow space for the extender's protruding element to sit inside. The rear lens element of your lens will come into
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