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I read about APS-C sensors EOS DSLRs, that if the focal length is 300mm and as the image ratio is 1.6 then the 300mm x1.6 = 480mm focal length. So if I add a 1.4x teleconverter to 300mm lens so I should be getting 480mm x1.4 = 672mm focal length?

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The focal length of the lens system with a teleconverter will be 300mm (from the lens) * 1.4x (from the converter). This will give you a lens system with a focal length of 420mm.

Cropping of the image by the sensor from the full field of view to the APS-C size doesn't change the focal length... it just gives you the same field of view if you had a lens that was 1.6x longer on a full frame camera. This distinction is key when you start looking at the depth of field calculations and the like.

The focal length of the lens does not change if you go into photoshop and crop the image to a smaller size. Nor does it change when you use a sensor that is smaller than the image circle projected.

In this case, the field of view would be the same as that of a 672mm lens on a full frame camera (the lens system focal length * 1.6).

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Yes, that's correct. Shooting a 400mm lens on the Canon 7D with a 1.4x converter, my effective focal length is 400X1.6X1.4=896mm equivalent.

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    Only insofar as the field of view, there are many other things 'focal length' is related to (depth of field, focal compression, etc) and those don't change as @MichaelT mentions – Shizam Aug 28 '14 at 0:20
  • @Shizam Well, they do or they don't, depending on the display size. If the cropped image is displayed at the same magnification, then the DOF, compression, etc will be the same. But if the cropped image is displayed using increased magnification to reach the same display size, then the DoF, compression, etc. will change. – Michael C Aug 28 '14 at 2:53
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    @MichaelClark By 'magnification' I assume you mean 'field of view' and I think what you're mentioning is actually a misconception. If you shot a landscape image with a 16mm lens that included a bird on a fence post and a barn 100' behind it and did a 50x crop on it such that it had the same FoV as a 800mm lens that shot just the bird, the DoF, compression etc would look very different on the two. Time to get some samples ;) – Shizam Aug 28 '14 at 21:05
  • @Shizam No it wouldn't because you would also be enlarging the cropped file by a factor of 50x more than the other file and thus enlarging the circles of confusion by a factor of 50 compared to the other file. Display size, along with viewing distance, affects the maximum size a circle of confusion can be and still be perceived as a point. By magnification I mean the ratio between the size of the image sensor and the display size. Printing an image from an APS-C camera at the same display size as an image from a FF camera requires 1.5x/1.6x more magnification (assuming neither is cropped). – Michael C Aug 29 '14 at 3:38
  • To put it another way, focal length of the same lens doesn't change when placed on a different camera. If one changes the shooting distance to get the same FoV with both cameras, the perspective (compression) will change because perspective is a function of subject distance and subject distance only. If one maintains the same shooting distance and crops the larger image to match the FoV of the smaller image, the images will be identical in terms of DoF, perspective (focal compression), etc. unless the resolution limits of one of the sensors compromises the amount of detail available. – Michael C Aug 29 '14 at 3:49

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