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DoF does change if you change the camera (so long as the sensor size is different). DoF is greater the bigger the sensor. Ever notice that point and shoot camera's give very little depth of field even with an f/2.8 aperture. There is even less DoF on a phones camera. The iPhone has an f/2.8 aperture. How often do you see pictures taken with a phone that have a lot of DoF... Never.
Dr Photo is correct. DoF does change when the camera's sensor is different.
Going from a DSLR to a Micro 4/3rds or iPhone is a whole different ball of wax due to the contraction of mirror lens placement. But if I take a 85mm prime lens at f/1.8 and take a head shot of you from 10ft on a 6D, then replace the camera with a cropped 600D and stand in the same spot as before. The DoF stays exactly the same. The only change is now you would be getting the nose and mouth shot instead of a full head shot. Its when one has to move further away from the subject that the DoF is lessened.
If you have an iPhone or iPod download Field Tools. Its a very helpful program that you can use to deduct your focal point and DoF range. Maybe it can help you understand the optical reasons behind what I was trying to explain.
For example on a Canon 6D with a 85mm prime at f/1.8 you DoF is at 9.8ft to 10.2ft, giving you 1/2 foot of play.
On a Canon 70D with the 85mm prime you must be at f/2.8 to have a 9.8ft to 10.2ft DoF. Also giving you 1/2foot of play.
Does this help?
Edit:
Hmm what I think confuses everyone is that with a Full Frame camera, the photographer can get closer to his/her subject and still get the subject in the frame. Its the act of being able to get closer that shortens ones DoF greater.
People generally say its the camera, because trying to explain in further detail is just to much for most people to fully understand. So we tell a little lie that its the camera even though its a lie, just in hopes they slightly understand something rather then nothing..
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