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I have tried to find the exact way to calculate the focal length of the lens I need but I have not been able to find a good resource to make this simple enough for my limited optics knowledge. Can you please explain a simple way to calculate the focal length of a lens given the following inputs as an example:

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I would prefer a simplified mathematical explanation so that I may use it to make similar determinations in the future using a "plug and chug" method.

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What you did looks correct, you are using a form of h=f*tan(theta) which is used a lot in optical design. Usually one would use half the vertical sensor size (7.02/2 = 3.51) and half the height of the object(91/2 = 45.5), but in this case it doesn't matter.

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It is important to note that this equation assumes some things, mostly that the axis of the lens is pointed at the person's shoulder area in the "desired result" frame that you gave, though the result holds if you depart from that a little bit.

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I need to purchase my first ever lens. So far I've only used lenses that were built into a camera. This specific lens is for the BlackMagic Deign Pocket Cinema Camera (a video only camera, but one that uses photography lenses). I would prefer this to be a prime lens.

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