# How does a change in FL relate to a scalar change in FoV?

Started Jul 28, 2013 | Questions thread
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Re: How does a change in FL relate to a scalar change in FoV?

edu T wrote:

Suppose I'm thinking about buying a longer lens and I want to visualize the effects of its narrower field of view by cropping-and-upsizing some already taken shots . Then,

• If I have a picture W pixels wide shot with a L-millimeter-long lens, to which W' should I crop the picture to match the FoV of an L' focal length which is n times M?

(Sorry if I'm not trying to figure this formula out myself, but still haven't found the rusty trigonometry that hopefully lies like flotsam in some backwater corner of my mind. Just wondered someone would know it more or less by heart?) Thanks!

You should understand that Thales law applies in linear dimensions and another law (I don't remember the name) for areas and focal length.

For linear dimensions to get from a 55 mm to 200 mm FOV you need to crop in such a way that the diagonal  is in the same proportion as the focal lengths. So if you have 3000x2000 original photo and 55 mm you get the same FOV as at 200 mm if the longest length would be 825 mm. The result image is 825x550 mm (to keep the proportions) so from 6000000 pixels you are left with 453750 thus the square of the focal lengths ratio. As the ration of focal lengths is 3,6363 the ratio of the area is 13,223 thus the the square of it.

BTW. It is better not to upsize.

Good luck!

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Nikon D5100 Olympus PEN E-PL5 Nikon D7200 Nikon AF-S DX Nikkor 16-85mm f/3.5-5.6G ED VR Tokina AT-X Pro 12-24mm f/4 DX II +13 more
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