Math/Optics: How can I derive the focal length of a lens from the magnification percentage of an image?
Math/optics wizards, please help. I need a precise, mathematical answer, not a guesstimate or a measure-it-in-the-field solution.
I need to derive the focal length of a lens that would have the same view as a magnified image.
I have two photos with identical dimensions in pixels:
WidePhoto is a photo taken with a camera with its zoom lens all the way wide. I know the focal length used for this photo, as well as the angle of view.
ZoomedPhoto is an image created by selecting a small area of WidePhoto and magnifying it to the same dimensions as WidePhoto. I know the dimensions in pixels of the selection area taken form WidePhoto to create this image. I also know the magnification factor as a percentage.
I've uploaded an example image here.
What formula do I use to derive the focal length of the lens needed to produce the "zoomed in" image?
If you can tell me how to derive the Angle of View from the image, I can calculate focal length:
(...that's right, isn't it?)
Thank you in advance for your help. My brain hurts from wrestling with this.