My camera employs a 30x optical zoom, with focal length ('f' from here on out): f = 4.3 mm to 129 mm.
If I am at 1x and I see an object as 100 pixels, to enlarge it to 150 pixels, can I set the zoom to 1.5x? This is the main question.
Then, I ask other questions from academic interests:
I understand that a zoom of 1.5x changes the focal length to 1.5*4.3 = 6.45. In "How do zoom, magnification, and focal length relate?", it is said that the the relation between focal length and the zooming-in is:
...quite linear. Double focal length , half width and height of the target in front of you.
So it should be correct to proceed as I initially said. However, I would like more information. Is it exact? What is the math behind it?
Following other answers, I get that varying the focal length varies the angle of view, and hence the size of the objects. On Wikipedia Angle of View there is a derivation for the angle of view. There are two questions: First, the formula is 2*atan(d/(2*f)). So, Wikipedia shows the relationship as not linear...? Second, the derivation assumes a focus at infinity. With a focus not at infinity, the angle of view also depends on the distance of the object! But probably for objects greater than or equal to 1 meter, there is no noticeable difference?