Why focal_length in viewport_height?

[xrailab]

Anyone explain to me why, in the section Positionable Camera, we have in the code

auto viewport_height = 2 * h * focal_length;

In particular, why do we multiply focal_lenght? I am sure it is important to have a viewport dimension that depends on focal_lenght , but I cannot realize the modelling rationale.

[hollasch]

You must multiply by the focal length in order to preserve the desired viewing angle. $tan(\theta) = y/x$, so $y = x \cdot tan(\theta)$. Here, x ⇔ focal_length.