How do you appreciate the coincidence of the experimental facts

How do you appreciate the coincidence of the experimental facts with the results obtained by a ray diagram in terms of behaviour of images formed by lenses ?

By using ray diagram, the reflected ray must be placed at a particular point by the principal axis. That means we have to find the images, shorter or longer.
By using ray diagrams, we are able to find the focal length from lens maker’s formula.
In many optical instruments, some lens combinations are used to increase (magnification) or decrease (diminished) of the image.
Shadows some times seems longer and some times shorter than original. When unit light passes through a prism then VIBGYOR is formed on the principal axis, that means converging take place.
So, I appreciate the coincidence of the experimental facts with the results obtained by a ray diagram in terms of behaviour of images formed by lenses.