Tele Wide Angle

Tele Wide Angle

how does the 'Focal Length' of a Lens alter the 'Angle of view' from wide to telephoto, what's the mechanism?

I know that a lens's focal length is the distance between its optical centre (the point at which the light rays begin to converge), and the focal plane (the surface of the image sensor).

But could you explain how does the focal length alter the angle of view from wide to tele???

I want to know the science behind it; the mechanism...how does it work? How is the angle of view from wide to tele achieved by varying the focal length of a lens?

Thanks.

Can't do much ray physics here but in brief;
All lenses spread their light from the back element out into a circle which covers the film or sensor format.
The difference you seek understanding of, is in how wide the scene is collected from the front element(s) - you appreciate I hope that good lenses have many pieces of different grades of glass inside.

Leaving aside zooms for a minute, consider two opposites in fixed focal length lenses;
Let's say first a 24mm focal length 'wide angle' lens; the front glass is sharply curved so it sucks in light from wide left and right, also up and down. It squirts the light through various correction glasses then out the back at the standard size of circle, onto the film or sensor. The result picture seems to be very 'wide' and takes in a lot of the scene, but still on the same sized sensor/film shape. Things seem further away than they were at the time, but there is more of the scene in the shot.
Now a 180mm medium telephoto; this only receives light from nearly straight in front, passing it narrowly down the tube through correction lenses again, giving the same same picture size result as above but now, only a small rectangle of the scene. So, the pic looks as though you were much closer than you actually were (same as using a telescope)

OK? Now zooms. By compromising the necessary optical corrections they move groups of lenses to and fro from 'wide' to 'telephoto'. To do that, they must have many more corrective glasses inside all moving to and fro on internal cams, (as you twist the barrel), in more and more complex ways. They usually have smaller light transmissions than single focus lenses, because they would be too heavy and expensive otherwise.
So a 24mm f 2,8 is common enough
A 180mm f 2,8 is less common but available for big money
A 24 to 180mm f 2,8 would be either mortgage money or, very cheaply made. If cheap, the bits of glass wouldn't be accurately curved and not carefully centred to each other, and that lens would never ever take a sharp picture.
Hope that gives you a taster. Get Collins Dictionary of Photography, or better yet, Gunter Osterloh's '50 Jahre Leica M' in which (in english as well) he explains just what Leica (and Zeiss and Nikon) go through to design and production engineer top quality optics.
This science is a couple of hundred years old and now, only a very few people can use the present day sophisticated computer programs with which the lenses are designed and put into production.
Even the coatings of the glass are a big design and production issue; these people are working to fractions of the lengths of various light colour wavelengths, mind boggling billionths of a millimetre accuracies are involved.