How does the focal length help in capturing wider or narrower picture?

Question

I have been trying to understand the science behind cameras and photography. I started with "camera obscura" and understood that * when rays of light are passed through a small hole (aperture) of a dark room (or box), the rays get inverted (upside down) and thus produces an inverted image

My understanding is that in most cameras there is a lens followed by the aperture, which is then followed by the image sensor (CMOS or CCD).

----rays-of-light-->    ||        ||       ||
                       Lens    Aperture   CMOS

If I am right, focal length is the distance between lens and convergence-point of the light on CMOS.

Quoted from http://www.howtogeek.com/63409/htg-explains-cameras-lenses-and-how-photography-works/

"Focal length also affects the kind of image your camera captures, as well. A very short focal length will allow a photographer to capture a wider field of view, while a very long focal length (say, a telephoto lens) will cut the area you’re imaging down to a much smaller window."

How does the focal length help in capturing wider or narrower picture ?

Answer 1

Think of it this way: say your eye is the CMOS sensor, and the lens/aperture is a small window in front of you. The closer you are to the window (the focal length) the wider your view will be. OTOH, if you're far away from the window you'll have a much smaller viewing angle.

I've drawn the projection lines through the center of the lens as if the lens was point-like, like a pinhole camera (camera obscura). A camera like this — with a pinhole instead of a lens — actually works but has a very low sensitivity; you'll need very long exposure times.

That's where the lens does its magic. Just making the hole bigger will get you a blurred image, but a lens focuses all the light coming from one point of your object to the same point on your sensor, as indicated by the red dashed lines.

Re focal length is the distance between lens and convergence-point of the light on CMOS: this correct for light rays coming from an object at infinity, i.e. as parallel rays. That's what defines focal length for a simple thin lens. When the object is closer the convergence point will be farther from the lens. Photographic lenses are a combination of often a dozen lenses which allow you to still focus nearby objects onto the sensor.