wham121736 Loc: Long Island, New York

I need a simple explanation of why on one lens f/2 provides a smaller DOF than f/16?

TriX Loc: Raleigh, NC

Try this tutorial: http://www.cambridgeincolour.com/tutorials/depth-of-field.htm

Leitz Loc: Solms

Kmgw9v Loc: Miami, Florida

Delete

lamiaceae Loc: San Luis Obispo County, CA

An explanation you will get (and have, two I see already). Simple, an illusion. This is why Photography was historically a science before it became an art. One of the very first Photographers was William Herschel who also was an Astronomer!

waegwan Loc: Mae Won Li

Is everything the same like sensor or film size and distance to the subject?

Manglesphoto Loc: 70 miles south of St.Louis

Simple answer:
Don't sweat the why, just accept the fact that it does!!!!!

jerryc41 Loc: Catskill Mts of NY

You know how when you have trouble seeing something you tend to squint? That's what the lens is doing. It's using a smaller aperture to cut out extraneous light.

Try this. Shape your hands into the shape of a pair of binoculars and look through them. What you see will be a bit clearer.

cthahn

There is no simple answer. Do some reading on lenses, optics, and depth of field. There are laws of optics. If you want a simple answer, the wider the lens opening, the less depth of field. The smaller the lens opening, depth of field increases. Take a course in the basics of photography and learn something.

Jack 13088 Loc: Central NY

There is if, and only if, geometry is "simple" to you. It may be a right brain/left brain thing or whatever. If it is obvious why the f/ number is defined as it is you are good to go. If that is a mystery than the explanation will remain a mystery so just accept as a fact. It is no less useful as a fact. BTW mentioning facts is not a political statement!

boberic Loc: Quiet Corner, Connecticut. Ex long Islander

I was jst about to say the exact same thing. As far as I am concerned there is a tiny little guy inside things that works with a calculator and figures out all those kind of things.

gvarner Loc: Central Oregon Coast

Ahhhhhhh yes, a science before it became art. I can see that now, why there is so much attention paid to technology and technique as opposed to artistic expression, and why GAS is so prevalent. It's our fascination with gadgetry. If we just mastered the science, the technology, the gadget, somehow art will pop out the other end. There are those who have mastered both worlds but for me, I'm still looking at art through my lens.

Jack 13088 Loc: Central NY

If you want to try geometry try Depth of field in Wikipedia. It is not too geeky (not that I can judge such things.)

Clapperboard

lamiaceae William Herschel -- Yes he was an astronomer and at one time he lived in Slough, Buckinghamshire, in England. His house which also housed his observatory was in Hershel Street in Slough. The street was named after the man.
To the OP
The simple reason for narrower depth of field at wider apertures is that all the lens makes up all the picture. At narrow apertures part of the rays coming through the lens is blanked off. At wider apertures the rays from the outer section of the lens also reach the sensor. As the rays from the outer part of the lens hit the lens at a greater angle of incidence than those hitting the more central part of the lens they have to be refracted more to be focused on the sensor. The lens cannot focus all the rays to an absolute point on the sensor. Thus a 'circle of confusion' is created. While that 'circle of confusion' is acceptably small, that is it is hardly noticeable to the human eye in the final print it is accepted as sharp, and the subject is regarded as being within the 'depth of field'. When the 'circle of confusion' becomes large enough to be noticed by the human eye it is regarded as out of focus and the subject, or that part that is then blurred, is considered to be outside the depth of field.
To keep this explanation simple I have avoided too many 'scientific references'. Be assured the explanation is correct, and accurate. I mention this because it will stand up to scientific appraisal.
By now of course I'll Bet You're Glad You Asked!!!!!!!

camerapapi Loc: Miami, Fl.

"I need a simple explanation of why on one lens f/2 provides a smaller DOF than f/16?"

Did you say on one lens? If you ask me ALL lenses set to f2 will ALWAYS have less depth of field than any other or similar lens set to f16. This is basic photography. The smaller the aperture (the higher the number) the more depth of field.
Depth of field is regulated by some factors that I will not mention here but a Google search will provide you with plenty of information.