X specification for quantifying zoom magnification

[Looper]

I can't seem to find a clear answer to this simple question no matter what kind of forum searching or googling I do:

When a camera states that it has a 3X optical zoom does that mean that the subject will appear:

A. As if you were 1/3 of the distance away that you actually are

B. 3 times larger in its image size by area (i.e. square root of 3 larger in either in height or width)

C. 3 times larger in its image size by height or width (i.e. 9 times larger in apparent area)

D. None of the above

I guess this must have been asked before but I couldn't figure out a good search term

Thanks

 

[Alpha]

A. Sort of.

Technically, I believe it means that the lens can zoom from say 50mm to 300mm (3x increase).

 

[Looper]

Thanks for the answer Max.
A bit of simple trigonometry suggests that A and C are actually effectively the same I think.
I am a little bit puzzled about the focal lengths you are talking about - 35mm equivalent?
The Lumix TZ3 has a 10x optical zoom which the marketing stuff says is 280mm equivalent in the old money (35 mm equivalent).
I remember from my old 35mm days that 50mm lens is 1X i.e. no zoom.
The question I was asking is really does the 3X magnification refer to 3X bigger in terms of area or 3X bigger in terms of width or height.
I think you are probably right. It is 3x bigger in width or height and therefore 9X bigger in area.

 

[Alpha]

You'll have to forgive me if what I'm about to type is incorrect. I've had a fair bit of wine tonight.

Here's my thinking in my inebriated state:
I do think it's a matter of focal length, as opposed to "size" per se. That is, your avg 35mm lens has a focal length of 50mm. Twice as long (2x) would be 100mm, and twice as long as that (3x) would be 200mm. I say that because it's not simple multiplication. I know for a fact that a 150mm lens will not produce an image appearing to be 3x as close as a 50mm. But if my memory serves me correctly, a 200mm lens would.

However, I don't know that it necessarily converts to subject "size." Or if it does, it's in the same multiple sort of way as the focal length, and not three times the size. So if you were looking at a subject through a 50mm lens, and on the neg it was 5mm tall, then it should be 10mm tall through a 100mm lens, and 20mm tall through a 200mm.

I'm gonna have to come back and read through what I just wrote in the morning.

 

[Looper]

Thanks for trying with the explanation Max (in your 200mm example wouldnt 15mm be 3X rather than 20mm? hmmmm)

I have searched quite a bit more on the amazing interweb but amazingly I cannot find any clear explanation.

3X magnification (as claimed by most cheap digital cameras) - it either means the 'normal' (50mm focal length for 35m cameras) image is magnified
A. 3X larger in width or height (9X larger in area)
or
B. 3X larger in area (1.732X larger width or height) (1.732 is root 3)

Who knows? not me

 

[Alpha]

Oh I dunno about the size thing... *sigh*

But I believe I'm correct on the focal length bit.