Gear: The Math Behind Zoom Lenses

"How far can you zoom with a lens like that?" That was a question I got from a relative of mine a while back. I remembered the specs, which said about 4:1 but, what does that really mean? To answer his question I rummaged through the folders in my photo-library and soon remembered shooting a view a while back using both of my two lenses...

So, to answer the question in a more graspable way, the first shot is taken with my Nikon lens at 18 mm, which is as wide an angle as I can get, and the bottom shot is taken with my Sigma lens at maximum zoom (300 mm). The bottom picture fits into the small area of the top one, and it paint's quite the picture, don't you think? I have to admit, I actually got a little surprised myself. A magnification factor of four does not sound that impressive after all. But when you think about it, magnification, when viewed in this context, is not linear, but rather geometric (since both height and width is involved), and that makes it all the more powerful.

So, to sum up, lets say that you would take one shot in 1:1 scale and then take several zoomed in shots and match them together like you would a jigsaw puzzle, making it into a bigger version of the 1:1 shot. In that case, twice the zoom is not equal to twice the area, as one might expect, but rather four times the area. And that means that four times the zoom is equal to 16 times the area! Cool huh?

I just love it when photography and math meet.

/MrsHjort