8x40 binoculars nowhere near 8x

facade

tempus_fugit said:

GDB2222 said:

What does 8 times bigger mean? 8 times bigger in each dimension?

This is a good question. To me “8x bigger” is simple in one direction, but when you have two dimensions as in a binocular view, I think most people reckon 8x bigger means 8 times longer in each dimension, whereas I do not think that will be the case. Because there are 2 dimensions effectively the proportion has to be squared. So something 2x as big in each direction is 4x as big overall. And something 3x as big in each direction is actually 8x as big (3 to the power of 2). So it sounds to me like the binoculars are magnifying things as I would expect.

k_man said:

With binoculars/optics the magnification level refers to linear dimensions, not size of area.

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Ahh!

I wonder if the first pair are measuring area magnification so 8x the area, sqrt 8 is close to 3....

I never thought of this.

I have really odd conventions, must come from a mix of model making, science and practicality.

A 1:72 model is 72x smaller than real life, and that refers to linear dimensions.

200x magnification on a microscope is linear dimensions, read the graticule and multiply by 200.

A3 paper is twice the size of A4, but that is area- fold A3 in half and you get A4

A 2 litre jug is twice the size of a 1 litre - volume. 

How odd to think that way, "size" and "scale" depends on an assumption of context.