Question

In photography, f-numbers represent lens aperture. Write the missing f-number in the sequence:
f/2.8, f/3.2, f/3.5, f/____, f/4.5, f/5.0, f/5.6

Hint:

Full stops multiply by \(\sqrt2\); third-stops multiply by \(2^1/6\). The common third-stop run around f/4 is: 3.5, 4.0, 4.5.

Answer 1

This is the standard third-stop f-number series. Each step multiplies the f-number by \(2^{1/6}\approx1.122\). \[ 2.8\times1.122\approx3.14\ (\to3.2), 3.2\times1.122\approx3.59\ (\to3.5), 3.5\times1.122\approx3.93\ (\to\boxed{4.0}), \] and continuing gives \(4.5,\ 5.0,\ 5.6\). Hence the missing value is \(\boxed{\text{f/4}}\).