# Photography/Optics Equations and Formulae

#### LP

##### Your Brown Banana for Scale
DONOR
I took a class on campus for photography because I was definitely limiting myself and not fully utilizing all the capabilities of the camera. The class took me from shooting in full program to shooting in Manual and Aperture priority.

However one thing it didn't do was explain why certain things were the way they were. For example, when my teacher wrote down all the f-stop numbers, he explained that "these numbers just are the way the are" and never bothered to explicate because I suspect the class was not math-savvy.

I was inclined to solve this myself, and so I went to wikipedia and looked the equations up and derived the reason myself. I thought I would post that here to get some confirmation on my calculations and to allow others to post their own formulas that they feel are relevant.

$N=\frac{f}{D}=\frac{f}{2R}\Rightarrow R=\frac{f}{2N}$

N = f-stop number, f = focal length in mm, D = diameter of the aperture, R = radius of aperture

Area of light entering the lens is then

$A=\pi R^2=\pi\left (\frac{f}{2N} \right )^2 = \frac{\pi f^2}{4N^2}$

So if you want to determine how much more light you're going to get between 2 different f-stop values:

In another way, if you want to know what aperture will drop you by 1 stop (aka half as much light):

$\frac{A_1}{A_2} = 2 \Rightarrow \left ( \frac{N_2}{N_1} \right )^2 = 2 \Rightarrow N_2 = N_1 \sqrt{2}$

If you want to know what aperture will give you an extra stop of exposure (aka twice as much light):

$\frac{N_1}{\sqrt{2}} = N_2$

Note that none of these require the focal length of the lens, meaning that it doesn't matter what lens you have on, these will apply.

To figure out how many stops a particular f-stop is from another:

$\frac{N_1}{N_2} = \sqrt{2}^x = 2^{x/2} \Rightarrow x = 2 \frac{\log(N_1)-\log(N2)}{\log(2)}$

Obviously it'd be way too fucking hard to be sitting out in the field dividing by square roots and doing logarithms, but if you needed to you could always approximate
$\sqrt{2}\sim 1.4 = \frac{7}{5}$
. I feel it's just nice to know where numbers like f/5.6 come from. The series doesn't make sense otherwise.

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#### Ramseus

##### Have you been high today?
$N=\frac{f}{D}=\frac{f}{2R}\Rightarrow R=\frac{f}{2N}$

N = f-stop number, f = focal length in mm, D = diameter of the aperture, R = radius of aperture
Theoretically, at least. Magnification and entrance pupil and stuff jumble the math up. How is a constant aperture zoom actually a constant aperture zoom when the aperture remains physically the same size? Magic! When you look at the front of a lens and see the aperture appear to grow/shrink when you zoom in/out it's not a trick to your eye, it's actually relevant to light transmission. I don't get it, optical engineering is weird.