Originally Posted by
Clockunder
1 stop more = double the amount of light
1 stop less = half the amount of light
Area of circle = pie * r^2
Area of circle twice the size above = 2 * pie * r^2
= pie * [(square root of 2) * r]^2
So the radius and diameter of the bigger circle is (square root of 2) of the radius and diameter of the smaller circle which is half the size of the bigger circle.
In other words, the radius and diameter of the smaller circle is 1/(square root of 2) of the radius and diameter of the bigger cicle which is twice the size of the smaller circle..
square root of 2 = 1.4142
In photography, F number is the diaphragm divided by the focal length.
For the same focal length, doubling the size of the diaphragm will let in double the amount of light = 1 stop more.
Although the diaphragm is not exactly a circle, the concept of area is the same.
Doubling the diaphragm will increase the radius/diameter by a factor of (square root of 2) or 1.4142.
Halving the diaphgragm will decrease the radius and diamenter by a factor of 1/(square root of 2 or 1.4142)
So the stops for F numbers are :
F/1
F/(1 * 1.4142) = F/1.4 which is 1 stop less than F/1
F/(1 * 1.4142 * 1.4142) = F/(1.4142)^2 = F/2 which is 2 stops less than F/1 and 1 stop less than F/1.4
F/(1* 1.4142 * 1.4142 * 1.4142) = F/(1.4142^3) = F/2.8
And so on……..
When F/1 and F/2 is only 2 stops difference, F/1.4 and F/1.8 can’t possibly be 2.5 stops difference.
In general :
1 stop difference = 1.4142
2 stop difference = 1.4142^2
3 stop difference = 1.4142^3
Each power difference of (square root of 2) is 1 stop.
To calculate the no. of stops between 2 F numbers :
Let A and B be the 2 F numbers and n be the no. of stops.
A = B * (1.4142)^n
(1.4142)^n = A/B
Log (1.4142)^n = log (A/B) ………………can use any logarithm base, 10 or natural or etc.
n * log 1.4142 = log (A/B)
n = [log(A/B)/(log 1.4142)]
General equation : n = (log F1/F2) / log (square root of 2)
Since square root of 2 = 2^0.5,
n = log (F1/F2) / log 2^0.5
= log (F1/F2) / 0.5 log 2
= 2 * log (F1/F2) / log 2
= 2 * lg (F1/F2) where lg is log base 2 (This is the equation given by grantyale).
The easier way on calculator is just use any log base with the equation
n = log (F1/F2) / log (square root of 2)
You may use 1.4 as square root of 2 for approximation because the F number we see are also rounded up/down figures.
For F/1.4 and F/1.8,
1.8 = (1.4)^n
n = log(1.8/1.4)/log 1.4
= 0.75
So F/1.8 is 0.75 stop less than F/1.4.
You may also use the same logic to calculate what the F number is given another F number and their no. of stop difference.
For e.g. what is the F number which is 2.5 stops more light than F/1.8?
A= B * (1.4)^n
1.8 = (B) * (1.4)^2.5
B = 1.8/(1.4)^2.5 = 0.78 = approximately 0.8
So F/0.8 is 2.5 stops brighter than F/1.8.
or
A = 1.8 * (1.4)^2.5
= 4.2
So F/4.2 is 2.5 stops less than F/1.8.
(No surprise since there is already 2 stops difference between F/2 and F/4).
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