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Shedding the light on F-numbers



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Focal ratio explained in plain language and simple straightforward steps.

photo by Le Anne E Crowe

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Learn photography - Introduction to F-numbers

By this point (if you have read focal length, aperture and f-numbers summarized ) you’ll already be aware that a lens marked 18 – 55mm f/4 – 5.6 will be a zoom lens with a focal length from 18mm to 55mm and a maximum focal length to aperture ratio of 4 to 5.6.

Armed with this information you will understand the following:

  • The extent to which these focal lengths affect the angle of view will depend on the image sensor size in your camera and that the difference from using the short (15mm) end to the long (85mm) end will give a magnification range of 55/18 = (approx) 3 , that is to say a 3x optical zoom.
  • That the F-numbers quoted refer only to the maximum aperture of the lens at each end of the focal length range (and not the total aperture range possible with the lens).
  • That when setting exposure – using the lens at f/4 will set a larger aperture than when at f/8.

If you have also read taking creative control over your digital photos , you will also be clear on the relevance of these factors in terms of their use to control the composition, exposure and creative effects over the resultant image.

So, if you know and understand all of the above – what else do you need to know about f-stops to learn photography?

Well, in truth you don’t really need to know any more than the above to become master of your photographic output. However, I am sure some of you (just like me) are curious as to why does

  • The focal length affect angle of view and how this has a magnifying effect?
  • The aperture and focal length work in a fixed ratio.
  • The f numbers follow this rather strange sequence of 1.4, 2, 2.8, 4, 5.6, 8 et (why cant they just be simple 1,2,3,4,5,6 etc.?)
  • Reducing the aperture from one f-number to next (e.g. f/4 to f/5.6) reduce the exposure by one stop (i.e. it halves the light)?

So, if you are interested in gaining a greater understanding of these factors (without needing a degree in applied mathematics!) then read on...


learn photography - Intensity of light over distance

Remember that in photography, that all the camera and lens are really doing is determining the intensity of light falling on the image sensor.

So understanding how the intensity of light changes over distance is of fundamental importance.

(Without going into the mathematics and physics that support the statement) it can be said that light intensity is inverse to the square root of distance.

This can be understood by considering a balloon.

Imagine drawing a circle on a partially inflated balloon. Now imagine blowing up the balloon so it doubles in size. The circle you drew will now also be twice as big but it will still only contain within its boundary the same amount of rubber – it will just be stretched more thinly – it will in fact only be ¼ as thick. If you keep blowing up the balloon, each time it doubles in radius the circle will also double in diameter but the thickness will reduce fourfold.

So in this example the balloons thickness is changing inversely to the square of distance, exactly in the same way the intensity of light does.


Learn photography
Relationship between focal length and aperture


OK, first we need to refresh our memories on some basic high school maths (don’t worry you wont need to do any calculations)

When the diameter of a circle is doubled its area increases by a factor of four.

When the diameter of a circle is halved, its area decreases by a factor of four.

Don't believe me? Trust me, if some one offers you a 6” diameter pizza for half the price of a 12” diameter pizza that’s not a great deal, as you are actually only getting ¼ the amount of pizza!

So the same applies to our apertures (which although due their construction are not strictly speaking perfectly circular, in reality the shape is close enough for the calculations to be applicable). When the aperture is doubled its area increases fourfold, so it will allow four times the amount of light to pass through. Likewise when aperture diameter is halved only a quarter the amount of light will pass through.

To see the relationship between aperture and focal length, lets return to our light intensity diagram demonstrated via an inflated balloon. (see diagram above)

Lets consider the circles we drew on the balloon. As the diameter of the balloon is doubled – so the diameter of the circle drawn on its surface doubles. As per our pizza example, we know that the area within the circle will be four times as much, however ... and this is the important point to grasp .... we also know that the wall thickness of the balloon has also simultaneously reduced fourfold at the same time. So the actual quantity of balloon material within the circle remains the same – imagine if you were to physically cut out the circle and weigh it, it would always remain the same, irrespective of how much it had been stretched due to being inflated.

So, if the diameter of the balloon represents the focal length (i.e. the distance light is travelling from the from the focal point to the image sensor) and the thickness of the balloon represents the intensity of light, we can see that as distance is doubled light intensity reduces fourfold.

If the circle drawn on the surface represents the aperture, we can see that as the diameter of the aperture doubles, its area increases fourfold, but due to the fourfold reduction in intensity over the same distance, the actual amount of light passing through the aperture remains the same! Thus we have a fixed ratio between aperture and focal length... and hence the reason F-numbers provide a universal way of adjusting exposure irrespective of focal length.

E.g. A 200mm lens at f4 will permit the same amount of light to pass through as a 50mm lens at f4 hence the exposure in both cases is the same!

learn photography
Understanding the F-number sequence

OK, So the reason that f-numbers are in ratio to focal length is now understood.

As is the understanding why the lower the f-number the higher aperture size. (see diagram above)

But WHY the strange sequence? Why do f-numbers not follow a simple sequence such as 1,2,3,4,5, etc.? After all, based on what we've learned if two lenses were to have for example f/5 they would both give the same exposure ... so why do we have f/5.6 instead?

The answer (i'm afraid) is to do with the maths! But don't worry i shall try to explain it in simple terms.

Lets return to our high school maths regarding circles

When the diameter of a circle is doubled its area increases by a factor of four.

When the diameter of a circle is halved, its area decreases by a factor of four.

This means if we take an f-number and half it - we will actually be reducing the intensity of light reaching the image sensor to only a quarter ...

E.g. f4 to f8 = aperture with half the diameter but only quarter the area = 1/4 the amount of light.

The requirement to finely control the exposure in photography is surprisingly small. If an image is under or over exposed, the logical first step to correct this is to halve or double the light intensity reaching the sensor.

This halving or doubling of light is officially known as adjusting by 1 E.V (E.V = exposure value) but more commonly referred to as 1 STOP.

So, lets suppose we take a photo at f4 that is too bright - and we want to adjust the exposure via the aperture. So our logical first step would be to reduce the light by half or 1 Stop. But we know that if we halve the f-number (ie halve the diameter) this will actual only give us 1/4 the exposure - which is the same as cutting it in half and then half again.. ie it is an adjustment twice as large as we are looking for or 2 stops

So, we have to ask ourselves "what reduction in aperture diameter will only cut the light by half?" which is the same as saying "what reduction in a circle's diameter will reduce it's area by half?"

Now if you do the maths you will discover that halving or doubling a circle's area involves multiplying or dividing the diameter by the square root of two - which happens to be 1.4 (approx)

Suppose we take a lens with a focal length of 100mm at f1 - the diameter of the aperture would be 100m/1 = 100mm

Now suppose we want to make a 1 stop reduction in exposure . To halve the area of the aperture we would have to reduce the diameter by dividing by 1.4

The new aperture diameter would be 100/1.4 = 71mm.

So the new f number (remember, this is focal length/ aperture) would therefore be 100/71 = 1.4

If we continue the sequence to reduce light in a series of 1 stop adjustments - we will need to reduce the diameter of the aperture by continually dividing the previous one by 1.4 - and thus the f-number sequence will also change by a factor of 1.4 at each stage, giving us the sequence

f/1 - f/1.4 - f/2- f/2.8 - f/4 - f/5.6 - f/7.9 - f/11.2 ....... look familiar?

You will see this is the typical f-number series that is used. (in practice as the need for absolute accuracy is not required, some of the numbers are rounded up or down e.g. f/7.8 is usually referred to as f/8)


Useful links "learn photography"

go to JARGON BUSTER digital photography terms explained

Focal length, Aperture, and f-numbers summarized

Exposure Explained

Whats your view? focal length, angle of view, magnification and crop factors explained

Depth of field explained

Take creative control over your digital photos

What equipment do I need for my style of photography?

Return from "learn photography" to Digital photography lessons

Return from learn photography - shedding the light on f-numbers to home page

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