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Light Transmission

This topic is one of the most difficult, but also one of the most important technical concepts to understand in photography.  Don't let all the numbers prevent you from reading and understanding it.  This knowledge is critical for exposing good images.

The aperture is the hole that allows light to pass through when you release the shutter, to expose the film or to allow the digital imaging chip to process and record the image.

The relative size of the aperture opening is indicated by the f-number.  If the f-number were to have a value of "4", it would be shown as f/4.  The "slash" in f/4 is there intentionally because this value is fractional in nature.

f-number defined

The f-number is defined as the focal length of the lens divided by the diameter of the aperture.  This value has no dimensions, or "units of measure."  For example, at a setting of f/11, the focal length is 11 times greater than the effective aperture diameter (called the entrance pupil).  The larger the f-number, the less light gets through.  The size of the entrance pupil is controlled by a diaphragm, which allows the photographer to adjust the f-number in order to control the amount of light that strikes the film or imaging sensor.  This further allows the photographer to control (within the limits of the camera and lens capabilities) the exposure time, depth of field, etc.

It's all relative

A 400mm lens set at f/4 has an effective pupil diameter of 100mm.
A 100mm lens, also set at f/4, has an effective pupil diameter of 25mm.

This is why the higher quality telephoto lenses are so big and heavy - they need to be!

For any given focal length, the larger the f-number, the smaller the opening.  An aperture of f/4 is larger than an aperture of f/8, just as a value of 1/4 (0.250) is larger than 1/8 (0.125).   However, because we are talking about properties of light, the relationship between these values is not quite this simple (it's not linear), but it's important to understand exactly what these numbers represent.

The following information may seem difficult to comprehend at first, but I believe that understanding this material will go a long way to helping you take better pictures.  I have not found the following information presented in any photography books that I have read.  This doesn't mean that it isn't out there, it just means that I haven't come across it yet, so I'm thinking that maybe you haven't either.

Where do these f-numbers come from?

Think of the aperture as the hole through which light must pass, in order to take a picture.  Think of that hole as nothing more than a circular window.  (In reality, they are not perfect circles, but they are close enough for us to approximate them as such.)

The bigger the window is, the more light will pass through it.  The size of that window is nothing more than the area of a circle.

The area (A) of any circle is the value of 'pi' (π = 3.1416) times the radius of that circle squared.  (The radius is half the diameter.)
So, A = π·r².  If you increase the radius of any circle by a factor of the square root of 2 (√2 = 1.4142), the area of that circle doubles in size.

Why is this important to me, as a photographer?

As you change the f-numbers on your camera, you are telling the camera how much light you want to allow through the aperture when the shutter is released (you're making the window larger [lower f-numbers] or smaller [higher f-numbers]).  Changing the aperture by one full f-stop will allow exactly twice as much light to come through (or exactly half as much, depending on which way you go with it).  An aperture of f/2.8 will allow twice the amount of light as f/4, while an aperture of f/5.6 will allow half the amount of light as f/4.  This also means that an aperture of f/2.8 will allow 4 times the amount of light as f/5.6, just as f/5.6 allows 4 times the amount of light as f/11.  As shown in Tables 1 and 2, the common aperture values are based on the square root of 2.

Compensating with Shutter Speed

As you adjust the aperture, you will need to compensate by also adjusting the shutter speed, in order to achieve the proper exposure.  Let's begin with the assumption that an image is properly exposed with an aperture setting of f/11 and a shutter speed of 1/320 [seconds].  If you decrease the aperture size by one full f-stop, to f/16, the 'window' is now half the size that it was at f/11, and will now pass only half as much light through.  To compensate for this, the shutter speed must be increased so that the window is held open for twice as long, to 1/160.  (Remember, these values are fractions.  A smaller number in the denominator means the value of the overall fraction gets larger.)

Conversely, if you increase the aperture size by one full f-stop, to f/8, the 'window' is now twice the size that it was at f/11, and will now pass twice as much light through.  To compensate for this, the shutter speed must be decreased so the window is held open for only half the time, to 1/640.

The proper combination of aperture setting and shutter speed will depend on your unique lighting situation, and the type of picture that you're trying to take.  Using an incorrect f-number and shutter speed could result in your image being either overexposed (too slow a shutter speed or too large an aperture) or underexposed (too fast a shutter speed or too small an aperture).

Table 2 will demonstrate what these f-numbers mean for calculating exposure values, and the impact that it has on shutter speeds.  Note that the values in the far right columns of Tables 1 and 2 are the exact inverse of each other, row by row.  This is because the aperture size and the required shutter speed are inversely related, as explained in the paragraphs above.

Table 2

The following values will
continually be multiplied
by √2

( f / ? )

Fast Lens vs. Slow Lens

When you hear the terms "fast lens" or "slow lens", this is actually a reference to the lens' largest possible aperture (smallest possible f-number).  Because a lens with a larger aperture will allow greater light transmission, it will allow for a faster shutter speed in order to achieve any given exposure.  An f/2.8 lens is faster than an f/4 lens.  An f/2.8 lens with a shutter speed of 1/500 will give the same exposure as an f/4 lens with a shutter speed of 1/250, only the f/2.8 lens can do it in half the time.  Faster lenses can be stopped down to achieve slower shutter speeds when needed (to capture the motion of flowing water, for example).  Either of these two lenses above could be stopped down to f/5.6, and provide an equivalent exposure with a shutter speed of 1/125.  An f/2.8 lens might have a full range of f/2.8 to f/32.

Slower shutter speeds can result in unwanted motion-induced blur, and is why a tripod, or some other stabilizing device, is needed when using slower shutter speeds.  In general, faster lenses have greater capability, and allow you to stop action with faster shutter speeds, corresponding to their larger maximum aperture.  Sports photographers, for example, will use a fast telephoto lens to stop the action at a soccer game or race track.  With everything else being equal, a faster lens will, of course, be larger, heavier, and more expensive than a slower lens.

Using Filters

Let's say that you're using a neutral density filter that changes your exposure by two f-stops.  This means that it allows only 1/4 of the light to pass through.  So, a 2-stop filter reduces light transmission by a factor of 4, not 2.  A 3-stop filter allows 1/8 of the light to pass through, etc.  Table 3 will show you various common designations that you may see, in reference to filters.

    
Illuminating your subject

In addition to controlling your exposure by changing your aperture setting (f-number), you can also control how much light falls on your subject by using an external light source.  However, it's very important to keep in mind that properly adjusting the light intensity may not be intuitive.

As light travels away from its source, the brightness of the light does not decrease in a linear fashion.  In other words, if a person is standing 50 feet away from a bright light, and another person is standing 100 feet away from the same light, you might assume that the light seems twice as bright to the person who is only 50 feet away (or half as bright for the person 100 feet away.)  This assumption is completely wrong!  See the example below for a detailed explanation why.  [The answer is 4 times as bright for the person standing 50 feet away.]

[The scientific reason why:  Light intensity obeys an inverse square law.  In other words, as you move away from a light source, the intensity of the light decreases in a manner that is inversely proportional to the square of the distance.  The intensity of a light will double (or halve) as you move closer (or farther) from it, based on the square root of 2.  Yes, the dreaded √2 is back.]

Changing light intensity based on distance

Suppose that you're using an artificial light source (not the sun) to illuminate a subject.  The picture is overexposed, so you want to put half as much light on your subject.  How far from the subject do you move the light?  Hint: It's not twice as far away.  Remember, light intensity doubles or halves based on the square root of 2.

If your light source starts out exactly 100 inches away from your subject, you need to move it the square root of 2 (1.4142) times away for half as much light to hit the subject.  Conversely, you need to move it 1/1.4142 times (0.7071) closer to put twice as much light on the subject.

With a starting point of 100 inches between your light and the subject, the subject will be half as illuminated if the light is moved to a point 141.42 inches away, and it will be twice as illuminated if the light is moved to a point 70.71 inches away.  If you moved the light to a point 50 inches from the subject, it would be 4 times as bright as it was from 100 inches away.  If the light were moved to 200 inches away, it would be only 1/4 as bright as from 100 inches away.

The Sun as a light source

While the inverse square law, as it relates to light intensity, will always be applicable, it's important to note that it relates to the distance between the light source and the subject.  If you are using only the sun as a light source, the inverse square law becomes irrelevant because you really can't change the distance between your subject and the sun.

You can change the distance between your camera and the subject, but this doesn't affect the illumination of the subject by the sun.  You could choose to use a light diffuser or some other device to block some of the light, or you could use a reflector to put more of the light on the subject, and possibly from a slightly different angle.

You can also use the various exposure settings of your camera to either increase or decrease the overall exposure, when modifying the light source is not an option (shutter speed, aperture, exposure compensation, etc.).