EXPOSURE and the EV INDEX

When the shutter speed and the aperture adjustments are used together we can then begin to understand the characteristics of exposure and learn how to control it. The most basic and widely used of all photographic mathematical formulae is the law of reciprocity.

e = i(t)

In this equation ‘e’ represents the total amount of exposure. ‘i’ represents the intensity of the light which is controlled by and generally represented by the aperture setting. ‘t’ stands for the time, or duration, that the light is allowed to expose the film which is controlled by and generally represented in turn by the shutter speed setting. This equation states that a directly related ratio of shutter speed and aperture will provide a certain amount of exposure to the film. As you will see later, if either i or t are changed then the other must also equally be changed to reciprocate the first, hence the name Law of Reciprocity.

We will now move on to the Exposure Value Index or EV Index. The table below shows us how different shutter speed and aperture combinations provide the same amount of exposure for film.

Exposure Value Index (using aperture and shutter speed)

	f/1	f/1.4	f/2	f/2.8	f/4	f/5.6	f/8	f/11	f/16	f/22
1 sec	EV0	EV1	EV2	EV3	EV4	EV5	EV6	EV7	EV8	EV9
½	EV1	EV2	EV3	EV4	EV5	EV6	EV7	EV8	EV9	EV10
¼	EV2	EV3	EV4	EV5	EV6	EV7	EV8	EV9	EV10	EV11
1/8	EV3	EV4	EV5	EV6	EV7	EV8	EV9	EV10	EV11	EV12
1/15	EV4	EV5	EV6	EV7	EV8	EV9	EV10	EV11	EV12	EV13
1/30	EV5	EV6	EV7	EV8	EV9	EV10	EV11	EV12	EV13	EV14
1/60	EV6	EV7	EV8	EV9	EV10	EV11	EV12	EV13	EV14	EV15
1/125	EV7	EV8	EV9	EV10	EV11	EV12	EV13	EV14	EV15	EV16
1/250	EV8	EV9	EV10	EV11	EV12	EV13	EV14	EV15	EV16	EV17
1/500	EV9	EV10	EV11	EV12	EV13	EV14	EV15	EV16	EV17	EV18

All exposure combinations on this table of equal value will give the same amount of exposure to the film. 1/125 @ f/4 will provide the same amount of exposure as will ¼ @ f/22. The same goes for 1/8 @ f/11 and 1/500 @ f/1.4. As each one increment change in shutter speed is either a halving or a doubling of the amount of time that light reaches the film, each one increment change in aperture is either a halving or a doubling in the geometric area that light passes through to reach the film. If you were to increase the amount of time that light reaches the film, let’s say, from 1/60 to 1/30 and you want to maintain the same amount of exposure, then you must decrease the size of the aperture from f/11 to f/16. If your subject calls for a general exposure value of EV13 according to the exposure value index then one setting would be 1/60 @ f/11. If you wanted instead to portray your subject darker you might decrease exposure by increasing to EV14, 1/125 @ f/11 or any other related combination. You could increase exposure as well by increasing to EV12, 1/60 @ f/16 or any other related combination. Please note that an increase of exposure, by using this table, is indicated by a decrease in numeric value, and a decrease of exposure shows an increase in numeric value.

Also I would like to differentiate between some terms here. If I am purposefully raising or lowering exposure I refer to it as increased exposure or decreased exposure, indicating control in the action. The terms overexposure and underexposure generally refer to errors in exposure.

There is also a way to estimate exposure using film speed ratings. There is another equation in photographic circles referred to as the ‘SLAT’ rule, a mere extension of the law of reciprocity. However, to maintain continuity amongst algebraic equations in this article we will refer to this rule as the ‘SLIT’ rule as ‘i’ has already been assigned to the intensity of light.

e = s(l) = i(t)

‘e’, as before, exposure value. ‘i’ still represents intensity of light and ‘t’ stands for time duration. Now we include the following. ‘s’ represents speed or a film’s ISO or speed rating and ‘l’ represents the additive light value or ALV for the ambient light in which you are shooting and is measured in candles per square foot. There are many guides for determining ALV and through experience you can familiarize yourself with these values. Below is another table that shows these new relationships within the Exposure Value Index.

EV Index (using ISO rating and Additive Light Value)

	6c/ft2	12c…	25	50	100	200	400	800	1600	3200	6400
ISO3	EV0	EV1	EV2	EV3	EV4	EV5	EV6	EV7	EV8	EV9	EV10
6	EV1	EV2	EV3	EV4	EV5	EV6	EV7	EV8	EV9	EV10	EV11
12	EV2	EV3	EV4	EV5	EV6	EV7	EV8	EV9	EV10	EV11	EV12
25	EV3	EV4	EV5	EV6	EV7	EV8	EV9	EV10	EV11	EV12	EV13
50	EV4	EV5	EV6	EV7	EV8	EV9	EV10	EV11	EV12	EV13	EV14
100	EV5	EV6	EV7	EV8	EV9	EV10	EV11	EV12	EV13	EV14	EV15
200	EV6	EV7	EV8	EV9	EV10	EV11	EV12	EV13	EV14	EV15	EV16
400	EV7	EV8	EV9	EV10	EV11	EV12	EV13	EV14	EV15	EV16	EV17
800	EV8	EV9	EV10	EV11	EV12	EV13	EV14	EV15	EV16	EV17	EV18
1600	EV9	EV10	EV11	EV12	EV13	EV14	EV15	EV16	EV17	EV18	EV19
3200	EV10	EV11	EV12	EV13	EV14	EV15	EV16	EV17	EV18	EV19	EV20

Now let’s assume the use of ISO 800 film. If you want to expose the full moon, the ALV of a brightly lit full moon is slightly more than 200 candles per square foot. You simply find your numeric representation for ISO800 film that is 7 and your ALV number, being about 6. 7+6=13. EV13. And now you can use any shutter speed/aperture combination that provides EV13 exposure to the film.

Please note that when changing film speeds, even though the EV numbers change in correlation to proper exposure, the shutter speed/aperture combinations that comprise specific EV numbers remain constant. These combinations are fixed and do not change due to a change in film speed. Rather, a different set of EV numbers is required.

Now you might have notice some dissimilarity between the law of reciprocity and the exposure value index. The law of reciprocity is multiplicative (e = i(t)) and the exposure value index employs additive values (6 + 7 = EV13). Though these two trains of thought use different modes of reaching the product or sum, they represent equal quantities. The reason for this is that in relation to photography, i represents the aperture setting which is how we control the intensity of the light on the film and t represents the shutter speed which is how we control the time the light is exposed. Intensity TIMES duration equals exposure. The exposure value equals the aperture’s numeric value PLUS the shutter speed’s numeric value. All one and the same when it comes to photographic exposure with simply two different means of achieving the same goal.

SIMPLICITY AND POURING BUTTERMILK

Still confused?  Let's try a little analogy.  Hopefully this will clear things up a bit for ya.

Picture that you have a gallon of buttermilk that you need to transfer to a one gallon pail.  You have two ways to achieve this one goal.  You can either pour it from another one gallon pail with a large opening or you can pour it from a one gallon jug with a narrow neck, a smaller opening.

I know.  Stick with me on this one.

First you try the pail.  You pour it in.  It pours quickly but it splashes a little here and there.  Kind of sloppy.  Now you try to do so with the bottle.  It pours much more neatly but it takes a long amount of time for the butter milk to reach the pail.  However, both means have helped you reach your desired end.  You moved the same amount of buttermilk in two different ways.

Stop shaking your head.  Here it comes.

Picture that you have a particular amount of photons that you need to transfer, via exposure, to a light-sensitive material like film.  You have two ways to achieve this one goal.  You can either use a large aperture or opening or a small aperture or opening.  First you use the larger aperture.  You let the light in.  It doesn't take much time but  also reduces the depth of focus, thus causing objects just in front and just behind the focal plane to appear sharply out of focus.  Kind of sloppy, but effective for isolating the subject from the background.  Now you try to do so with the smaller aperture.  Now things appear much more neatly on the film.  You have a greater depth of focus in your photograph which is optimal for a vast landscape where you want a good deal of your subject area to be in reasonable focus.  But it takes a long amount of time, comparatively, to allow the light to reach the film.  However, both means have helped you reach your desired end.  You have produced the same amount of exposure on the film in two different ways.