Rebecca and I often receive photography questions via email. If we feel that our answers might benefit some of the readers on this site, then we will post our answers here.
Here's the question we received via email: "I have a question for you regarding the Sunny 16 rule. I know by reading if you have your ISO set to 100 at f/16, your shutter speed should be 100. So if your f-stop is set to 2.8 and your ISO is still 100, how do you know what the shutter speed should be? How do you figure that out??" [Editor's note: The Sunny 16 rule provides the general guideline that in "sunny" conditions, your shutter speed should be equal to 1/ISO at an aperture of f16. For more discussion of the Sunny 16 rule you can read this thread:
http://community.spiritofphotography.com/index.php?topic=37.msg137#msg137 ]
In essence, this question has three parts, first, how does an aperture number like f16 relate to one like f2.8, what's the math? The second part of the question is "how does a change in aperture value relate to a change in shutter speed." The third part of the question is "how do I apply this using the "Sunny 16" rule.
I'll start with an explanation of the aperture numbers first.
Very few photographers actually do the math in their head, but instead choose to remember the numbers associated with a one stop difference, beginning with f1.4. The next "smaller" (because it lets in half as much light) aperture in the sequence (in one stop increments) is f2.0, then 2.8, 4.0, 5.6, 8.0, 11, 16, 22, 32, 45, 64, etc. Most people just remember the values between f1.4 and f16, because that is what you use most often.
As a side note, you will often hear photographers use the terminology "stop down" when they are talking about reducing the amount of light, for example going from f1.4 to f2.0. They will use the term "open up" when they are talking about opening the lens diaphragm to increase the amount of light, for example from f16 to f11. This helps to alleviate some of the confusion that might be caused if they simply said "use a smaller aperture." A novice might be confused about whether they mean "smaller" with respect to the size of the lens opening, or "smaller" with respect to the aperture number.
If you really do want to know the math, you have to first understand that the aperture values you see on your lens represent the relative size of the diaphragm or light-regulating opening in the lens in relation to the focal length of the lens. The relative values of these two variables determines the intensity of light that will be delivered to the film or sensor. In practical terms, the aperture value is equal to the focal length of the lens divided by the diameter of the lens opening. For a 50mm lens, a diaphragm opening of 25mm would result in the ratio of 50mm/25mm, or a ratio of 2/1, expressed as f2.0. A diaphragm opening of 12.5mm would result in the ratio of 50mm/12.5mm, or a ratio of 4/1, expressed as f4.0, and so on.
Each "stop" or EV (exposure value) change is defined as a factor of 2 change in the amount of light hitting the film or sensor. If you are going towards the larger lens openings, you are doubling the amount of light being transmitted through the lens, by doubling the area of the lens opening. The area of the diaphragm opening is proportional to half the diameter squared. So if you reduce the area by 1/2, you would calculate the f-number by multiplying the "starting" f-number by the square root of 2 (1.41) to calculate the next f-number in the sequence. (NOTE: You don't need to remember the formula for reducing the area by 1/2, you just need to remember the number 1.41.) Said another way, you need to multiply an aperture by 1.41 to calculate the aperture value associated with the next smaller lens diaphragm opening in a sequence spaced 1 "stop" or 1 EV apart. The numbers are rounded, resulting in the sequence of f1.0, f1.4, f2.0, f2.8, f4.0, f5.6, f8.0, f11, f16, f22, f32, etc. Make perfect sense?
The next part of the question, was "how do I relate aperture values to shutter speeds?" The "common unit" in relating these two values is the EV (exposure value) or "stop." Again, a one unit change in EV values results in a factor of 2 change in the amount of light hitting the film or sensor. Said another way, a +1EV change doubles the amount of light hitting the sensor, while a -1EV change halves the amount of light hitting the sensor. So, doubling the time a shutter is open will double the amount of light hitting the sensor, and a shutter speed of 1/100 (seconds) is +1EV more than a shutter speed of 1/200 (seconds).
So let's see what the sequence would look like if we matched aperture values and shutter speeds that would result in the same amount of light hitting the sensor. (An increase in aperture equivalent to +1EV would need to be matched with a decrease in shutter speed of -1EV in order to result in an equivalent amount of light hitting the sensor.)
| Aperture (+1 EV for each value from left to right) | f16 | f11 | f8 | f5.6 | f4.0 | f2.8 | f2.0 |
| Shutter Speed (-1 EV for each value from left to right) | 1/100 | 1/200 | 1/400 | 1/800 | 1/1600 | 1/3200 | 1/6400 |
So, to answer the question at the beginning of the thread, a "sunny sixteen" exposure setting of f16 and 1/100 would be equivalent to a "sunny sixteen" setting of f2.8 and 1/3200. (Although I can't think of any "real life" scene where I would use that combination of aperture and shutter speed values.)
I hope this helps with your understanding of aperture values, their relation to shutter speeds, and how we might apply them to the "sunny sixteen" rule. If you have any questions, please ask.
Keith
