What Does F&F Mean

What Does F&F Mean

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Martin Saunders

15 February 2016 | 10:41 AM

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In school. At a football match. In a superhero movie. At the pub. In the supermarket. In an ever-so-slightly edgy pop song. We hear the f-word so often these days that much of the time it simply washes past us. Used not only as a curse or a graphic substitute for 'sex', but also as the Oxford Dictionary puts it, as 'an intensifier', it's got to be one of the most popular words in the English language. We all learn it from a kid in a corner of the playground at about age eight – at the latest – and many of us barely stop using it from that day on.
A few decades back, Christians held a fairly high line on 'bad language'. It probably came from a biblical disdain for blasphemy – a linked area – and that nagging concern that increased swearing indicates the gradual disintegration of Western civilisation. Today though, we've relaxed considerably, perhaps not in our own use of certain words (the Bible does tell us to "not let any unwholesome talk come out of your mouths" [Ephesians 4:9] after all), but in our acceptance of them. "The swearing didn't bother me", is a common response to profanity-filled films and TV shows. There are just more important things to get upset about.
Yet we all shudder the first time we hear our children use the word; even to ask what it means. I think that's because the f-word is much more problematic than we give it credit for – it's not just that its use demonstrates a lack of linguistic imagination.
The problem is rooted, I think, in its origin. You've probably allowed it to roll around your head a few times since you started reading this (be absolved; that's totally my fault), and perhaps you've noticed what a harsh, unfriendly word it is. When you trace it back through the ages, you discover that it seems to have two distinct roots of meaning. One is sexual – referring to the act of intercourse – but the other is more troubling. A lot of the words from around the world which linguists think feed in to our modern f-word don't refer to sex, but violence. These words are defined "to hit", or "to strike". The etymology eventually tracks back to the Latin root Pugnus ; the same word that takes us to fighting, punching and fist.
So when we use the modern form we're using a word which encapsulates both sex and violence. To make love AND to strike. All wrapped up together.
I don't think Christians should be upset about the f-word because it marks some sort of moral decline. I think we should be upset about it because it's casual misogyny (another root meaning is 'penis'), which takes the beauty, intimacy and love of the sexual act and corrupts it. We're probably all still agreed on the ugliness of violence. As Christians, we probably all still agree that in hitting one another, we strike the image of God in another person and marr his image in us. Sex and violence are never things that should be twinned together, yet in this word that's exactly what we find. Are there really so many more important things to get upset about?
I have a nagging feeling that among all the areas in which Christians have relaxed in recent years, this might be one that some of us have got wrong. In assuming we're chilling out about some of the non-essential issues, we've missed something quite important. What does it mean that a word with these meanings – and deep down, I think we have to concede that they ring true – is right there at the heart of our culture? Heard every day, billions of times, all around the world, far more often than words of worship or love. Should we really just be waving it past without critique?
I don't think so. Once you know what the f-word really means, you can't simply give it a free pass on the grounds of avoiding irrelevance. It's not just a holiness issue – although I think that's part of it – but a justice issue too. My hunch is that if more people knew the ugly, violent roots behind the f-word, they might just stop using it so much (and so maybe we should tell them). If the swearing doesn't bother you, maybe it's time that it did.
Martin Saunders is a Contributing Editor for Christian Today and the Deputy CEO of Youthscape . You can follow him on Twitter: @martinsaunders
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Now that we have explored derivatives, we can begin to assess
what f' and f'' say about f . You may already
have recognized some properties of first and second derivatives,
but here we will lay them all out.
a.) If f'(x) >0 on an interval, then f is
increasing on that interval.
b.) If f'(x) <0 on an interval, then f is
decreasing on that interval.
c.) If f''(x) >0 on an interval, then f is
concave upward on that interval
d.) If f''(x) <0 on an interval, then f is
concave downward on that interval.
e.) If f'(x)=0 , then the x value is a point of
inflection for f .
To illustrate these principles, consider the following problems.
a.) On what interval is f increasing? On what interval
is f decreasing?
b.) Does f have a maximum or minimum value?
2.) Sketch the graph of a function whose first and second derivatives
are always negative.
3.) Sketch the graph of the function that satisfies the given
conditions.
4.) The cost of living continues to rise, but at a slower rate.
In terms of function and its dertivatives, what does this statement
mean?
5.) The president annouces that the national deficit is increasing,
but at a decreasing rate. Interpret this statement in terms of
a function and its derivatives.

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Copyright © 2022 · Photography Life
PL provides various digital photography news, reviews, articles, tips, tutorials and guides to photographers of all levels
By Spencer Cox 92 Comments Last Updated On April 6, 2022
As a beginner photographer, you might have heard of such terms as f-stop or f-number and wondered what they actually mean. In this article, we will dive into these in detail and talk about how to use them for your photography.
As we have previously defined, aperture is basically a hole in your camera’s lens that lets light pass through. It’s not a particularly complicated topic, but it helps to have a good mental concept of aperture blades in the first place.
Yes, aperture blades , which are also known as the diaphragm in optics.
Take a look inside your camera lens. If you shine a light at the proper angle, you’ll see something that looks like this:
These blades form a small hole, almost circular in shape — your aperture. They also can open and close, changing the size of the aperture.
That is an important concept! Often, you’ll hear other photographers talking about large versus small apertures. They will tell you to “stop down” (close) or “open up” (widen) the aperture blades for a particular photo.
As you would expect, there are differences between photos taken with a large aperture versus photos taken with a small aperture. Aperture size has a direct impact on the brightness of a photograph, with larger apertures letting in more light into the camera compared to smaller ones. However, that isn’t the only thing that aperture affects.
The other more important impact is depth of field – the amount of your photo that appears to be sharp from front to back. For example, the two illustrations below have different depths of field, depending on the size of aperture:
Adjusting your aperture is one of the best tools you have to capture the right images. You can adjust it by entering your camera’s aperture-priority mode or manual mode, both of which give you free rein to pick whatever aperture you like. That is why I only ever shoot in aperture-priority or manual modes!
Before you try it out for yourself, though, there are a few other things you might want to know.
The f-stop , which is also known as the f-number , is the ratio of the lens focal length to the diameter of the entrance pupil. If you did not understand that, don’t worry, because there is a much easier explanation of it for beginners. In very simple language, f-stop is the number that your camera shows you when you change the size of the lens aperture.
You might have seen this in your camera before. On your camera’s LCD screen or viewfinder, the f-stop looks like this: f/2.8, f/4, f/5.6, f/8, f/11, and so on. Sometimes, it will be shown without a slash in between like f2.8, or with a capital “F” letter in the front like F2.8, which means the exact same thing as f/2.8. These are just examples of different f-stops, and you might come across much smaller numbers like f/1.2 or much larger ones like f/64.
Why is your aperture written like that? What does something like “f/8” even mean? Actually, this is one of the most important parts about aperture: it’s written as a fraction .
You can think of an aperture of f/8 as the fraction 1/8 (one-eighth). An aperture of f/2 is equivalent to 1/2 (one-half). An aperture of f/16 is 1/16 (one-sixteenth). And so on.
Hopefully, you know how fractions work. 1/2 cup of sugar is much more than 1/16 cup of sugar. A 1/4 pound burger is larger than a 1/10 pound slider.
By that same logic , an aperture of f/2 is much larger than an aperture of f/16. If you ever read an article online that ignores this simple fact, you’ll be very confused.
Pop quiz: Which aperture is larger — f/8 or f/22?
You already know the answer to this question, because aperture is a fraction . Clearly, 1/8 is larger than 1/22. So, f/8 is the larger aperture.
If someone tells you to use a large aperture, they’re recommending an f-stop like f/1.4, f/2, or f/2.8. If someone tells you to use a small aperture, they’re recommending an f-stop like f/8, f/11, or f/16.
See the below diagram that shows different sizes of aperture to understand:
A lot of photographers ask me an interesting question: What does the “f” stand for in f-stop, or in the name of aperture (like f/8)?
Quite simply, the “f” stands for “focal length”. When you substitute focal length into the fraction, you’re solving for the diameter of the aperture blades in your lens. (Or, more accurately, the diameter that the blades appear to be when you look through the front of the lens).
For example, say that you have an 80-200mm f/2.8 lens fully zoomed out to 80mm. If your f-stop is set to f/4, the diameter of the aperture blades in your lens will look exactly 20 millimeters across (80mm / 4), whereas at f/16, the diameter will be reduced to mere 5 millimeters (80mm / 16).
This is a cool concept. It also makes it easy to visualize why an aperture of f/4 would be larger than an aperture of f/16. Physically, at f/4, your aperture blades are open much wider, as shown below:
Unfortunately, you can’t just set any f-stop value that you want. At some point, the aperture blades in your lens won’t be able to close any smaller, or they won’t be able to open any wider.
Typically, the “maximum” aperture of a lens, which is also often referred to as “ wide-open ” aperture, will be something like f/1.4, f/1.8, f/2, f/2.8, f/3.5, f/4, or f/5.6.
A lot of photographers really care about the maximum aperture that their lenses offer. Sometimes, they’ll pay hundreds of extra dollars just to buy a lens with a maximum aperture of f/2.8 rather than f/4, or f/1.4 rather than f/1.8.
Why is large maximum aperture in a lens so important? Because a lens with a larger maximum aperture lets more light into the camera. For example, a lens with a maximum aperture of f/2.8 lets in twice as much light when compared to a lens with a maximum aperture of f/4.0. This difference could be a big deal when shooting in low-light conditions.
Since people care so much about maximum aperture, camera manufacturers decided to include that number in the name of the lens . For example, one of my favorite lenses is the Nikon 20mm f/1.8G . The largest aperture it offers is f/1.8.
If you have a 50mm f/1.4 lens, the largest aperture you can use is f/1.4. Professional constant aperture zoom lenses like a 24-70mm f/2.8 will have f/2.8 as their maximum aperture at every focal length. Whereas cheaper consumer-grade lenses such as 18-55mm f/3.5-5.6 will have their maximum aperture change depending on focal length. At 18mm, the maximum is at f/3.5, while at 55mm, it changes to f/5.6. In between is a gradual shift from one to the other.
Photographers generally don’t care as much about the smallest or “minimum” aperture that the lens allows, which is why manufacturers don’t put that information in the name of the lens. However, if it matters to you, you will always be able to find this specification on the manufacturer’s website. A lens’s smallest aperture is typically something like f/16, f/22, or f/32.
Along with the amount of light a lens aperture allows, it has one other huge effect on your photos – depth of field.
I always find that it’s easiest to understand depth of field by looking at photos, such as the comparison below. In this case, I used a relatively large aperture of f/4 for the photo on the left, and an incredibly small aperture of f/32 for the photo on the right. The differences should be obvious:
This is very interesting! As you can see, in the f/4 photo, only a thin slice of the lizard’s head appears sharp. The background of the photo is very blurry. This is known as depth of field .
You can think of depth of field as a glass window pane that intersects with your subject. Any part of your photo that intersects with the window glass will be sharp . The thickness of the glass changes depending upon your aperture. At something like f/4, the glass is relatively thin. At something like f/32, the glass is very thick. Also, depth of field falls off gradually rather than dropping sharply, so the window glass analogy is definitely a simplification.
This is why portrait photographers love f-stops like f/1.4, f/2, or f/2.8. They give you a pleasant “shallow focus” effect, where only a thin slice of your subject is sharp (such as your subject’s eyes). You can see how that looks here:
On the flip side, you should be able to see why landscape photographers prefer using f-stops like f/8, f/11, or f/16. If you want your entire photo sharp out to the horizon, this is what you should use.
Here’s the aperture scale. Each step down lets in half as much light:
These are the main aperture “stops,” but most cameras and lenses today let you set some values in between, such as f/1.8 or f/3.5.
If you’d prefer to see that information in a chart, here you go:
Usually, the sharpest f-stop on a lens will occur somewhere in the middle of this range — f/4, f/5.6, or f/8. However, sharpness isn’t as important as things like depth of field, so don’t be afraid to set other values when you need them. There’s a reason why your lens has so many possible aperture settings.
The second page of our aperture article dives into every single effect of aperture in your photos. It includes things like diffraction, sunstars, lens aberrations, and so on. However, as important as all that is, it’s not what you really need to know – especially at first.
Instead, just know that the two biggest reasons to adjust your aperture are to change brightness (exposure) and depth of field. Learn those first. They have the most obvious impact on your images, and you can always read about the more minor effects later.
Hopefully, you now have a good sense of f-stop and the ways it affects your photos. To recap:
That’s it! If you understand the basic bullet points, you’ve got the basics of f-stop and aperture.
Of course, putting everything into practice is another matter. Even if this entire article makes sense for now, you’ll still need to take hundreds of photos in the field, if not thousands, before these concepts become completely intuitive.
Luckily, you have the building blocks. Aperture and f-stop aren’t complicated topics, but they can seem a bit counterintuitive for photographers who are just starting out. Hopefully, this article clarified some of the confusion, and you now have a better understanding of the fundamentals of aperture.
Below are some examples of photographs captured at different f-stops from f/2.8 to f/16, to give you an idea of how they are used in the field:
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I'm Spencer Cox, a macro and landscape photographer based in Denver. My photos have been displayed in galleries worldwide, including the Smithsonian Museum of Natural History and exhibitions in London, Malta, Siena, and Beijing. These days I'm active on Instagram and YouTube .
OMG! i am taking a class, and this wa so benificial to me. Ive read an entire chapter on the camera and got more out of your article than I did the book…Thank you so much…I can take my test now, lol!
You’re quite welcome, I’m glad you found the article so useful!
Brilliant, I’m a bit confused in regard to the pictu
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What Does F&F Mean

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