Formula for converting between f-number and numerical aperture

Artists use f-number (f#). Scientists use numerical aperture (NA). I use both.

f# = sqrt(1/NA^2 – 1)/2
NA = 1/sqrt(4f#^2  + 1)

Yeah!!!

For quick mental approximations, the following can also be used and is easier to remember:

f# ≈ 1/(2NA)
NA ≈ 1/(2f#)

It took me 3 years to reach this 10th post.

Growing with your photography: stepping out of auto mode

Thousands of photographs I have taken in the past are taken to simply "record information". A camera records light from a scene, so it is just natural. Events, places, people, even technical info and "evidence material", all sort of things I want to look back to someday, these are among the things I have recorded.
All is well and good until thee day, that I decided to create a Flickr account. I realized that most of my photos look so dull and boring! I'm just lucky to be in the right place and the right time for about 5.13% of my shots, so they are interesting enough to be shared.

Auto pilot

Technology has made it so easy to take photographs, that we got too dependent on it. Good cameras that are almost new are being sold second hand since people are finding out that phones are already good. We don't have too fiddle so much, and if we get it wrong, we know right away, and just take another shot. Even the most advanced cameras have shortcuts meant for the common consumers. Auto mode is too convenient and comfortable that a lot of us never grow out of it. And that's fine and acceptable for a lot of us. Democratization has a lot of benefits and the world today would be different if it is difficult for average people to capture and share their special moments.
For years, I already had a very capable Canon point & shoot. I considered myself as one of the average, casual occasional camera person so I had only used the scene modes and auto mode until just recently. What is Tv? Television? And is Av audiovideo?? When I dial into these modes, the picture just gets dark so what's the point? I just go back to Auto, if what I'm shooting does not fit in one of the scene categories, i.e. flower mode, face mode, mountain mode & running mode. Just go with what my friends always say, "just use auto".

When auto fails

With live view LCDs behind cameras, you can easily compare what has been shot and what is in the real world. And except for gently but brightly illuminated outdoor scenes and inside buildings where the lighting electric bill is not a concern, there is always something noticeably different in the photographs taken in auto mode. Some parts are either too dark or too bright. And if you're unlucky, the whole picture is either too dark or too bright. Fortunately, most interesting scenes happen when there is enough light.
Oh, another thing is that blown-out flash! The camera is smart enough to figure that there is little light on the scene, so it adds its own, with unpredictable results (or perhaps predictably rubbish). I don't get to see a lot of this in my collection as the results are so useless that they are immediately deleted after previewing.

Blurry and noisy

And just delete if it is also under or over exposed. Shooting in low light might be the holy grail for casual shooters. When it's dark, the camera just decides to use more time to take the picture so any small motion of my hands will motion blur the shot. Is that the moon? Or just some white odd oval? And what are all those speckles?
Even in good light, photographs can get blurry. I realized this when I handed my camera to another person to take pictures of me and set the camera in "portrait mode." So how can we avoid this mishaps? As it turned out for me, the answer was to know your camera more. A good start is to know what parameters in a camera can be changed and how the different shooting modes play with these parameters.

Knowing your camera more

Auto SPAM

It's jsut more memorable that way. The abbreviations of the modes actually differs between manufacturers. As I started with Canon, I have Tv and Av instead of S and A. You most likely know already what "Auto" does. Just to make more sense of these abbreviations, here is what they stand for:

• S or Tv: Shutter or Time priority
• P: Program mode.
• A or Av: Aperture priority
• M: Manual.

Switching to one of these modes allow the shutter speed (S) or aperture (A) or both (M) to be adjusted. Typically, there are buttons or dials in the camera that would allow the user to incrementally change the values of these, instead of letting the camera decide. My mistake before was to switch in one of these modes, then that's it, treating it as another scene mode, unaware that I have to do further fiddling when in these modes. I blamed the condition of whatever picture appeared in the screen to that mode instead of the settings of the mode. Now that I know more, the default settings for aperture and shutter speed when I just dialed to these modes, and which I did not change, are likely not the best for the scene. But what is shutter speed and aperture in the first place?

Shutter speed (or exposure time)

This controls the amount of time the camera is collecting light. If a scene is dark, a longer exposure time will help brighten up the photo like leaving a glass below a faucet for a longer time will collect more water. If something is moving while during the shutter's open time, motion blur would be captured. Fast shutter speeds help prevent this motion blur by not giving the subject enough time to move. There is also motion blur caused by shaky hands supporting the camera. To avoid the effect of shaky hands either use fast shutter speeds, or be more stable like using a tripod if slow shutter speeds are needed.

Aperture

This controls the amount of light that comes in per unit time. As the word suggests, aperture is an opening. Like curtains in a window, the less curtains are covering the window, the brighter the room gets. Unlike shutter speed, the words used to quantify aperture variations are lesser known. WTF are those F numbers?? For now it is enough to know that the LOWER f-numbers correspond to a BIGGER open window in your camera allowing MORE light to come in. Perhaps the tricky part here is getting accustomed with the bigger f-numbers allowing less light. Aperture actually does more than adjust the brightness, but that's a topic for another day, and the other effects are less pronounced with point and shoot or phone cameras (which AFAIK have unchangeable apertures).

ISO

Where did that came from?? I'm moving ahead but ISO is part of the holy trinity of photographic exposure that also includes shutter speed and aperture. The so called "exposure triangle". These trio is something you would always see with photos in Flickr (if the user decides to share it) so they're probably important. Despite being part of the triangle, cameras typically have a different approach for changing the ISO compared to shutter speed and aperture and it might be buried deep in the camera's setting menu system.
ISO controls how sensitive the camera would be. In dark conditions, higher ISO's help see things. However, a more sensitive camera is also more sensitive to noise. Just like a more sensitive microphone due to a higher input level will pickup more background noise (hiss) that we normally do not hear. This explains why pictures taken in the dark with automatic/semi-automatic modes can end up noisy. The scene may not look noisy to our eyes, but there is also noise in the camera itself!
ISO sensitivity can be tweaked independently of the SPAM modes. The ISO can be set to a fixed value or to automatic. If the ISO is in auto, the camera would figure it out for you, given the other settings you fix. Personally, I prefer to use the lowest ISO possible and compensate by being very steady with slower shutter speeds, especially if there's a tripod available or if I can rest the camera on some flat support like a fence, wall or furniture top.

All of these 3, shutter speed, aperture and ISO, will affect how much light is captured in the picture and have their respective trade-offs. It is up to the camera user to decide which to prioritize, whether to go for less hand shake motion blur or less noise. With these 3 quickly introduced, we may now go back to the less automatic camera modes.

Auto SPAM modes

Auto

The camera's brain takes over, deciding what aperture, shutter speed ans ISO should be. Some extra settings such as white balance and timer can still be tweaked. Manual focusing might also be disabled, making it a problem in difficult situations like in low light or abstract and empty scenes. Flash control might even be disabled. But if the flash is the type that mechanically pops up, you can just keep it down if you don't want it.
The rest of the SPAM modes allow custom focusing like manual or macro (for close objects). There are also special scene optimized modes which are aimed to be user friendly and which I had been using for years. These scene modes differ from camera to camera. Some camera intended for beginners only have automatic and the scene modes and no SPAM (hooray!).

Shutter priority (semi-automatic)

This camera mode lets you decide how long the exposure would be and the camera decides the settings for aperture and ISO (if automatic) to get what the camera thinks is the "good" exposure.

Program mode (semi-automatic)

Program mode is probably the next easiest mode to try after automatic. It's like automatic, but will respect your set ISO, allows you to change the focus and overall exposure (general "brightness" of photo). The camera decides the shutter speed and aperture to come up with a "good" exposure given the other things you tweaked. Some cameras even allow the user to adjust either aperture or shutter speed while in this mode then it will respectively adjust the other setting for you to still end up with the overall set exposure.

Aperture priority (semi-automatic)

This camera mode lets you decide how big the aperture would be and the camera decides the settings for aperture and ISO (if automatic) to get what the camera thinks is the "good" exposure.

Manual (yeeha)

You control the aperture and shutter speed. The ISO can actually still be automatic, so you might also decide to set a fixed value for this for greater control.

Moving forward

It will take some practice to tweak around these 3 settings to get the picture that you want. You might not get the combination right at first, but at least you are in control of both your failure and success and not blindly relying on the camera's decision making and getting disappointed when it fails. There are things in the camera that can help. There is an exposure gauge where you try to put the mark at the middle meaning that it is not under (left) or over (right) exposed. Some cameras have tone mapping feature wherein the live view screen updates to approximate what the final photo would look like. As aperture had little noticeable effect besides brightness in my camera or in the stuff that I shoot, I first delved into shutter priority and played around with long exposures. Unlike in the days of film, practice is easy and you're free to take photos around your home while experimenting with such settings. When practice is over, you can simply delete the test shots, unless something worth saving comes out of it.
These days, manual is now my default setting. It make me think artistically and it gives me the photos that look the way I want them. But when I don't want to think and fiddle around and just capture the damned moment as it happens, or when I'm just capturing to document "evidence" automatic and preset scene modes are still good. If I still need some control, but still don't want to be left behind by the fast pace of things, program mode is also cool.