The Exposure Triangle

There are 3 factors that control the amount of light that enters your camera: Aperture, Shutter Speed and ISO. Those factors are called the exposure triangle.

My favorite metaphor for the exposure triangle is that taking a picture is like filling a bucket with water, to get the correct exposure you need to get the right amount of light into the camera (or water into the bucket), to control the amount of water you can keep the water flowing for shorter or longer amount of time (shutter speed), use a ticker or thinner water pipe (aperture) or replace the bucket with a smaller or larger bucket (ISO speed).

It’s worth noting that the exposure triangle has nothing to do with the triangle shape we all know and love, but “exposure triangle” is a catchy name (better than the more geometrily correct exposure cuboid).

Changing the amount of light with any one of the 3 factors will give the same brightness as changing the same amount with any other factor – but not the same image because aperture also affects depth of field (among other things), shutter speed controls how you capture motion and ISO changed the amount of digital noise in the image.

To demonstrate this I’ve set the camera on a tripod in front of a toy microphone, set it to manual exposure and manual focus, and I’ve also set the white balance (because auto white balance can change white balance between pictures)  – and took 13 photos , 1 correctly exposed according to the camera light meter and then for each of the 3 factors I took 4 pictures at +2, +1, –1 and –2 stops from the correct exposure.

I took the JPEG images right out of camera and combined them into the table below to show that the brightness really does change by the same amount.

Combined

The darker band on the right side of the pictures is actually the corner of the room.

You can’t see the changes in depth of field or noise in those small images but that’s ok because you also can’t see them in the full size, the maximum aperture is small enough to get the entire microphone in focus and the background is a solid color – so no visible change in depth of field, also, there is plenty of light and my camera has good high-ISO performance so there’s no visible noise in the high ISO images.

Also, the “correct exposure” picture is too dark and the over-exposed pictures are better – this is because the light background fooled the camera, exactly why this happened and how to deal with this will be the topic of a future post.

Understanding f Numbers

In photography the size of the aperture is measured in f numbers, a lot of people just learning photography find f numbers confusing, this starts with them being backwards (smaller aperture = larger number) and continues with the fact that to double the amount of light you multiply the number by 1.4.

The aperture has a huge impart on the photo you make, so being confused about it is not a good thing.

Basically it’s rather simple, an aperture of f/2 (for example) means the width of the hole in the lens is the focal length divided by 2 (and f/8 is divided by 8, f/2.8 is divided by 2.8, etc.) so if you have a 50mm lens at f/2 the width of the hole in the lens is 25mm – it’s even written as a math equation.

Now the reason for the numbers being backwards is obvious, dividing by larger numbers give smaller sizes.

The reason for multiplying by 1.4 now also becomes simple – you just take the formula for the area of a circle and you get that to make the area twice as large you have to increase the diameter by the square root of 2 (or approximately 1.414) – I’ll skip the math, you can easily check this for yourself if you want.

Now the only question left is – why do we specify the aperture size in relative terms? and to answer that I took a few pictures, both pictures were taken with the Canon EFS 18-135 f/3.5-5.6 IS using the same camera settings (ISO 100 f/7.1 1/160sec) from the same location – the only thing that changed between pictures was the focal length (I zoomed in and out) – the first picture was taken at 18mm and the second at 135mm:

And for you convenience I’ve cropped the 18mm photo to show the same area as the 135mm photo:

Apart from the effect of the focal length on depth of field (that’s the topic of a different future post) both images look the same, if you look closely at the middle flower you will see the same colors and the same exposure in both pictures.

But the diameter of the hole in the lens is 18/7.1 = 2.5mm for the first picture and 135/7.1 = 19mm for the second – a 7x difference! and yet they both let the same amount of light into the camera – and that’s why we measure aperture in f numbers – if we used the size of the aperture the exposure would have changed radically when zooming in or out.

And, as a side note, it’s now also easy to see why cheaper lenses have variable max aperture – the same size hole has different f numbers at different focal lengths, and making a lens that can open up at the same ratio at both ends for a large zoom range requires a very big lens (or a tiny aperture at the wide end).

Creating Motion Blur

Motion blur is created when the shutter is open long enough for the subject to move – not very complicated.

Unsurprisingly you control motion blur by changing the shutter speed, first a little experiment to show the effect of shutter speed on motion blur – and then we’ll add some flash magic to make the photos more interesting.

To demonstrate this I needed something that moves in a constant speed so I’ve used a small spring-loaded toy, the camera is on a tripod and pre-focused, the train moves at exactly the same speed in all pictures and I’ve pressed the shutter when the train reached the same location (more or less).

Because I didn’t want to change depth of field the aperture is the same in all pictures (f/5) , I’ve shoot those pictures in Av mode, I’ve manually set the aperture and ISO and let the camera calculate the shutter speed, all pictures are strait out of camera with no processing (except for reducing the size so they fits here).

The settings described below are for example only, the required shutter speed depends on the speed of the subject – and unless you are photographing the same spring loaded toy train I did you will need to adjust.

We start at f/5 1/100sec ISO6400 – the picture is very noisy due to low light/high ISO but there is very little motion blur.

At f/5 1/50sec ISO3200 (look at how halving the ISO exactly doubles the shutter speed) there’s enough motion blur to be really noticeable but not enough to look like we did it on purpose.

At f/5 1/25sec ISO1600 there’s significant motion blur.

At f/5 1/13sec ISO800 the train is so blurry it’s becoming unrecognizable.

Everything continues at 1/6sec ISO400 and 0.3sec ISO200

And finally at f/5 0.6sec ISO100 the train disappeared and all we are left with is some blur

The kind of blur we’ve seen so far actually doesn’t feel like motion, it’s just too blurred – but there’s a very nice technique that turns the picture above into this:

This picture was taken with the same camera settings as the previous one (Av mode, f/5, ISO100, same location and light) but with an added flash, I’ve used the camera’s pop up flash, with flash exposure compensation dialed down all the way to –2 stops (because a direct on-camera flash would slightly over expose the train and background resulting in washed up colors and the unnatural hard shadows pop up flashes are famous for).

What happens is that we get the same blur we got before – and then the flash fires and we get a clear sharp image of the subject at the time the flash fired.

It’s important to note the flash is set to rear curtain sync (or 2nd curtain sync) – in this mode the flash fires at the end of the process right before the shutter closes instead of at the beginning right after the shutter opens, if we didn’t set the flash to rear curtain sync the blur would have been in front of the train instead of behind it.

Aperture

Aperture is the physical hole in the lens, changing the aperture opens and closes the hole in the lens, in the picture on the right you can see the hole and the “blades” around it that are used to make it smaller or bigger.

The Aperture size is measured in a unit called f number – a larger f number means smaller aperture (large number = smaller hole – yes, it’s reverse, but that’s how this is measured). On most DSLR cameras each “click” of the aperture wheel is 1/3 stop – so 3 clicks will double or halve the light coming into the camera (depending on the direction you turn the wheel, obviously)

The most important effect of the aperture is the bigger the hole in the lens the more light comes in – and wen more light come in we either get a brighter picture or we can compensate by changing the shutter speed or ISO – for example  by changing the aperture from f/8 to f/5.6 (3 clicks) we double the amount of light coming in – so we can compensate by halving the shutter speed, so if I go shooting handheld with my 50mm lens in f/8 and the camera tells me I need a shutter speed of 1/40 – at that shutter speed it’s really difficult to take a good picture handheld and it’s very likely I’ll get a blurry picture – but changing the aperture to f/5.6 will get me a shutter speed of 1/80 – in that settings it’s pretty easy to shoot handheld with a 50mm lens.

Quick tip – the aperture and shutter speed camera controls are usually set in the same increments so a single aperture “click” change the exposure by exactly the same amount as a single shutter speed “click”.

Aperture also controls the “depth of field” (background blur) of the picture, larger aperture (smaller f number) means shallower depth of field (less in focus and more background blur), let’s demonstrate this with some pictures.

Nothing says aperture like a stuffed lion toy  – so I’ve placed a toy lion on top of a trampoline (really) balanced on a plastic slide in front of a bamboo fence, I’ve put the camera (Canon 550D/T2i) with a 50mm f/1.8 II lens on a tripod, focused on the lion eyes and set the camera to manual focus, the white balance is set to daylight and the pictures ware taken during sunset with the sun behind the camera, I was pretty close to the lion because I wanted a very shallow depth of field in order to exaggerate the aperture effects), the pictures were taken on Av mode.

Here are the pictures, almost strait out of camera with no post processing what so ever (the pictures on this page are scaled down, click on the picture to see a bigger version that much larger but also scaled down a bit):

The first picture (right) is at f/1.8 1/100sec ISO200, the lions nose is super-sharp, the eyes are a little soft (you can see it in the full size version – I probably accidently bumped the tripod a little and moved the focus from the eyes to the nose – the depth of field is so shallow with the lens wide open) the ears are obviously out of focus even in the scaled down web version and the background is a nice undefined wavy pattern.

In the second picture (center) I stopped down to f/2.5 (1/50 ISO200), the eyes are not as soft as the f/1.8 version but still out of focus.

In the next picture (right) at f/3.5 1/20sec ISO200 the eyes are finally fully in focus, the ears are still clearly out of focus, the background is completely blurred but you can already guess it’s a bamboo fence.

Stopping down again we get to f/5 (1/10sec ISO200) on the left and then to f/7.1 at 1/2sec on the center. On the right at f/10 0.4sec ISO200 the downscaled version is already sharp with maybe just a tiny amount little blur in the background, in the full size you can see the background is still blurred (pictures become sharper when you scale them down) but the entire lion in completely in focus.

The background continues to get more details at f/13 0.6sec (left) and the last picture I took is at f/20 1.6 seconds (still ISO 200, on the right).

We clearly see that increasing the f number (or closing the aperture, also know as “stopping down”) – increases the depth of field, in each picture more of the lion is in focus and the background becomes more defined.

And we also clearly see that id we get the depth of field too shallow we take the risk of missing our focus – and your model might not be very happy you’ve chosen the tip of her or his nose as the focal point of the photo.

There’s another effect of the aperture size I want to talk about quickly – with large aperture (small f number) lights seem to glow, with small aperture (large f number) they become star shaped, I’ve taken some photographs of the lights above a highway near my home to demonstrate this.

This time I used my EFS 18-135mm f/3.5-5.6 IS lens, again the camera was on a tripod and the white balance was set to daylight (I had no idea what’s the color of the lights and didn’t care if the colors are off as long as they are consistent – but I’m happy with the results) the pictures were taken at night the lens was zoomed all the way to 135mm and on manual focus, the pictures were taken on M mode.

Here’s a picture with the aperture wide open at f/5.6 1/20sec ISO200 – you can see the strong round-ish glow around each lamp and the huge halo around the entire thing (I really love the “molten metal” look of the pole)

Here’s another picture of the same lights with the lens stopped down to a ridicules f/36 with 1 second exposure at ISO 100, now the big halo is gone and each light has a very nice “starburst” effect – in this experiment I didn’t keep the exposure constant between pictures if you do the math you can see I’ve closed the aperture by 5 and a third stops, lowered the ISO by one stop and reduced the shutter speed by 4 and a third stops – resulting in a two stop difference between the two shots (or in another words, the second picture has only one quarter of the light in the first picture)

And finally, if we combine both settings by opening the aperture to f/5.6 and setting the long 1 second shutter speed (at ISO 100) it looks like our street light is now powered by a thermonuclear device (this is 5 and a third stops brighter the previous photo – or approximately x39 the amount of light)