We refer to lenses by their focal length, and usually convert that to a full-frame 35mm equivalent. But since different sizes of sensor or film have different equivalent focal lengths that give the same field of view, we might do better to talk about lenses in terms of their angle of view. Then we would know exactly what we were talking about (a world first!). So my new compact camera that has a fixed zoom would make sense to me – I have no idea just by looking at it what equivalent in 35mm terms the 7.4 – 44.4mm zoom is. All the numbers tell me is that the lens is a 6x zoom.
There is also a difference between what the lens does and what the sensor or film uses. The lens projects a cone of light, but the sensor sits inside that cone and captures a portion of it. Since the sensor is usually square or rectangular, the most it can capture would be when the cone of light just covers the diagonal of the sensor. I think that’s misleading in real terms though – it’s like the way TV screens are described by measuring the diagonal of the screen. In practical use, what matters is the angle of view seen by the longest side of the sensor. That sets how wide you can capture a landscape or how tall a building (unless you are shooting a square format, in which case they are the same). So a 60 degree angle of view lens on my 6×9 roll film camera will get the same shot as a 60 degree lens on my APS-C digital. The difference will be in the amount of detail captured. If I changed format to say a 6×17 camera, I would still get the same side to side angle of view if I used a 60 degree lens. All that would change is that I would lose a lot of the vertical dimension. I could get the same picture by cropping down a different camera to the letterbox format, providing I was still using a 60 degree lens.
You still need to think in terms of the focal length though, if you switch lenses between different formats. A 40mm lens on 6×6 covers the format and provides a 70 degree angle of view. Put that lens on an APS-C camera and the smaller sensor can only see a portion of the field of view. The focal length stays the same but the angle of view seen by the sensor changes, in this case to a 33 degree lens. It is a handy way to get cheaper long lenses to use on smaller format cameras though – I’ve used what would be mild portrait lenses on medium format as long tele lenses on APS-C to shoot sports. The famed Kodak Aero Ektar at 178mm focal length was the same angle of view on aero film as a 50mm lens on 35mm/ full frame. Stick it on a medium format camera and you have a decent portrait lens (in terms of angle of view).
Who cares? Well, it makes it much easier to understand what a lens will do than quoting the focal length. My Canon compact has a 54-10 degree zoom lens, equivalent (in old money) to a 35-200mm zoom on 35mm or 23-131mm on APS-C.
Working with angle of view rather than focal length means I could do some test shots on ‘free’ digital with say, 90 and 60 degree lenses and know exactly what lens to take if I wanted to use a different camera for the final shot, without having to do sums.
Of course, if we wanted to be even more practical we would measure our lenses in mils rather than degrees. The army uses mils, as it makes it much easier to correct the aim of things or estimate distance. I only found out about these when I borrowed an army compass and saw that it had too many numbers on the dial. Mils might be more useful than degrees when you are shooting pictures at a distance. Knowing roughly how wide a stage is and how far away you are, you can fairly easily look up the angle of view of the lens you need to cover it. Want the singer to roughly fill the height of a horizontal frame? Same calculation:
Angle in mils = subject size in mm / distance in metres.
So if you were shooting a car race and wanted to fill the frame you could work out what lens to use. Say you are 60m from the track and you want the field of view of the camera to be 4m wide. You need a lens with an angle of view of about 67 mils. A 500mm lens on 35mm gives you 73 mils, so that’s what you would take (or a 300mm if you were shooting on APS-C).
The army does this sort of thing a lot, so they have ready-reckoners for working out the size of a distant object in mils so that you can estimate the range (or in our case, pick the right lens out of the bag). The width of one finger held out at arm’s length is about 30 mils. Two fingers together are about 70 mils. Work out what combination of fingers matches your lenses and you can work out what you need before you take it out of the bag. The other trick with mils is that it makes it easier to estimate distances:
Distance in meters = size of object in mm / width or height of it in mils.
So a 3m long car covered by my single finger (30 mils) is 100m away. For closer work you could use a card rangefinder.
But I expect that in a hundred years time we will still be talking about lenses by their 35mm format equivalent focal length.
6 thoughts on “Angle of view”