## Sharper Image

Cameras today come with all sorts of bells and whistles.  With so much choice, it can be difficult to understand what separates one camera from another. For many of us, the end result is that we simply use the cameras on our phones. But the question remains: what sorts of features are we missing out on, and if you like taking pictures, are they worth investing in?

That's a pretty big question, and one that probably can't be answered adequately in a single blog post. So let's focus our attention on just one aspect of the camera: the lens, and some of its features.

When you look at a lens online, some of the first numbers you see describe its focal length.  Let's not get into a technical definition; the gist of it is that the longer the focal length, the more "zoomed-in" the camera's view appears.  To put it another way, the longer the focal length of a lens, the smaller the field of view, which measures how much the camera can see.  For example, with a 50mm focal length, a 35mm camera can "see" with an angle of 27 degrees in the vertical direction:

but with a 200mm focal length, the same camera can only "see" around 6.9 degrees:

Now, the zoom doesn't just affect how close you appear to be to the object you're photographing; it also impacts how difficult it is to capture the image at all.  This is because when the focal length is large (i.e. when you're more zoomed in), the camera is more sensitive to motion.  Even small movements are enough to make for a blurry image at a high focal length.

That's one blurry, zoomed-in picture of an apple.

We can model how much of an error we can expect with a little bit of mathematics.  Suppose you're standing a distance d away from the object you're trying to photograph, and your vertical viewing angle is α.  In this scenario, the camera's total vertical coverage would equal 2d tan(α/2).

But now imagine that your breathing causes unwanted upwards motion by an angle of θ.  The bottom half of your vertical coverage won't change, but the top half will increase; instead of a total vertical coverage of 2d tan(α/2), it will now equal d tan(α/2) + d tan(α/2 + θ):

For example, if you're standing 50 feet away from your subject with a 200mm lens, your vertical coverage will equal 100 tan(6.9°/2) ≈ 6.03 feet.  But if the camera moves upwards by as little as 2°, then the vertical coverage (including the error) then becomes 50 tan(6.9°/2) + 50 tan(6.9°/2 + 2°) ≈ 7.78 feet.  In other words, this tiny movement results in an error of 7.78 — 6.03 = 1.75 feet, or 1.75 ÷ 7.78 ≈ 22% of the total vertical coverage! That much error can only mean one thing: a blurry image.

This is why some lenses (especially ones with long focal lengths) come with vibration reduction (VR) technology. VR effectively reduces movement error by a factor of around 16, i.e. a 2° error without VR technology would be only around a 1/8° error with it.  And as you can see, the resulting error percent becomes significantly smaller too:

But is VR technology worth the additional cost? Well, it depends. If you don't need a lens with a long focal length, then VR may not be worth it, since the percent error you'll get from movement is already pretty small. You also may not need VR technology if you do most of your photography outside with a lot of light. This is because the more light you have, the faster you can make your shutter speed; the faster your shutter speed, the less time the camera has to capture light and create a blurry image.

That same apple looks much less blurry when a picture of it is taken outside.

So in the end, whether to go for VR depends on the kinds of pictures you want to take. If you've ever wished that the phone in your pocket took better pictures, sorting out these kinds of scenarios might just help you make a more informed purchasing decision.

Teachers: want to talk to your students about cameras? Then check out our latest lesson, Sharper Image.