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Camera shake is the cause of many blurry photos and a frustration to new photographers. The photo can be perfectly framed, in focus, but still not sharp. At the core, the result of this is a shutter speed that's too slow. But when is a shutter speed too slow and how can you help avoid it?
The general rule of thumb to avoid camera shake is, your shutter speed must be as fast or faster than your focal length. Now, like most rules, there are exceptions, but this rule can generally be applied to any camera, DSLR or point and shoot, amateur or professional.
In the above photo the focal length is 33mm and the shutter speed was 3.2 seconds. This clearly shows camera shake, that is the photographer not able to hold perfectly still through the entire frame, and partly because the subjects moved. In order to avoid camera shake in the example above, a shutter speed of at least 1/50th would be needed.
There are two ways you can increase the shutter speed for any given shot in order to follow the general rule avoiding camera shake. the first is to open up your aperture setting more, thus letting in more light. The more light that comes in, the faster the shutter can open and close. The downside to this method is that it will effect your depth of field which may not be desired. The second alternative would be to increase the ISO of your camera. The higher the ISO the more sensitive the sensor is to light, the faster the shutter speed. While this won't have an effect on the depth of field it could have a negative effect on the digital noise, sometimes called grain, in your photograph.
When neither of these two options are possible, the last alternative would be to utilize a tripod. A tripod will only work though when the subject matter doesn't move so it's best suited for landscapes and architectural work.
The earlier mentioned exceptions to general rule of thumb for avoiding camera shake by using a shutter speed as fast or faster than your focal length is when blurring is a desired effect in the photograph. Using shutter priority mode, most commonly used by action photographers, is where the rule goes right out the window.
Photography is an art, with all art is interpretation, utilizing specific skills will make you far more efficient and take the frustration out of learning the art of photography.