The shutter speed determines how long the film or sensor is exposed to light. Normally this is achieved by a mechanical shutter between the lens and the film or sensor which opens and closes for a time period determined by the shutter speed. For instance, a shutter speed of 1/125s will expose the sensor for 1/125th of a second. Electronic shutters act in a similar way by switching on the light sensitive photodiodes of the sensor for as long as is required by the shutter speed.
Some digital cameras feature both electronic and mechanical shutters. Shutter speeds are expressed in fractions of seconds, so that each higher shutter speed halves the exposure by halving the exposure time: 1/2s, 1/4s, 1/8s, 1/15s, 1/30s, 1/60s, 1/125s, 1/250s, 1/500s, 1/1000s, 1/2000s, 1/4000s, 1/8000s, etc. Going in the opposite direction you are doubling the exposure time, so a move from 1/250s to 1/125s is double the exposure. Long exposure shutter speeds are expressed in seconds, e.g. 8s, 4s, 2s, 1s.
Matching shutter speed and focal length
The optimal shutter speed depends on the situation. A useful rule of thumb is to shoot with a shutter speed above 1 times the focal length to avoid blurring due to camera shake. for example if you are shooting with a focal length of 200mm then have your shutter set to minimum of 1/250. Below that speed a tripod or image stabilization is preferable.
Freeze action shots
If you want to “freeze” action, e.g. in sports photography, you will typically need shutter speeds of 1/250s or more. But not all action shots need high shutter speeds. For instance, keeping a moving car in the center of the viewfinder by panning your camera at the same speed of the car allows for lower shutter speeds and has the benefit of creating a background with a motion blur. Prosumer and professional cameras provide shutter priority exposure mode, allowing you to vary the shutter speed while keeping exposure constant.
The diagram below illustrates how slowing the shutter speed effects movement in the image, and the point when hand holding your camera is no longer recommended. The shutter speed is one of the three controls that allows you to control exposure, the other two being aperture and ISO setting.
The follow video from Michaelthementor gives a good explanation about shutter speed, which is worth a look
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