Let there be light -- or else this incident meter won't work.
Photography literally means "writing with light," and your camera must read the writing properly to get the picture you want. A photographers uses an incident light meter to measure how much light is falling on his subject; he uses a reflective light meter to check how much of that light the subject is bouncing his way, and therefore toward the camera lens and the film (or electronic sensor) that records the image.
Incident Meter
This handheld meter shows you how much light is falling on the subject you want to photograph. The meter's sensor is found under a small white dome that resembles half of a ping-pong ball. The face of the meter has a dial that you can adjust according to your camera's film sensitivity or sensor power. The meter then displays a reading that you can use to set your camera's shutter speed (how fast the picture will be taken) and aperture (the size of the lens opening that lets the light into the camera). Incident meters are also called "spot" meters because they measures the light in a particular part of the image, not the whole scene at once.
Reflective Meter
A reflective meter measures how much light is being bounced off the subject you're photographing and into the camera's lens; many modern cameras have this meter built-in. In some cameras, it's the small window next to the lens and viewfinder that your owner's manual told you that you shouldn't cover with your thumb; more sophisticated cameras have the reflective meter built in behind the lens (a mirror swings out of the way when you take the picture). Usually the meter sets your shutter speed and aperture automatically according to the readings it takes, but you also can turn off your camera's reflective meter, point a handheld incident meter at your subject and take a reading, using your incident meter is a reflective meter.
Handheld vs. Reflective
Handheld meters usually have larger sensors than built-in reflective meters; the bigger the sensor, the more data collected and the more accurate the light reading. Built-in reflective meters are also designed to take an average of the light reaching the camera; this can be good enough for most pictures, but not for scenes that are very light, very dark or contain both large light and dark elements -- think of the bride's white dress and the bridegroom's black tuxedo at a typical wedding. Such large areas of contrast throw off the average of the reading. Using a handheld meter, instead of the camera's built-in version, lets you take multiple readings of various parts of the scene to get the final exposure just right.
Tips
If you're short on setup time or are photographing a fast-changing scene, the built-in reflective meter may be a better bet. If you're shooting color in a studio with adjustable lighting and ample time make such adjustments, a handheld incident meter is better. Some high-end cameras have reflective meters that can also be used as spot meters. Never point a camera meter or handheld meter directly at the sun or any other strong light source.
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