Guide number (GN) of a camera flash light (or studio flash light) used in photography is for giving us the indication of how powerful is a flash light. Higher the GN value, more powerful is the flash. This number is the result of distance (between the flash light and the object) multiplied by the aperture of the lens, for a given ISO value.
GN is either calculated in feet or in meters. For example, if ISO is 100 and the distance between a flash and a subject is 10 feet, and we get a proper exposure at f-11, then the guide number of the flash light is 10 (feet) x 11 = 110 feet. (for 100 ISO)
If this calculation is done in meters, then if the subject is at 3.0 meters, and the required aperture is f-11 to get a proper exposure, then the GN will be 3 (meters) x 11 = 33 meters.
Generally, this number is given for 100 ISO in instruction manual book of a flash. If we set ISO to 200, then for the same result in exposure, we will need aperture f-16. So the GN will become 10 (feet) x 16 = 160 feet (for 200 ISO)
So, D x A = GN (Distance x Aperture = GN) or A = GN/D
We have to keep this number in mind to select the correct aperture. For example, if we are using a flash which has a GN 80 feet (for 100 ISO), then, if we are shooting a subject which is 15 feet away from the camera, the required aperture will be GN divided by the distance, which is in this case, 80/15 = 5.33, means our aperture setting should be f 5.6 (the nearest value of 5.33)
GN for portable head on camera flash, is calculated and calibrated for a room of size 10 feet x 12 feet (with ceiling height 9 to 10 feet) with light colored walls and white ceiling. This means that the reflected light from walls and ceiling is also adding some light in the exposure. Should we shoot a subject in a lager room or in an open area, then over expose the aperture value by one f stop to compensate the loss of reflected light. On the other end, if we are shooting in a small room, (say a bathroom) which has glazed tiles, then under expose the aperture value by one f stop to compensate the added light from highly reflective walls.
If we are using an automatic thyristor flash, then there is no need to bother about all these calculations. The photo-sensitive device will take care of the out put of the flash light. Most of cameras with in-built flash, including DSLRs with pop up flash light, are thyristorized.
Read more about:
Flash light meter
How to use a flash light meter
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