Luminous intensity in candela

is the SI unit of luminous intensity. The definition is not simple.

Explaining the definition of a candela

The human eye is sensitive to a very narrow range of electromagnetic radiation and within this visible spectrum it is especially sensitive to colours around green. The definition of the candela therefore centres upon a single wavelength of light in the green part of the visible spectrum. Specifically that is a source that emits monochromatic radiation of frequency 540 × 10¹² Hz and that has a radiant intensity in that direction of 1/683 watts per steradian. Not the easiest definition to remember!

Luminous flux (in lumens)

is a measure of the total amount of light a lamp puts out. The luminous intensity (in candelas) is a measure of how bright the beam in a particular direction.

If the luminous intensity is one candela and the lamp only shines over this angle of 1 steradian then the luminous flux is 1 lumen. However iff the luminous intensity is one candela but the lamp actually emits light equally in all directions with the same luminous intensity.Then since the total area of the sphere is  4πr²  The luminous intensity will be 4π lumens.

The Lux

Photographers are far more interested on how much light is shining on a particular area, this is measured in Lux. The definition is the amount of light in lumens shining on each square metre. That is lm/m²

The intensity changes with distance according to the Inverse Square Law

At three times the distance from the lamp the lux will be one ninth because the light is spread over nine times the area. At double the distance from the lamp the lux will be one quarter because the light is spread over four times the area.