The light intensity of a source is 100 candelas. The illuminance on a surface is 4 lux. How far is the surface from the source?

The answer is 5 meters.

The illuminance on a surface (E) is equal to the light intensity (I) divided by the square distance from the light source (d):

E = I : d² [=] candela / square meters = lux.

The unit of the illuminance is lux.

So, it is given:

E = 4 lux

I = 100 candelas

d = ?

If:

E = I : d²

Then

d² = I : E

⇒ d² = 100 : 4

⇒ d² = 25

If we put both sides of the equation under the square root, then:

√ d² = √ 25

⇒ d = 5 meters.

Therefore, the surface is 5 meters far from the light source.