Dimmable Lamp - Luminous Intensity

Welcome to the forum and I hope that you find great insigh and some fun here.

Just like Newton's second law, this law also remains intact.

Luminous flux (passing through a unit area) is proportional to the intensity of the (point) source that it originated from (The "I" in the equation), the distance that you are from it and the area of your collector (2*pi*(1-cos(angle/2)).

Why do you say the equation isn't adequate?

Consider if instead of a point source there were two "equal" point sources, each conforming to the formula. The "apparent" intensity would be double, the flux would be double, all would be well.

Then consider that you "dim" this by removing one of the point sources. The formula exactly predcits what happens.

Even if the "colour" characteristics of the source change (Colour temperature) through dimming then the effect will still be exactly characterised by the formula.

The equation is basically saying that the flux from a point source is dispersed evenly over a spherical projected area and the flux that you will observe is proportional to the area of the projected spere that you measure.

Isolux diagram serves for reading luminous intensity under certain angle for lamp which emits certain luminous flux (and that is always showed under maximal power of lamp).

The formula which is mentioned before doesn't represent dependence read from isolux diagram(calculated values for luminous flux or luminous intensity are not real).

By changing lamp power intensity, luminous flux is being changed, but there is no isolux digram for other power than maximal.

Also, every lamp has its maximal angle under which it lights, while formula returns values which represents that lamp is lighting above that angle.

Isn't it?

Go back to the basic physics of what you are asking.

If the light "pattern" doesn't change, then the isolux pattern will remain the same (but at the new intensity) represented by the dimmed condition.

Basically you have less light "particles" being spread through the same distribution "histogram" so the isolux contours are unchanged, just with lower intensities.

1) F=I*2*pi*(1-cos(angle/2)) is for a point source, where its intensity is constant over all angle. In the isolux plot, you may see a perfect circle, which represents same intensity at different angle.

2)The relation between (I) and (F) is different between different lamps (because not all lamps are point source). With common practice, (F) will be considered with (I0) instead of (I). (I0) is the intensity at angle=0.

3)The relation between (I) and (F) will not change with different power. Imagine a lamp which illuminates 90% of its total light inside a cone substended by 40deg; if this lamp has total power decreases, the abosolute value of total light will also decrease, but there is still 90% of its total light inside that cone.

Thanks for the answers!

2) Every lamp have its own relation between I and F irrespective from that lamp is point source or not, in other words every lamp is a point source if distance between lamp and measured point on working area is at least five times bigger then biggest dimension of the lamp.

I have situation(perchance) were all of the lamps are point sources, and I know relation between lamp power and luminous flux F.

Isolux diagram is not defined for lamp which is point source or something else, thus formula should be valid and for intensity „I" (agreeable with isolux) when power and flux are maximum.

Therefore, which relation exists between I and F, that formula returns real values for I or F (values are especially ireliable for small and bigger angles)?

Sorry for confusion. F=2*pi*I*cos(1-angle) is for UNIFORM point source, where intensity is constant at all angles.

At >5x distance away from the lamp, a lamp can be treated as a point source. But the lamp may not be UNIFORM point source. e.g. a spot lamp illuminate at particular angle, i.e. intensity is higher at particular angle and not constant at all angle. At >5x dist away from it, the spot lamp can be treated as point source, but not UNIFORM.

The I and F has a linear relationship. Therefore, no need for any formula. e.g. If F=100lm & a contour=10lux in the isolux diagram; when F decrease 50% to 50lm, then the same contour will also decrease 50% to 5lux

How are you sure for linear relation between flux F and intensity I, because manufacturers don't provide that informations for luminary power (and flux) lower than maximal?

P.S lux is unit for illumination (which depend from intensity)!