Why do you get a lot more light from a diffuser lamp than you would just with a bulb?

Question

Isn't that an oddity of physics? I mean here you are, a little lightbulb in your hand - not much happening; then you put a diffuser or reflector behind it, and you get this huge burst of light. Doesn't that mean that the light has multiplied without extra energy input? That's impossible though. What's happening there?

Answer 1

Not an expert, but let me try:
You and @steve are correct, the amount of lumens (a measure for the visible light-"current") coming out of the lamp does NOT change.

The small filament area of the bulb has an even light light distribution in all directions. Assuming the room is predominantly 'black', with few reflections coming back to you, you see only what enters into your pupil, coming DIRECTLY from the (almost) point source.

I am too lazy to do the calculation, but you are NOT seeing maybe > 99.99+ % of the lumens emanating from the point source.

The magic words in your question are "reflector", and "behind" the point source:

If you use a reflector e.g. a white sheet of paper/ cardboard with typically a Lambertian (cosine) re-distribution, you are looking at factors of "amplification":
One, most of the light sent out to the rear of the bulb (which was lost anyway) is now redirected to you, or to objects in the vicinity of the bulb.

The second effect is 'saturation' on the retina. With a point source the sensor on the retina cannot integrate in linear fashion, the "brightness" of the point source. When that light however is spread out, because of the paper diffusor, over a larger area on the retina, it is messaged to the brain as being "brighter".

PS the lens of your eye, when it creates an image of an "area source" (e.g. the sheet of paper) in the room will always focus the SAME number of lumens PER AREA on your retina, this irrespective of its distance from you. That is why objects have identical "surface brightness" as interpreted by your retina (repeat, regardless of distance). If the objects were true point sources their light intensity would decrease with the inverse of the distance squared. And second, because most objects have a Lambertian distribution that "surface brightness" stays IDENTICAL, even when it is tilted at an angle to you.

Answer 2

You don't get more light; you get light coming from a lot more directions than the essentially point source of the bulb.
You can verify this with a photographer's light meter.