Which lampshade is brighter? My room has a single light bulb. It's a bit grim, so I decide to decorate. I have a choice of two lampshades. Both are paper ball designs. One has twice the diameter of the other. The paper is the same thickness in both.
Obviously the room will be slightly darker than it was with the naked light bulb. But which lampshade will preserve, i.e., transfer to the room,  the most light?
Picture of a paper lampshade http://i.imgur.com/bIIbMQU.png
 A: Usually the attenuation of light due to scattering or absorption follows an exponential decay of intensity as a function of distance, i.e., $I(z) = I_0 e^{-\lambda z}$. As the thickness of each lampshade is the same, we can simply write $I_\mathrm{outside} = \alpha I_\mathrm{inside}$. Thus each lampshade will absorb a constant fraction, regardless of it's radius.
A bigger contributing factor is that the two balls might not be exactly proportional. For example, the larger ball won't necessarily have thicker wires, so could actually pass more light.
Also, those lanterns might not be meant for use around a bulb, and could be purely decorative. Watch out for fire.
A: In the smaller shade, a larger proportion of light which is reflected back from the shade is absorbed in the bulb or bulb holder. This might have a noticeable effect on the total luminosity even if the holder is white, as incandescent lamp or fluorescent lamp acts as a rather black body to the radiated spectrum (even if it is a fluorescent lamp, the radiation peaks are also the absorption peaks).
Thus the larger one will probably be slightly brighter.

Remark (added later): A paper usually reflects much more back than lets through. Thus inside the lampshade, the paper appears much brighter than from the outside. This significantly amplifies the effect described here. 
