Originally Posted by kgphoto
I think you are wrong.
IF you raise the flash power setting and move the light back so you keep the camera at the same f:stop OR lower the power as you move the light closer to the subject, the background will still appear darker when the light is is the main position.
As you move the light backward and increase the light output so that you can keep the same f-stop for the subject, the background will get brighter, not darker as you suggest.
Think about it using my above example, but let's take "b" to an extreme...
a. Light --- 2m --- Subject --- 2m --- Background
b. Light --- 20m --- Subject --- 2m --- Background
In the second example, you've really gotta crank up the power to the light that's now 20 meters from the subject to maintain the same f-stop you had in the "a" example. Since the background is only 10% further, it will be brighter. Inverse square law says that in "a" the background is getting only 25% of the light that the subject is, whereas in "b" the background gets 82.6% of the light reaching the subject.
The second half of your statement ... moving the light closer...will indeed darken the background.