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Not Roger,

Before a rather brief answer in comparison to what an answer to those questions could be I do recommend you read up further on this subject (as well as the replies you get here)! These are the building blocks of good lighting so knowing them and understanding them is quite a good idea.

"Whats the difference of the  fall-off when we use different diffusion outside the window in a daytime interior, a light diffusion vs a heavy diffusion.  "

A rather broad subject mixed in with a smaller subject. I'll ignore the daylight interior and focus on the light diffusion vs a heavy diffusion. Diffusion is when 'Light diffuses when it bounces off the many angles of a rough surface, or when it travels through a substance that changes its angles.' A heavier diffusion scatters the light more than a lighter diffusion therefore creating a 'softer' (diffused) look. However a heavier diffusion will also cut more light. I highly recommend you buy a piece of Muslin off amazon and compare it with a piece of tracing paper. Fold it for an even heavier diffusion and I'm sure you'll see a difference!

The fall-off. The inverse square law states that at double the distance you get 1/4 of the light. Now a number of things to take into account. A medium/heavy diffusion will act as a 'new source' in a way (at least from what I've studied and my experience). So you take your inverse square law into account from the diffusion not the original source. On lighter diffusions (much lighter) this doesn't apply as much. For example bounce off a piece of muslin you take inverse square law from the muslin bounce. Bounce off a mirror and you take the inverse square law into account from the original source. 

"To get a gradually falloff  What's the best way to achieve it ?"

Place the source further away from the subject. If you look at the way light falls off it doesn't fall off linearly it falls off in a curve. Inverse square law you get 1/4 of the light at double the distance. So from 1ft to 2ft you loose 3/4 of your light. From 100ft to 200ft you loose 3/4 of your light (5ft-10ft 20ft-40ft so on). Extreme examples but I feel it shows the point. Now of course there are always exceptions some fixtures have more "throw" such as a ellipsoidal reflector spotlight (such as a Leko).

"I am a bit confuse about the distance. I know it's best to use a large bounce or diffused source but I am a bit confuse about the distance."

'Best to use a large bounce' that is entirely up to you! Softness of the light is dictated by the size of the source relatively to the subject. If you want a hard light for example a kicker. A larger bounce would be a bad idea a smaller bounce that's less diffused such as a mirror would be great! 

The size of the source relative to the subject. The sun is a very large source however very very very far away so it casts a harsh shadow and is considered a hard light. A fluorescent tube in comparison is tiny however at 6ft away from your subject placed horizontally it is a softer source. 

I feel like I've only scratched the surface and it is quite late (midnight) so I have probably missed a fair bit. Theres a lot to read into for example a larger bounce may be better for a softer quality of light but if you don't have the firepower to fill the bounce the larger bounce is essentially useless. 

Best thing to do is grab a light even a flashlight and practice!

 

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