Does a len`s F stop change with the crop factor?

[AlbertTRAL]

Your 40 is a 40 but sees like a 60. So let's think it's a 60 and... your 1.4 fstop stays that always.

Nice wording and spot on Don! I will add:
Your 40 sees like a 60 but almost feels like a 40 (interpreting feels as DOF).
DOF will remain almost that of a 40mm in FF (this means bigger than a 60 in FF)

Bigger than a 60 in FF but slightly smaller than a 40 in FF...

How much means "almost" and "slightly"...

As I pointed previously, taking your lens DOF marks for FF, you should use +1stop marks for the GXR A12M (roughly, just a little less even). This means stopping down to 8, use DOF marks of 5.6 to evaluate your DOF.

Using one of the DOF calculators pointed by Don:

40 FF 2.8 @1m 0.106mDOF
40 FF 2.0 @1m 0.075mDOF
40 FF 1.4 @1m 0.053mDOF

40 APS-C 2.8 @1m 0.071mDOF (almost as FF @ 2.0, just a little less as said >> +1stop marks)
40 4/3... 2.8 @1m 0.053mDOF (as FF @ 1.4 >> +2stop marks)

Obviously your lens DOF marks are and act as one of those "old" slide rule or "slipstick" (mechanical analog computer) . Will always work, even without batteries, and it is soldered to the lens!

[britinjapan]

Many thanks - now this has nailed it on the head!

[Duane Pandorf]

With the two fixed lenses I have on my GXR, (A12 28mm and Leica 40mm on the M Mount), I just move forward, backward, or left and right, or pivot around to get the framing I need.

I use the f stop to get all that I want in focus or as little as I want.

Shutter speed and ISO to expose what I want.

[streetshooter]

Duane, if perspective is not an issue, moving around is fine. If it is....uh oh...

[britinjapan]

Apologies, but a last question. I`m back to the original - a simple answer is best - Lets take the example of a 2x crop factor (micro 4/3) for ease of calculation - the 20mm lens gives the same effect as 40mm on full frame, but what about the F2 stop? Does the same amount of light enter?