LFingar Loc: Claverack, NY

Lay a piece of paper on a table. 8x10, for example. That is your sensor. Suspend a flashlight above it. That is your aperature. The paper will be illuminated to whatever level the light provides. Check it with a light meter if you have one. Now, substitute that paper for a 5x7 piece. The 5x7 will be illuminated exactly as the 8x10 was, just over a smaller area. It doesn't get darker because of the smaller area. All that happens is that the light that is falling on the empty space that was a larger piece of paper, or sensor, is now un-used by the camera.

Blurryeyed Loc: NC Mountains.

Maybe it helps to consider the difference between a full frame sensor and a crop. The light coming into the camera is the same, the difference is that with the crop sensor the light is hitting a smaller area so you are only capturing a portion of the image that would be captured on a full 35mm sensor, but the intensity of the light hitting the crop sensor and the same area on the 35mm sensor is the same even though the 35mm sensor is collecting more light across the full area of the sensor simply because it is seeing a larger image.

f/2.8 is f/2.8 no matter which camera you are using, the earlier explanation about DOF is correct, with a crop to make the image appear to be the same size you will have to shoot from a greater distance from your subject increasing the DOF at any particular f-stop.