I'm capturing a picture during night and to a street with a lot of cars running over the street.
What happens (in general, from a theoretical point of view) if I shoot the same photo under the following conditions?
tp = t * v, such that the amount of captured light is the same as (1)Under condition (1) the picture captures the lights of the cars over the street. Does it also happen under condition (2) or not?
1) Open diaphragm will result in a shallow depth of field, which means that a lesser portion of the image will be in sharp focus. Like this shot of the Blue Mosque (notice the further away from the camera the more blurred the image becomes). You will see car trails if cars move fast enough and you expose long enough. 2) Closed diaphragm will bring up the so-called star trails on lights. Like here on the bridge. Car trails will be longer than in the first case, because with a lesser apperture you exposition time increases to compensate for the reduced portion of light.
What you describe as the lights of the cars, the car trails will be longer the longer the exposure time you choose. The trails appear as the camera captures light spots over time. If cars move during exposure, their lights will move from pixel to the next, which is how the trails appear.
If shooting in RAW, you can always overexpose your scene by 1 stop and then recover details in bright areas in Adobe Camera Raw or Lightroom. In that case, you will get even longer car trails. Or the other way round, i.e. underexpose.
Yes, Scenario 2 will also capture the car lights, because they are so intense relative to everything else that it does not matter all that much what aperture you are shooting at. They will be somewhat dimmer relative to everything else compared to an open-aperture, fast-shutter-speed photo but this may not matter much. Because of the long shutter speed, the car-lights will be captured as streaks running across the picture, rather than as distinct points of light.
http://www.flickr.com/photos/hidesax/8174120933/
First photo I googled up... It was made this way. Cool effect.
Incidentally, this is a good way to photograph fireworks or lightning... slow shutter speed and closed aperture. The light from fireworks/lightning is more than bright enough to get a good photo regardless. Just make sure the camera is on a solid tripod, on a rock-solid surface.
It will vary somewhat with the actual conditions, but in general, if you open the aperture diaphragm, a shorter exposure time will be needed, so Case 1 will show more movement of car headlights. Stopping down (closing the aperture diaphragm) will require a longer shutter speed for the same exposure, so you'll get longer trails.
Whether this happens under condition 2 or not depends on how long the exposure time ends up being for the particular scene, and that depends on a number of factors. Lenses vary, so the difference from your two cases could be two stops (4× faster shutter) or it could be nine stops (500× faster!).
The result will also depend on the amount of ambient light and how fast the cars are traveling. A longer exposure (with a closed-down aperture) will be more apt to reduce the cars themselves to a blur, possibly leaving only the lights visible.
The nice thing about digital is that you can experiment. You can shoot in manual mode, or use shutter priority (often labeled Tv for "time value") mode, which will let you control the time while setting the aperture automatically (in that case, you may want to use negative EV compensation). Start with an exposure of, say, 1 second and whatever aperture combination works to get the exposure you want. Review the result, and increase the time if you want more streaking. If long exposure is your intent, you probably want to fix the camera to a low ISO, but if it's dark and you want to include some of the ambient scene without having to put the shutter to several minutes, you might try raising that as well.
