Law of Reciprocity: an increase of brightness by a certain factor (controlled by the aperture) is exactly compensated by a decrease of exposure time by the same factor.
Essentially, the Law of Reciprocity tells us that if you open the aperture by one stop and increase the shutter speed by one stop you will maintain the same exposure value. This law remains true up to a point but, the longer film is exposed to light the less responsive it becomes.
An exposure is made when light, a stream of discrete photons, interacts (hits) the light-sensitive grains (silver halide crystals) of the film. Each grain on the film needs to absorb a certain number of photons before a reaction takes place and an image starts to form. In low light conditions an insufficient number of photons will reach the film in time to complete the reaction. Once too few photons reach the emulsion the response from the silver halide to light is no longer linear which means that a longer exposure time is required. This is Reciprocity Failure - when the Law of Reciprocity goes tits up.
Reciprocity failure means that the film becomes slower over time, behaving as if it had a lower ISO value. The effect of this on black and white film is under-exposure... you will produce a "thin" negative if you don't compensate with a longer exposure time. With colour film you will likely also see a colour shift, probably a magenta cast over the image, this will need to be filtered out for printing.
Fortunately, it isn't difficult to calculate a new, compensated exposure time to correct the reciprocity failure.
Unfortunately, every film emulsion reacts differently and so the compensated exposure for each film needs to be calculated individually.
Fujifilm's Acros 100 is barely affected by reciprocity failure, exposures between two minutes and sixteen minutes simply require an additional 1/2 stop of exposure time. Fomapan 100, on the other hand, requires a one stop adjustment after just one second of exposure.
Every film will have a datasheet to specify the exposure compensation for that particular emulsion. I keep a file on my phone that contains adjusted exposure times for the film stocks that I regularly use. This probably isn't ideal as I need to estimate the compensated time when the metered time isn't specified in my notes. Not really a big deal though as I'm not particularly fussy about exposure times, as long as I err on the side of over-exposure (I usually only shoot negative film). If you shoot transparency film you need to be more accurate.
There are some phone apps that can calculate the compensated time for you, you just select the film you are using and input the metered time. You could also print out a chart to keep in your camera bag, whatever works for you.
Here are examples of two films showing the metered times and corrected times:
|Kodak Ektar 100
As you can see from the above chart, Ektar 100 requires no compensation under eight seconds exposure time while HP5 Plus needs 1/3 extra stop after only two seconds. A four minute exposure on HP5 Plus blows out to 22 minutes or nine minutes for Ektar.
One side effect of increasing the exposure time can be an increase in contrast. This can be offset somewhat by reducing the development time (pulling the film).
You really need to experiment with adjusted times for both exposure and development to find something that works for you and can produce consistent results. If you do much long exposure work it is worthwhile sticking to one particular emulsion and learning its characteristics.