Reciprocity Law in Photography

Fujifilm X-T2 demonstrating constant exposure and reciprocity law
This ani­ma­tion demon­strates the rec­i­p­ro­cal rela­tion­ship between the aper­ture, shut­ter speed, and ISO, and its effect on effec­tive expo­sure (image bright­ness). The first two frames start at ƒ/5.6, ISO 400, and 1/500 s. Rais­ing the ISO to 800 (and then 1600) requires adjust­ing the shut­ter to 1/1000 s (and then 1/2000 s), to main­tain con­stant effec­tive expo­sure. In the frames where the ISO remains sta­t­ic, a con­stant expo­sure is main­tained despite adjust­ments, because as the aper­ture f‑number is increased (reduc­ing light), the shut­ter speed is slowed (increas­ing light) pro­por­tion­ate­ly: ƒ/5.6 and 1/2000 s; ƒ/8 and 1/1000 s; ƒ/11 and 1/500 s; ƒ/16 and 1/250 s. The process revers­es to the start before repeat­ing anew.

Combining the aperture and shutter speed

At the begin­ning of this chap­ter, you were intro­duced to the for­mu­la Expo­sure = Inten­si­ty × Time. This equa­tion express­es a rec­i­p­ro­cal rela­tion­ship between the inten­si­ty of light pass­ing through the lens and the dura­tion that light is per­mit­ted to fall upon the image sen­sor. It demon­strates that you can achieve equiv­a­lent expo­sures by vary­ing both the aper­ture and shut­ter speed in inverse pro­por­tion to one anoth­er. Giv­en their rec­i­p­ro­cal rela­tion­ship, we can make the fol­low­ing state­ments:

  • If you decrease the light inten­si­ty, expo­sure time must be increased pro­por­tion­al­ly to pro­duce the same total expo­sure; and
  • If you increase the light inten­si­ty, expo­sure time must be decreased pro­por­tion­al­ly to cre­ate the same over­all expo­sure; and so on.

To deter­mine whether the cor­re­spond­ing changes are inverse­ly pro­por­tion­al, refer back to the con­cept of the pho­to­graph­ic stop as a unit of rel­a­tive change. When con­sid­er­ing the total expo­sure of the image sen­sor (and even effec­tive expo­sure, if dis­cussing ISO), a stop is a stop—it rep­re­sents either dou­bling or halv­ing the exposure—irrespective of whether you’re chang­ing the aper­ture or shut­ter speed. When con­sid­er­ing the total amount of light act­ing upon the image sen­sor, you may add one stop by open­ing the aper­ture from ƒ/8 to ƒ/5.6, or you may add one stop by increas­ing expo­sure time from 1/1000 s to 1/500 s, or you can add two stops by doing both. With this in mind, the state­ments above may be rephrased with the fol­low­ing exam­ples:

  • If decreas­ing the light inten­si­ty from ƒ/8 to ƒ/11 (-1 EV), expo­sure time must increase from 1/250 s to 1/125 s (+1 EV); and
  • If increas­ing the light inten­si­ty from ƒ/5.6 to ƒ/2.8 (+2 EV), expo­sure time must decrease from 1/250 s to 1/1000 s (-2 EV); and so on.
Reciprocity law, aperture and shutter speed trade-offs
This series of images demon­strates the trade-offs or com­pro­mis­es that are required when bal­anc­ing the expo­sure using rec­i­p­ro­cal vari­a­tions of the aper­ture and shut­ter speed. A) The rel­a­tive­ly fast shut­ter speed freezes the out of focus car in place, but the large ƒ/2.8 aper­ture ren­ders the back­ground out of focus. B) The slow­er shut­ter speed (1/60 s) is ade­quate enough give the car some sem­blance of speed while keep­ing it rec­og­niz­able, and the small­er ƒ/5.6 aper­ture ren­ders the back­ground with more clar­i­ty. C) The small ƒ/16 aper­ture casts the back­ground into greater focus (although, not per­fect­ly so), but at the cost of requir­ing a much longer 1/4 s expo­sure, which depicts the pass­ing car as a dis­tinct blur. In sit­u­a­tions where you require a small aper­ture and fast shut­ter speeds, you will have to raise your cam­er­a’s ISO speed.

Exposure is a zero-sum game

The exam­ples above demon­strate that equiv­a­lent expo­sure is a zero-sum game: to main­tain expo­sure across var­i­ous com­bi­na­tions of aper­ture and shut­ter speed set­tings, the sum of the adjust­ments, expressed in stops, must equal zero. Any devi­a­tion from zero will result in a cor­re­spond­ing increase or decrease in expo­sure. This is true whether your changes are in full stops or frac­tions of a stop, such as half-stops or third-stops.

At this point, you should have a foun­da­tion­al under­stand­ing of how com­bin­ing the aper­ture set­tings with shut­ter speed influ­ences expo­sure, how ISO changes effec­tive expo­sure, and the units describ­ing their rela­tion­ship. How­ev­er, it’s help­ful to rec­og­nize that each of these parameters—aperture, shut­ter speed, and ISO—imparts a unique aes­thet­ic to your pho­tog­ra­phy, and that cor­rect effec­tive expo­sure is a del­i­cate bal­ance of all three. In the fol­low­ing chap­ters, you’ll be intro­duced to the lens focal length, aper­ture, and their effect on depth of field; about shut­ter speed and its impact on the per­cep­tion of move­ment; and, last­ly, ISO and image noise.