Inverse Square Law of Light

Words like “Inverse Square” do frighten people. But the law is not that bad. In fact, it helps us tackle lighting and exposure difficulties with on camera flash. So readers can expect them at better position and knowledge to do flash photography!
Lighting Difficulties always arise when we try to photograph a group of people, standing or sitting at different distances from camera. These difficulties multiply when we are using camera's built-in or dedicated flash. No matter how powerful our flash is; subjects at different distances do get lit differently. Now this is common sense that as we go away from the light, the intensity decreases. So lets do case study.

So in this diagram, we can see 4 subjects at different distances from camera. So, to photograph all of them, we need to do focusing we can use higher aperture to keep all of them in focus. But It will be little harder for the flash to make them properly lit. more the distance between the subjects, poorer lit the scene. That, if we focus at subject 1, ONLY subject 1 will be properly lit. subject 4 may not be visible. Then, if we focus at subject 2, ONLY subject 2 will be properly lit and subject 1 will be overexposed! It is then obvious that subject 3 and 4 will be gradually underexposed!!

Essentially, we need to know how the intensity of light decreases with increasing distance. Studying physics may give us an answer. But hold on, we need to not to do a Ph.D on it. There is a simple law named “Inverse Square Law of Light”(See the diagram.). Actually speaking, this law is not only for light but for any point source which spreads its influence equally in all directions without a limit to its range. Gravitation, Electrostatics, Electromagnetic Radiation as well as light obey this law. We have got nothing to do with the former three things, so we better concentrate on how light obeys the law. From the simplest point of view, doubling the distance between the light and the subject results in one quarter of the light hitting the subject. Now there cannot be simpler interpretation than this.
Scientific statement of the law (relating to light)can be like, “The intensity (or illuminance or irradiance) of light or other linear waves radiating from a point source (energy per unit of area perpendicular to the source) is inversely proportional to the square of the distance from the source.” Big bad scientific sentences again! This is great but how to use it in daily life? Lets get back to that case study again(Refer to the right half of the diagram). Assume that the distance between camera and subject 1 is 2 feet and the distance between each if the subject is 1 foot. So the distance between camera and subject 4 is twice than that of between camera and subject 1. Hence, the incident light on subject 4 is a quarter of that incident on subject 1. In photographic terms, subject 5 is underexposed by more than 2 stops. Exposure difference of 2 stops is not acceptable at all. Now don't tell me you shoot in RAW and will later change the exposure; That is not real photography!
We need to be a bit innovative to use this law of Inverse Square of Light. Let us play around the law to understand it better. Go through the following 3 statements.
1.Focus and expose for subject 3.
2.Now the distance between light source and the subject 3 is 4 feet. So the distance between camera and subject 1 and between subject 3 and subject 5 is 2 feet(half of 4 feet).
3.Hence the incident light on subject 3 is one quarter of the incident light on subject 1. And incident light on subject 5 is further one quarter of that on subject 3.

Then what will happen if go away to 4 feet distance from subject 1?; keeping the distance between each subject constant at 1 foot. Refer to the diagram and read the statements.
1.Focus and expose for subject 1.
2.Now the distance between light source and the subject 1 is 4 feet. So the distance between camera and subject 1 and between subject 1 and subject 5 is 4 feet again.
3.Hence the incident light on subject 5 is one quarter of the incident light on subject 1. Or this makes subject 5 two stops underexposed than subject!
This worsens things. After careful analysis of the above said examples, we can arrive at a conclusion. Halving and doubling of the light depends upon the distance between light source and the subject. As we go near the subject, distance at which the light intensity doubles also lessens; and vice versa. Practically speaking, if we focus and expose for 2 feet distance, light intensity will halve at 2 feet distance.
I hope it isn't getting too much of science. As it can be fun doing this much of simple maths and visualizing different situations! The final solution for the problem from first diagram is exposing for subjects from the distance more than double of their range. That is for our problem, as our subjects are spread over 4 feet distance, we should expose from 8 to 12 feet distance!

The Photogrpahic Term of Reciprocity Failure

I accidentally happened to come over a big bad and strange phrase, “Reciprocity Failure”. Before this, the jargon of photography never feared me. But now I can say that it’s not that bad how it reads! Yes, I am going to explain that. You need not be afraid though. Because I have already simplified this kind of nerdy stuff! So let’s plunge!!

So let us divide the phrase into two. ‘Reciprocity’, and ‘Failure’. Hence Understanding this phrase becomes as easy as combining both the meanings! The two most appropriate meanings of this word are, ‘Mutual action and reaction’ from Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc. & ‘a relation of mutual dependence or action or influence’ from WordNet® 3.0, © 2006 by Princeton University. This mutual thing happens between our aperture and shutter speed. When this relations or rule fails, there happens a failure!

For a photographer, it is quite a common sense that a combination of a shutter speed of 1/125th of a second with an aperture of f8, which is referred to as an exposure setting of '1/125th at f8', will give the same exposure to the film or digital sensor as 1/250th at f5.6, which is the same as 1/500th at f4 etc. This relation or phenomena between aperture and shutter speed is termed as reciprocity. So in theoretical terms, it refers to the inverse relationship between the intensity and duration of light that determines exposure of light-sensitive material. Within a normal exposure range, for example, the reciprocity law states that exposure = intensity × time. Therefore, the same exposure can result from reducing duration and increasing light intensity, and vice versa. So in practical life, what we actually do is using this law of reciprocity. This again refers to the relationship whereby the total light energy, proportional to the product of the light intensity and exposure time (controlled by aperture and shutter speed, respectively), determines the effective exposure. We use these different combinations to cater our special needs of focusing and depth of field.

Now here is a game, this law does not hold true in extreme conditions; like in long exposures or too fast exposure like 1/10000 seconds. I don’t know who is in that hurry to click this much fast. For most photographic materials, reciprocity is valid with good accuracy over a range of values of exposure duration, but becomes increasingly inaccurate as we depart from this range. Only in such conditions, certainly not in our daily life (oh, what a relief!), this reciprocity does not hold. As the light level decreases out of the reciprocity range, the increase in duration required to produce an exposure becomes higher than the formula (exposure = intensity × time) states. This breakdown in the relationship between aperture and shutter speed is known as reciprocity failure.

So you interested in getting deeper! Some physics/chemistry jargon comes into play. I have already simplified everything to my best. Still, if you stuck upon some word. Just google it! So here it goes…

Each grain must absorb a certain number of photons for the light-driven reaction to occur and the latent image to form on the film. In particular, a few dozen photons are required for the surface of the silver halide crystal to result from absorption to its developable rendering. At low light levels, i.e. few photons per unit time, photons impose upon each grain relatively infrequently; if the four required photons arrive over a long enough intervals, the partial change due to the first one or two are not stable enough to survive before enough photons arrive to make a permanent latent image center. Reciprocity failure may also affect the tonal range of a photographic scene when at the limit of exposure, resulting in burnt highlights while losing detail in the shadows.

This was all for film. But digital is neither a different story. On one hand film prints are affected by graininess, on the other hand, digital photographers may experience excessive noise, even at lower ISOs. That is all. It is not that frightening as you must have thought before is it?

I owe the information to the links that appear on the first page when I googled the term!