Shortening a flash-duration would not increase the instantaneous power output of the flash, it would stay the same. To attain the same overall light output hitting the subject, you'd have to increase the instantaneous power output of the flash.
You are right in practiice: control of flash duration is actually used for switching light outpu. I was thinking of an energy/time couple where one could control one element, but the spent work, the quotient, would be constant.
This is not the case. But there also is no W/sec in reality. As no flash extends to a second. Still we use this analogon, as if the flashlight always does the same electrical work.
I take it you've never studied calculus? It includes a study of limits (as in the limit when something approaches zero or infinity).
I just don't think the phrasing is very meaningful. For example I think something like "increases without bound" might be a better way to phrase it than "approaches infinity".
To be frank, whilst the theory can be fascinating, it has no practical use in photography once you get less than a useable distance from the point source, especially when the source no longer can be classed as a point source.
Who is actually making images at less than 3" from a source using something that equates to a point source, a single LED perhaps? To use the inverse square law practically you need to be able to measure the light at one point to be able to use the ISL to calculate the light strength for another, at very close distances this becomes extremely impractical.
Nowadays if someone is using d*****l they just chimp the image until they get it as they want it, if small point sources of light are being used to highlight parts of an image, the image was also chimped in the pre-d*****l days with the use of a polaroid.
To be frank, whilst the theory can be fascinating, it has no practical use in photography once you get less than a useable distance from the point source, especially when the source no longer can be classed as a point source.
Who is actually making images at less than 3" from a source using something that equates to a point source, a single LED perhaps? To use the inverse square law practically you need to be able to measure the light at one point to be able to use the ISL to calculate the light strength for another, at very close distances this becomes extremely impractical.
macro/micro photographymoving a flash gun extremely close to max light intensity,being aware of light loss dou to bellows extension
Light is weird stuff. It can be wave or particle, depending on whether someone is observing it (see double slit experiment). That's why photography is really a magical-alchemical process, even while we imagine it's a practical-mechanical one. Summoning the muse is much cheaper and infinitely more effective than throwing money at new gear.
"Line and plane sources can appear as point sources if the distance from source to
measurement point is great enough. There is a rule of thumb used when considering a
source a point source. A source will exhibit the characteristics of a point source if the
measurement point to source distance is greater than three times the largest dimension of
the source."
Radiation, whether it's visible light falling on a photography subject or gamma radiation dosing a worker works the same.
As we get closer to the light source, we eventually get to the point that it no longer can be approximated by using rules of a point source.
If it were - in fact - a "true point source" then if you crossed into the singularity it would be infinite, maybe. The math breaks down in stuff like that.
So, the formula isn't wrong, nor is the theory. What's wrong is the assumption that the illumination source is a point. But the math to calculate it, vs the math to approximate it, is orders of magnitude different.
A plane source, like the surface of the bulb, will have a constant dose (or in our case illumination) regardless of the distance so long as we stay within in the 3x parameter. For example, if we are 2cm away from a 5cm bulb radiating surface, and we move to 4cm we will not effectively change the illumination of the subject. If we move to 10cm we will not "effectively" change the illumination. If we move to 15cm we will not effectively change the illumination. But if we move to 30cm we will get the inverse square illumination.
Again, these are rules of thumb that plenty darn good enough approximations to live with. While the actual mathematical calculation isn't difficult in principle, it is devilishly difficult to compute in a practical sense.
That is a good explanation, Michael.
I am not doing macro but yesterday I made a graph based on my earler post.
The vertical scale is 'relative EV" to indicate change in camera settings for example f/ (by taking log-base2 of the change in luminance [cd/m^2]
Graph is for a 65mm long flash tube.
It also shows that after the distance is further than 2~ 3 times the length of the flash tube, the Gauss Law (inverse square)
is quite accurate.
Closer than that, the EV settings do not change so much.