The boring explanation Here follow some technical explanations: First of all
, my deepest apologies to those not familiar with mathematicsor physics…
But the conclusions are very interesting…. (see at the end) I did some
serious thinking to understand the rule of thumb of using a shutter speed
equal to the inverse of the focal distance. Here are the results: first some
(half-serious) maths: Let's start with the basic definitions and
assumptions: To simplify the calculations, we assume we can model the lens
with only one convex element with a focal distance f. We also assume that we
focus on infinity and the picture is forming on the sensor at a distance
corresponding to the focal distance. Let's call h = the height of the sensor
(16mm for a Nikon D70 for instance, a 1.5 crop sensor camera) v = the
vertical resolution of the sensor (2000 for a Nikon D70 for instance, a 6MP
camera) s = shutter open time in seconds The angle of view can easily be
computed like this: Examples: 50 mm lens on a D70: 2 arctan (16/100) 18°:
vertical angle of view Usual definition (taking the diagonal size into
account) 50mm lens on a D70: 2 arctan (28.8/100) = 32° diagonal angle 50 mm
lens on an F100: 2 arctan (43.2/100) = 46.7° diagonal angle(full frame or
film format) If we assume that the blur due to your own movements is
depending on the angular velocity of your movement (you usually use the left
hand to hold the lens at a certain distance from the sensor, and the longer
the lens, the larger the movement). The maximum angle variation during the
shot should correspond to maximum one pixel on the sensor: d(a) = arctan (h/
(vf)) approx= h/(vf) for small angles If you induce a movement resulting in
an angular velocity of w, you need a shutter time s so that w x s <= d(a) (
in other words, you have to shoot fast enough so that the angular movement
you generate is less than the angle variation corresponding to a pixel on
the sensor). The conclusion : Combining the formulas I get s (shutter time
in seconds) = d(a)/w = (h/v) * w * (1/f) or in other words s = constant * (1
/f) which is the well known thumb rule: HOWEVER, that constant factor
depends on three factors: -the lower your own angular velocity (shake) the
lower the allowed shutter speed (evident) -the shutter time should be
proportional to the height of the sensor (h) –this is also known: DX sized
(16mm) vs FF-35mm (24mm) means the safe shutter speed should be multiplied
by the crop factor, 1.5 -the shutter time should also be adapted based on
the RESOLUTION of the sensor (v) If linear resolution is increased by a
factor 2, the safe speed should be as well: to be clear if 1/100sec is safe
on a D1, you NEED 1/ 200sec on a D2X to get a sharp picture at pixel level.
Disclaimer: there are some approximations in the reasoning, but the
qualitative conclusions are valid. I will try to rephrase the conclusions
using normal words: The concept of a "safe shutter speed" based on focal
distance is scientifically correct: (to compensate motion blur due to the
photographer) 100mm means 1/100sec on a FF or 35mm camera 400mm means 1/
400sec etc... but the following elements also have to be taken into account:
-your own "shaking" ability -evident -the crop factor 100mm means 1/100sec
safe on an F100 BUT 100mm means 1/150sec safe on a D70 or D200 or D2X... -
the sensor resolution 1/100sec just safe (for you) on a D1 means 1/200sec (
also for you) will be needed on a D200 or if 1/100 is safe on a D70 you'll
need 1/125 on a D200 otherwise you'll get the impression that your pictures
are not too sharp. Hope this makes the point a bit more understandable.
