# AF Sensitivity and Function

Started Oct 14, 2008 | Discussions thread
Kerry's Experiment #2: The Light Cone

With everything set up as in Part #1, now put the lens back to maximum aperture.

Slowly slide the screen toward the back of the lens, and observe that the tiny light spot gradually grows into a larger and larger solid circle. The illumination across the diameter of this circle is very even. If we plot the diameter of the circle versus the screen position, we will find a simple linear relationship; as the screen moves, it is sampling cross sections of a 3-dimensional cone of light.

It's a little cumbersome to study the circle diameters this way because of the small space between the screen and the back of the lens. The distance from a focused image to the rear of the lens mount is only about 38mm. To get more working room, we can alternatively look at the rear cone of light, which forms behind the plane of focus.

Set the screen back to position where the light spot is well focused. Set a metric ruler against one side of the screen's box, and slide the box back along the ruler exactly 100mm. We now have a much larger solid circle of light to examine (although it is also much dimmer). Use the ruler to measure the diameter of the circle in milimeters. Calculate the value of 100/diameter; this should be the same as the f-stop of the lens (assuming the lens is still wide open).

Set the lens aperture to a few other values, and observe that as you stop the lens down, the size of the circle reduces. Also, notice that as the circle shrinks, the brightness of its interior does not change. [You can confirm this by photographing the circle at different lens aperture settings (used locked manual exposure settings on the camera when doing this), then checking the images that you obtain.] Thus, changing the lens aperture alters the size of the circle (i.e., the diameter of the light cone), which by itself determines the total amount of light passed by the lens - the intensity or concentration of light within the cone remains constant.

Measure the diameter of the circle for several different lens aperture settings, and for each one, calculate the value of 100/diameter. The calculated value should agree with the f-stop set. This set of measurements does not depend on the lens focal length. You can repeat this experiment with other lenses and you will again find that 100/diameter = f-stop.

Now we know that the width of the light cone relates directly to lens aperture, and in fact the height of the light cone, divided by its base diameter, is the same as the lens focal ratio or f-stop.

For the last demonstration in this part, slide the screen back to position where the light spot is well focused. Set the lens back to maximum aperture. Take a small dot of paper, about 1/4" diameter, and hold it with tweezers or stick it onto the end of a toothpick or similar. You can move this dot across the back of the lens, through the light cone, and no matter what position it is held in, the projected light spot will still be observed. It will drop slightly in brightness while the paper dot is within the light cone, but it cannot be cut off.

On to part 3 . . .

Complain
Post ()
Keyboard shortcuts: