where m is the magnification, N is the f-number and c is the circle of confusion.
For more information on circles of confusion see this Wickipedia article which gives a value of c = 0.018mm for the Canon APS-C sensor.
The following table and chart show the DOF in millimetres at various f-stops for reproduction ratios from quarter life size to twice life size calculated using this formula for the APS-C sensor:
I wanted to try and demonstrate this for talks I give on macro photography. What I came up with was to take a series of photos of a relatively small subject (an 18cm tall figure of an Uruk-hai from Lord of the Rings) using a series of different focal lengths, but moviing the camera so that the subject was kept at the same size in the viewfinder (hence maintaining the same reproduction ratio). Here is the setup:
The Uruk was placed, standing on a ruler, in the garden and a piece of string stretched from his middle across the garden. At each focal length, the camera was positioned with the lens aligned along the string to keep the same angle of view and then moved backwards and forwards until the Uruk was positioned in the same way in the viewfinder with his feet on the bottom of the frame and the top (active) focus point on his chest armour:
|400mm (at 5.8m)|
|200mm (at 3.2m)|
|100mm (at 1.7m)|
|50mm (at 90cm)|
|35mm (at 74cm)|
The effect of the focal length of the lens on the working distance for macro shots can be seen in the following shots. Here is the Uruk's lovely face at a reproduction ratio of 1:1:
|1:1 shot of the Uruk-hai's face|
|100mm macro focused on the face at 1:1|
|65mm macro focused on the face at 1:1|