العوامل المؤثرة في المسافة فوق البؤرية ١-a .. كتاب آلة التصوير

Factors affecting the suprafocal distance:

The suprafocal distance of any lens depends on the following factors;

First: The diameter of the actual diaphragm hole:

It is possible to calculate this diameter easily if we know each of the following:

(a) focal length of the lens (p)

(b) the focal number of the lens (q)

As the diameter of the aperture (s) = the focal length on the focal number =
p / f
(Please refer to p. 53).

Second: The ratio between the focal length of the lens to the diameter of the permissible mixing circle (x):

That is, the second factor = the focal length of the lens over the diameter of the permissible mixing circle = p / x

And since the diameter of the permitted mixing circle is one-thousandth of the chord that connects two opposite corners of the image area (which is chord A in Figure 69 p. 102) or equal to the average focal length of the lens suitable for the camera, so we see that:

Allowable mixing circle diameter = the appropriate average focal length of the camera at 1000

Thus, we conclude that the second factor = the actual focal length of the lens / the appropriate average focal length of the camera at 1000

Calculating the suprafocal distance:

Based on the foregoing, the suprafocal distance is calculated as follows: suprafocal distance = the first factor × the second factor (1)


= focal length of the lens on the focal number X the focal length of the lens on the average focal length suitable for the camera / 1000 (2)

= focal length of the lens on the focal number x 1000 x the focal length of the lens on the average focal length .. (3)

The focal length of the lens on the focal number = the diameter of the diaphragm aperture

- The focal length of the lens on the average focal length =
Zoom power

...superfocal distance (2) = 1000 x diameter of the diaphragm aperture x magnification power (4)

(1) This is because the degree of enlargement of the image (i.e. the extent of the relative space occupied by the image on the negative) depends on the ratio
The actual focal length of the lens over the medium focal length of the lens (i.e. when the lens has a long focal length or telephoto for example) the greater the magnification ratio, i.e. the greater the relative area occupied by the image of the object over the negative. And vice versa, as the relative area occupied by the image is less than the negative, that is, the transfer of the magnification ratio, if the actual focal length of the lens is less than the average focal length.

(2) This was stated by Arthur Cox in his book Photographic opties in the tenth edition of 66, the following equation for calculating the superfocal distance, f × 1000 on N + f = H
where H is the suprafocal distance, f is the focal length of the lens, and N is the focal number. Accordingly, the suprafocal distance is estimated as follows, according to Arthur Cox:
Suprafocal distance = focal length of the lens + 1000 x focal length of the lens over the focal number of the lens.

This equation has been greatly simplified and has the following form, given that the value of the focal length is relatively small:
Suprafocal distance = 1000 x focal length of the lens divided by the focal number of the lens
Given that the focal length of the lens on the focal number of the lens =
Diaphragm hole diameter
... supfocal distance = 1000 x diameter of the diaphragm aperture

This equation is the one we mentioned in the book The Foundations of Photography, and it is consistent with the equations that came in this regard in many foreign references, but we see that it is not completely accurate except in one case, which is when the focal length of the lens is medium, and vice versa, we find that in introducing a magnification force The lens as a factor influencing the hyperfocal distance, which leads to very correct results in all cases, regardless of the lens and regardless of the negative area.

It became possible to put equation No. 7 in the following simplified form (1).
e = p2 over f x f
All suprafocal distance calculation tables have been developed according to either Equations No. 4 or 7.
And since Equation No. 7 (2) included all the factors that affect the suprafocal distance, so it can be applied to calculate the suprafocal distance directly.

Some references believe that equation No. 4 should be applied, but after dividing it into two parts according to the following formula:

Superfocal distance (3) = Diaphragm aperture diameter x 1000 on first part x magnification on second part

Some tables depend on only the first part of this equation, provided that the photographer multiplies this distance that he deduces from the table by the lens’s magnification power (which is equal to the actual focal length of the lens over the suitable medium focal length of the camera).
On page 201 you can see a table for calculating the supfocal area. On pages 202 and 302 there are notes about him that must be studied first before taking any data from him.