American Cinematographer - December 1980 - 20

TALKING TECHNICALLY
Continued from

lens in front of

Page 1206

number.

Having got the hyperfocal distance, then you can work out
depth of field with the following simplified formulae:

the
1).

Nearest distance =
acceptable focus

Hyperfocal distance x disjance focussed

Farthest distance

Hyperfocal distance + distance focussed

in

2).

in

Hyperfocal distance + distance focussed

=

acceptable focus

Hyperfocal distance

distance focussed

-

Taking an instance with the same 100mm lens at
cussed on 20 ft., the near distance is:
Example Display
Key Sequence
Enter
Touch

hyperfocal distance
+

115

115

+

115

20

Enter distance focussed
'Touch

-t-

Touch

=

Touch

x

Enter

Touch

(to find reciprocal)

0.0074074
0.0074074
115
0.851851

20
=

-

20
17.03702

Answer 17 ft.

Enter
Touch

Example

hyperfocal distance

115

-

-

20

'Touch
-s- (to find reciprocal)
Touch
=
Touch x
Enter hyperfocal distance
Touch x
Enter distance focussed
Touch
=

Display
115

115

Enter distance focussed

reference viz:

20
95

-5=

0.0105263

X

0.0105263

115

115
1.2105245

X

20

H

pupil is in front of the focal plane

Nearest distance

(Hyperfocal distance + a) x focussed distance

in

(Hyperfocal distance
=

acceptable focus

-

a) + focussed distance

(Hyperfocal distance + a) x focussed distance
(Hyperfocal distance

-

a)

-

focussed distance

and where the front entrance

pupil of the lens falls behind the focal plane the
following formulae must be used:
Nearest distance
in

Farthest distance
in

=

acceptable focus

acceptable focus

(Hyperfocal distance

-

a) x focussed distance

(Hyperfocal distance + a) + focussed distance
=

(Hyperfocal distance

-

a) x focussed distance

(Hyperfocal distance + a)

-

focussed distance

10

a =

-

0.8

Enter H Touch
+

=

stop

9.2 ft, H + a = 10 + 0.8

then calculate

can

Nearest distance in
Key Sequence

as

Example

Farthest distance in

Touch

9.2

X

10.8
X

=

0.0704225

0.0704225
10.8
0.760563
5

3.802815

acceptable focus = 3 ft. 9-5/8 in.
acceptable focus:
Example

(worked out in advance)

-

10.8
-

Enter focussed distance
'Touch
+
Touch =
Touch x
Enter H - a (worked out in
Touch x
Enter focussed distance
Touch =

5
14.2

5

Key Sequence
a

+

=

-

Nearest distance in

9.2

-7-

advance)

Display

9.2
5

'Touch
-sTouch = (to find reciprocal)
Touch x
Enter H + a (worked out in
Touch x
Enter focussed distance
Touch

Enter H +

10.8 ft.

acceptable focus:

(worked out in advance)

a

=

follows:

Enter focussed distance

5
-r
=

X

advance)

9.2
X

5
=

Display
10.8
10.8
5
5.8

0.1724137
0.1724137
9.2

1.586202
5

7.93103

acceptable focus = 7 ft. 11 Vs in.
4 ft. 11/2 in.
Which, of course, is significantly different from the 3 ft. 4 in. to
10 ft. and at a depth of field of 6 ft., 8 in. If the variation between
the front entrance pupil and focal plane was not taken into
Depth of field

pupil of the

=

consideration.

■

*Not all calculators find a reciprocal by pressing the
key fol¬
lowed by the =. Some have a 1/x key, others have no means, in
which case the result of the below the line calculation must be put
in the memory until the calculations above the line are done and
then divide the result by the number in the memory. (When using a

memory the memory dear key must sometimes be pressed twice
to make sure it is clear of a previous calculation).

**With

Where a' is the distance of the front entrance
1222

x

Farthest distance in

where the front entrance

Farthest distance

(in.)

viz:

-

We

acceptable focus

0.000129

Working this out, we find that for all practical purposes the
hyperfocal distance at 25mm is 10 ft. and at 250mm is 1000 ft.
Working out the depth of field by the simple formula, we
would have found the 25mm to be in acceptable focus from 3 ft.
4 in. to 10 ft., a depth of field of 6 ft. 8 in., and the 250mm to be
from 4.975 ft. to 5.025 ft., a depth of field of 1/2 inch.
From this we can also deduce that there is so little depth of
field at the 250mm end that for most applications it is pointless
to work it out. The 25mm one is worth having right, however,
and to do this we need to use the expanded formula.
Looking at the graph we see the value for 'a' at 25mm focal
length is + 0.8 ft. and before we make our calculations it is
advantageous to add and subtract 'a' values to and from the
hyperfocal distances (H) and note them down for future refer¬
ence,

20

Depth of field = 7 ft. 2Vz in.
(Note: if the distance focussed is greater than the hyperfocal
distance, the far distance is infinity and does not have to be
calculated.)
These formulae, whilst reasonably accurate for all normal
lenses, particularly when the point of focus is twenty times the
lens focal length or more, are not accurate for the wide angle
end of zoom lenses at close focussing distances. For lenses
which are physically long, an expanded equation, which takes
into consideration the position of the entrance pupil relative to
the focal plane, must be used.
The reason for this is that depth of field is calculated from the
entrance pupil of a lens and we cameramen measure our focus
from the focal plane. At far distances this discrepancy is negli¬
gible and does not present a problem, but for close focussing,
especially for zoom lenses (where the front entrance pupil may
well be 11 inches in front of the focal plane at the wide angle
end and 5 inches behind the focal plane at the long end) the
differences can be quite significant.
A formula for Depth of Field which is accurate in practice for
close distances measured from the focal plane is:

in

x

24.21049

=

Answer 24 ft. 2Vi inches.

=

f2(mm)

=

20

X

Enter distance focussed

seen

circle of confusion

=

Touch

be

can

H

135

X

x

f/8 fo¬

-5-

115

hyperfocal distance

The far distance is:
Key Sequence

(+) or behind (-) the focal plane.
from the accompanying graph, the front
entrance pupil of a 25-250mm Cooke Cine Varotal zoom lens
(when set at infinity) is 9.65 in. (245mm) in front of the focal
plane at the 25mm end and 5.3 in. (135mm) behind the focal
plane at the 250mm end. (At close focussing distances at the
long focal lengths it is even further behind.)
To take examples when focussing at 5 ft. distance with focal
lengths of 25 and 250mm, and a circle of confusion of 1/1000
or 0.001 in. (0.025mm) at T/8 we must proceed as follows:
First we need to know the hyperfocal distances of these two
focal lengths at that aperture and note them down for future
As

calculators it may be necessary to enter the lens focal
second time in order to square it.

some

length

a

AMERICAN

CINEMATOGRAPHER, DECEMBER, 1980
American Cinematographer - December 1980

Table of Contents for the Digital Edition of American Cinematographer - December 1980
