Theatre Design & Technology - Summer 1980 - 17

2. The spread of a spotlight is the angle that defines the
edges where the light cuts off. When the unit produces a very
soft-edged field, an arbitrary angle is selected, frequently that
angle at which the intensity falls to 10% of the central intensity. Significant angles within the total spread are those
where the intensity falls to 50% of central, sometimes referred
to as the "beam"; the angle at which 10% central intensity occurs, called "field" and the cut-off angle where zero is
reached.
The diameter of a lighted area may also be calculated from
the diameter of the gate, the focal length of the lens system,
and the distance of throw.
Diameter of Area =
Diam. of Gate
Focal Length

-:-:----,-,----,-,-- X

.
(Distance of Throw - Focal Length)

Spread is usually given in degrees. To obtain the degrees
of spread from the diameter of the area and the distance of
throw, divide half the diameter of the area lighted by the distance of throw; then find the angle whose tangent (called the
arc-tangent) is equal to that decimal fraction. This, multiplied
by 2, is the total spread.

The customary gate has a diameter of about 3" or .25 feet.
(Calculations are simplified if the same unit of measurement is
employed consistently.) The maximum gate size is established
in the design of the unit. The user can reduce it by means of
shutters, an iris, or template; but to enlarge the area lighted he
must increase the distance of throw or use shorter focal
length lenses.
3. The focal length of a single lens is a choice made when
designing or ordering but there is a limit to shortness of focal
lengths when the diameter is fixed. (Fresnel or stepped lenses
can be made with very short focal lengths but they do not
have as sharp performance when used to project an image.)
To reduce focal length with plano-convex lenses, therefore, it
is necessary to employ two lenses acting together as a lens
system. The focal length of such combinations is:
Focal length =

f, X f 2
f
d

f, and f 2 are the focal lengths of the first and second
lenses, and d is their distance apart.
The distance between them, measured between the extremes of their curved surfaces, is adequately accurate for
theatrical purposes. Note that if the curved surfaces touch,
the focal length is shortest, the product of the two focal
lengths divided by their sum. As they are moved apart, the
focal length of the system increases.
4. Zoom systems take advantage of the facts just presented
to provide an adjustable focal length system allowing a variation in the size of the lighted area. The diameter of the area:
USITT /Summer, 1980

Diam. of area =

.
f,
(Distance of throw - f 2 )
Dlam. of gate
(f, - Distance between gate and nearer lens)

Positioning the lenses for both a given sized area and
sharpness is somewhat more difficult than with a unit having a
fixed focal length. John Schwiller, an English designer writing
for Tabs in 1978, explains his method of "setting" the lenses
of a zoom system: "I have found that the best way to focus a
variable beam angle lantern is to start with the lenses always
at their extreme positions with a maximum separation between
them .... Now to select a wider beam angle if we require it,
the front lens should be moved back to give the desired angle.
This process marginally softens the edge of the beam and this
can be refocussed by moving the rear lens forward."
With widely differing focal lengths as .20 and 1.5 feet, the
range of spread is quite extensive, from about 5° to almost
30°; and this five to one range is very useful for a follow spot.
A current zoom system for an acting area spotlight has focal
lengths of .42 and .54 feet with a published range of spread
from 22 ° to 35 0 , a range of a little more than one and one-half
to one.
Although such variability has an undeniable appeal, it is
wise to examine the economic trade-offs. How often will the
instrument be called upon to serve at different distances? Is it
less costly than adding a second lens head? Might the same
result be accomplished with a unit having an adjustable field
as described in the next section? A zoom-equipped spotlight
is, nonetheless, an adjustable single unit and each user must
weigh the alternatives for his purposes to make a wise selection.
The relationships discussed allow the calculation of all of
the dimensions commonly required when using this type instrument. Note that it is always best to check the actual diameter of the gate since its size may vary from one manufacturer
to another and even between different catalog listings from
the same company.
5. The modern spotlight has a field pattern adjustment that
allows the user to vary the field distribution continuously from
a "hot" center to a very smooth field. When set for a hot center, the beam width (where V2 central intensity is reached) is
reduced, and so is the field (where '/,0 central intensity is
reached); even the limit of the lighted area may be reduced so
that the defining hard-edge disappears. When this occurs,
one of the prime reasons for the selection of the ellipsoidal
spotlight becomes invalid. If, however, the size of the gate is
reduced by an iris, templates, or shutters, a cosine distribution may be recovered along with the sharp, defining edge. In
this way the unit may serve, without any serious sacrifice in
performance, longer throws, often 50% additional throw distance.
When an area of light stands alone, the smoothest possible
field may be desired. The field pattern adjustment moved in
the direction opposite to that which produces the "hot" center will give the most uniform pattern of intensities. In both instances, longer throw and narrower beam, as well as smoothest field, efficiency is sacrificed while the usefulness of the
unit is extended. This adjustment should not interact with the
means provided to center the filament. Simplicity and ease of
setting are very important in the theatre.
When areas are to blend into each other, cosine distribution is the answer. Three theoretical distribution curves are
shown, all from the same unit; set for "peak" with the gate reduced, set for "cosine" with the gate full-open, and set for
"smoothest" field also with the gate full-open. With the gate
reduced while the lamp is set to produce peak intensity, cosine distribution is recovered.
Theatre Design & Technology

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