Controlling Factor

TM 9-258

b. Controlling Factor. The angular limit of

NOTE

resolution can be proved to be related inversely to the

All values in this formula are in millimeters.

diamter of the lens. According to Dawes' rule (an

Although the resolving power of the human eye

approximation): a (in minutes of arc) = 1/Do (in fifths of

normally is equal to 1 minute of arc, for long

an inch, fig 5-32); thus it is advisable to have large.

continued observation this becomes 2 or 3

objectives for sharp definition.

The observation

minutes (due to fatigue). This, for continous

telescope has such an objective of large diameter. The

observation an instrument of greater power is

targot shooter uses a telescope of 1 1/4-inch diamter

needed to provide the same definition obtainable

objective or larger. The 7 x 50 (7-power, 50-millimeter

with a lower power telescope used for short

diameter) binocular provides good resolution because of

intervals. Transparent foreign material such as

the large diameter objective and for this reason is better

grease or fingerprints on a lens will impair

in daytime than a 7 x 35.

definition (resolving power). Opaque foreign

c. Normal

Magnification.

Normal

material on the eye-lens either may impair

magnification is that power of a telescope giving an exit

definition or blot out small portions of the field.

pupil diameter just equal to that of the eye usually

5-31. Optical Glass Used in the Design of Military

standardized at 2 millimeters (Some authorities,

Instruments.

however, consider the eye to provide the best resolution

a. Common Types.

Although there are

at an aperture of 4 to 5 millimeters.) For example:

numerous types of optical glass in the design of optical

D (Objective)

systems for military instruments, five types in common

Normal magnification = ----------------

use are as follows:

C (Pupil of Eye)

Index of

Critical angle

or, normal magnification = 25.4 Do over 2 to 4,

Name

refraction

in degrees

where Do is in inches.

Boro silicate crown

1.5170

Normal magnification is one of three factors limiting the

Barium crown

1.5411

magnifying power obtainable with a given objective lens.

Baryta light flint

1.5880

The other two factors are the resolving power of the

Ordinary flint

1.6170

given lens (RP = 1/α para 5-30a) based on diffrection

Dense flint

1.6490

effects, and the quality of the lens (precision of grinding

It will be noted that as the index of refraction increases,

and polishing and absence of aberrations) measurable

the critical angle decreases.

by labratory methods (fig 5-32).

b. Specific Uses. Boro silicate crown normally

d. Other Resolving Factors. The foregoing

is used for the collective lenses and dense flint for the

equations are in agreement if the entrance pupil of the

dispersive lenses in objectives, erecting lenses, and

eye is 2 millimeters. The plus 2 to 4 results in empty

eyepieces. In the Kellner eyepiece (A, fig 4-5), boro

magnification, an increase in image size of fine details so

silicate crown is used for the field lens, barium crown for

the eye can more readily see them, but without any

the collective element, and either light flint or ordinary

increase in telescopic resolving power.

For best

flint for the dispersive element of the achromatic doublet

resolution, the power of the eye piece in the system is

eyelens. Prisms, generally, are made of boro silicate

determined by the formula:

crown. For wide-angle instruments, however, baryta light

Focal Length Eyepiece = Diameter Eye

flint is used. Reticles are usually made of baryta light

Focal Length Objective

flint because it etches best and windows usually are of

Pupil X

boro silicate crown.

Diameter of Objective

5-18