Power of Eyepiece

TM 9-258

c. Power of Eyepiece. Eye relief also is

illumination at any given light intensity, exit pupil of

instrument must equal entrance pupil of eye under the

inversely related to the power of the eyepiece; i.e.,

same condition.

Also, with any instrument, retinal

replacing a low-power eyepiece with one of higher power

illumination never is greater than with the unaided eye.

will reduce the eye relief.

Opaque foreign material such as dust or lint on any

5-28. Light Transmission or Ilumination.

optical surface, except one in a real image plane, will

a. Pupils.

The illumination of the image

reduce the illumination of the system.

depends on the amount of light received by the objective

5-29. Night Glasses. When subjected to intense

and the specific intensity (whether bright daylight or

illumination(brilliant daylight), the entrance pupil of the

twilight) of these light rays. The amount of light received

eye may be stopped down to 2 millimeter diameter.

is determined by the diameter of the entrance pupil (clear

When used under this illumination, an optical instrument

aperture, abbreviated as AP) of the objective. The

need have an exit pupil only 2millimeter diameter. When

amount of light entering the eye is limited either by the

the eye is subjected to very faint illumination, as at night,

exit pupil of the instrument or the pupil of the eye,

the pupil opens to a diameter of 8 millimeters. Thus, for

whichever is smaller.

use at night an optical instrument must have an exit pupil

(1) An S x 30 (8-power, 30-mm diameter)

of at least 8 millimeters provide the pupil of the eye with

glass in daytime (eye pupil diameter of 5 millimeters),

all the light it will admit. The relationship between the

since amount of light entering the instrument is

size of the exit pupil and the power of an instrument is

proportional to area of entrance aperture and thus to the

square of its diameter, picks up (30/5 ) or 36 times as

important. For example, a 7 x 50 binocular is suitable for

much light as the naked eye. The area of the retinal

nighttime use because if the clear aperture of the

image in the eye, however, is 8 or 64 times as large as

objective (50) is divided by the power of the binocular (7)

with the unaided eye. Thus, we have 36 times as much

(para 5-21), the exit pupil diameter is determined to be

light distributed over an area 64 times as great, so

7;15 millimeters. This is able to pass approximately all

illumination on the retina is only 36/64 or 56.3 percent of

the light the eye pupil can use at its widest aperture.

that with the unaided eye.

Now a 7 x 35 binocular provides ample illumination in

(2) Consider now an 8 x 40 binocular. In

daytime because its exit pupil diameter is 5 millimeters,

this case the amount of light entering the eye is (40/5 or

which is larger than the eye's 2-millimeter opening under

64 times that entering the unaided eye. There is now 64

intense illumination and ample for its 5-millimeter

times as much light falling on an area 64 times as large

opening under moderate illumination but insufficient for

(power is 8, thus the comparative area of the retinal

the 8-millimeter eye opening at night.

image is 8 ). In this case, illumination is the same as

5-30. Resolving Power of Optical Systems.

with the unaided eye.

a. Definition. The numerical measure of ability of an

(3) In an 8 x 50 glass, illumination will not increase with a

optical system to distinguish fine detail is called resolving

5-millimeter eye pupil because the iris of the eye will stop

power. It is further defined as the reciprocal of the

and the extra light from the extra 10 millimeters of

smallest angular separation (angular limit of resolution)

diameter of the objective. Since,

between two points which can be distinguished or

resolved as separate points. Resolving power = 1/α,

Entrance Pupil

Power = Exit Pupil

(para 5-21).

where α = least angular separation in radians (fig 5-32).

the exit pupil of this 8 x 50 glass is 50/8 or 6.25

As the angle becomes smaller between two points that

millimeters; therefore, the eye pupil of 5 millimeters will

can be resolved, the resolving power increases and

not admit all this light.

definition, therefore, is better.

b. Maximum Illumination.

For maximum

Figure 5-32. Angular limit of resolution.

5-17