8.6 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Eyepiece | 2/7 | https://en.wikipedia.org/wiki/Eyepiece | reference | science, encyclopedia | 2026-05-05T09:47:24.682125+00:00 | kb-cron |
f
E
{\displaystyle \ f_{\mathsf {E}}\ }
is the focal length of the eyepiece. Magnification increases, therefore, when the focal length of the eyepiece is shorter or the focal length of the objective is longer. For example, a 25 mm eyepiece in a telescope with a 1200 mm focal length would magnify objects 48 times. A 4 mm eyepiece in the same telescope would magnify 300 times. Amateur astronomers tend to refer to telescope eyepieces by their focal length in millimeters. These typically range from about 3 mm to 50 mm. Some astronomers, however, prefer to specify the resulting magnification power rather than the focal length. It is often more convenient to express magnification in observation reports, as it gives a more immediate impression of what view the observer actually saw. Due to its dependence on properties of the particular telescope in use, however, magnification power alone is meaningless for describing a telescope eyepiece. For a compound microscope the corresponding formula is
M
A
=
D
⋅
D
E
O
f
E
⋅
f
O
=
D
f
E
⋅
D
E
O
f
O
{\displaystyle \ M_{\mathsf {A}}={\frac {~~~D\ \cdot \ D_{\mathsf {EO}}\ }{\ f_{\mathsf {E}}\ \cdot \ f_{\mathsf {O}}\ }}={\frac {D}{~f_{\mathsf {E}}\ }}\cdot {\frac {~~D_{\mathsf {EO}}\ }{~f_{\mathsf {O}}\ }}\ }
where
D
{\displaystyle \ D\ }
is the distance of closest distinct vision (usually 250 mm).
D
E
O
{\displaystyle \ D_{\mathsf {EO}}\ }
is the distance between the back focal plane of the objective and the back focal plane of the eyepiece (loosely called the "tube length"), typically 160 mm for a modern instrument.
f
O
{\displaystyle \ f_{\mathsf {O}}\ }
is the objective focal length and
f
E
{\displaystyle \ f_{\mathsf {E}}\ }
is the eyepiece focal length. By convention, microscope eyepieces are usually specified by power instead of focal length. Microscope eyepiece power
P
E
{\displaystyle \ P_{\mathrm {E} }\ }
and objective power
P
O
{\displaystyle \ P_{\mathsf {O}}\ }
are defined by
P
E
=
D
f
E
,
P
O
=
D
E
O
f
O
{\displaystyle \ P_{\mathsf {E}}={\frac {D}{~f_{\mathsf {E}}\ }}\ ,\qquad P_{\mathsf {O}}={\frac {~~D_{\mathsf {EO}}\ }{~f_{\mathsf {O}}\ }}\ }
thus from the expression given earlier for the angular magnification of a compound microscope
M
A
=
P
E
×
P
O
{\displaystyle \ M_{\mathsf {A}}=P_{\mathsf {E}}\times P_{\mathsf {O}}\ }
The total angular magnification of a microscope image is then simply calculated by multiplying the eyepiece power by the objective power. For example, a 10× eyepiece with a 40× objective will magnify the image 400 times. This definition of lens power relies upon an arbitrary decision to split the angular magnification of the instrument into separate factors for the eyepiece and the objective. Historically, Abbe described microscope eyepieces differently, in terms of angular magnification of the eyepiece and 'initial magnification' of the objective. While convenient for the optical designer, this turned out to be less convenient from the viewpoint of practical microscopy and was thus subsequently abandoned. The generally accepted visual distance of closest focus
D
{\displaystyle \ D\ }
is 250 mm, and eyepiece power is normally specified assuming this value. Common eyepiece powers are 8×, 10×, 15×, and 20×. The focal length of the eyepiece (in mm) can thus be determined if required by dividing 250 mm by the eyepiece power. Modern instruments often use objectives optically corrected for an infinite tube length rather than 160 mm, and these require an auxiliary correction lens in the tube.
=== Location of focal plane === In some eyepiece types, such as Ramsden eyepieces (described in more detail below), the eyepiece behaves as a magnifier, and its focal plane is located outside of the eyepiece in front of the field lens. This plane is therefore accessible as a location for a graticule or micrometer crosswires. In the Huygenian eyepiece, the focal plane is located between the eye and field lenses, inside the eyepiece, and is hence not accessible.
=== Field of view ===
The field of view, often abbreviated FOV, describes the area of a target (measured as an angle from the location of viewing) that can be seen when looking through an eyepiece. The field of view seen through an eyepiece varies, depending on the magnification achieved when connected to a particular telescope or microscope, and also on properties of the eyepiece itself. Eyepieces are differentiated by their field stop, which is the narrowest aperture that light entering the eyepiece must pass through to reach the field lens of the eyepiece. Due to the effects of these variables, the term "field of view" nearly always refers to one of two meanings: