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the lens or combination of lenses in an optical instrument nearest the eye of the observer


A lens or optical system which offers to the eye the image originating from another system (the objective), at a suitable viewing distance. The image can be virtual. See Optical image

In modern instruments, most eyepieces (also called oculars) are not independently corrected for all errors. They are designed to balance out certain residual aberrations of the objective or (as in the microscope) of a group of objectives, for instance, chromatic difference of magnification. See Aberration (optics)

The Ramsden eyepiece consists of two planoconvex lenses, the field lens and the eye lens, with their plane sides out. Both of these lenses have the same power and focal length; their separation is equal to their common focal length. See Geometrical optics, Lens (optics)

The Huygens eyepiece also consists of two planoconvex lenses, but the plane sides of both lenses face the eye, The focal length of the field lens is in general three times that of the eye lens, and the separation is twice the focal length of the eye lens.

Types of eyepiecesclick for a larger image
Types of eyepieces


The magnifying system of lenses through which a telescopic image is viewed. It normally comprises a field lens, which receives the light rays, a stop, which defines the field of view, and an eyelens, which directs the light into the eye. The magnification of a telescope is normally varied by using a short focal length eyepiece to give high powers, and one of long focal length for low powers.

Some eyepieces are shown in the illustration. The Huygens eyepiece consists of two planoconvex lenses with their flat faces toward the eye and a field stop between them. The field lens has two or three times the focal length of the eyelens and their separation is half the sum of their focal lengths. Although it has good eye relief and little chromatic aberration, the large spherical aberration gives poor performance except with long-focus refractors. The Ramsden eyepiece has two identical planoconvex lenses mounted with their convex faces together and separated by 2/3 to 3/4 of their focal length. It has much less spherical aberration than the Huygens but suffers from troublesome chromatic defects. The Kellner eyepiece is a Ramsden with an achromatic eyelens. It is an excellent eyepiece, widely used in binoculars and field glasses. For best results the lenses must be coated to minimize ghost images formed by internal reflections. The orthoscopic eyepiece, in its commonest form, has a planoconvex eyelens and a cemented triplet field lens. Although it is expensive, this eyepiece gives excellent results and has a long eye relief, which suits the bespectacled user. The Plössl eyepiece has two identical achromatic doublets mounted close together with their biconvex elements facing each other. The field is wider (about 40°) and flatter than that given by orthoscopics, with sufficient eye relief for comfortable use, so that the Plössl is preferred by many observers. Several manufacturers have modified the design.

By the use of extra lens elements and specially figured (aspheric) lenses, wide-field eyepieces may be obtained; these have fields subtending up to 90° at the eye; the Erfle has a field of 68° and the Nagler and Bertele up to 80°. Such eyepieces are useful for observation work requiring exceptionally wide fields, such as novae and comet searches, but they are very expensive and will not fit a standard draw tube. See also Barlow lens.



the part of an optical system—field glass, telescope, binoculars, or microscope—that faces the eye of the observer. An eyepiece is used for visual examination of a real optical image, called the intermediate image, which is formed by an objective or other part of an optical system (for example, a combination of an objective and an optical inversion system) that precedes the eyepiece in the path of the light rays. Most eyepieces are positive—that is, they collect (focus) the beams of light rays that pass through them.

The action of an eyepiece is similar to that of a magnifier. The eyepiece is placed in such a way that the intermediate image is located immediately behind the first focal plane (virtually within the plane) of the eyepiece; under such conditions, the eyepiece produces a virtual image that is also magnified with respect to the intermediate image. The virtual image is converted by the optical system of the eye of the observer into a real image, which is projected onto the retina of the eye. A positive eyepiece is distinguished from a magnifier in that the aperture of the beam of light rays incident on it is significantly smaller than that of a magnifier; this difference is due to the use of the eyepiece in a complex optical system that includes an objective.

If a positive eyepiece is shifted relative to the intermediate image such that the intermediate image is in front of the focal plane of the eyepiece, then the eyepiece becomes a projection system that produces a real image of the object. Such an image cannot be viewed directly by the eye, but it can be reproduced on a screen or photographic emulsion. Special devices called photoeyepieces and projection eyepieces exist for this mode of operation; strictly speaking, they are not true eyepieces.

The optical properties of an eyepiece are characterized by the following quantities: (1) the focal length fʹ and the angular optical magnification Гʹ, which is determined by fʹ and is the ratio of the tangent of the angle at which the virtual image is visible in the eyepiece to the tangent of the angle at which the eye would see, without the eyepiece, the intermediate image on a screen or photographic emulsion placed at the normal viewing distance (250 mm for a normal eye); (2) the field of view 2ω in the image space, that is, the angle between the extreme outside rays leaving the eyepiece; and (3) for positive eyepieces, the distance d from the last lens of the eyepiece to the exit pupil, that is, to the objective image produced by the eyepiece. For the most comfortable location of the observer’s eye, d should be 12–15 mm or, if eyeglasses are worn, up to 25 mm. Strong eyepieces (with a small fʹ) of a special design satisfy these requirements.

The optical magnification Гʹ of an eyepiece is 250/fʹ, if fʹ is given in mm. The range of Гʹ is usually 5–20×, although in certain cases it may be as high as 40–60× or as low as 1.5–3.0 ×. The optical properties of an eyepiece also affect the general characteristics of the optical system in which the eyepiece is used. For example, the total magnification of a system for field glasses and telescopes is γ = Fʹ/fʹ, where is the focal length of the part of the system that precedes the eyepiece, and for microscopes, γ = βГʹ where β is the linear magnification of the objective. The field of view in the object space is angular (2ω) for field glasses and telescopes and linear (2l) for microscopes. It is described by the formulas tan ω = tan ωʹ/γ and 2l = tan ωʹ/β.

The first eyepiece, used by Galileo in 1609, was a simple negative (diverging) lens. (Such eyepieces are called Galilean eyepieces.) The intermediate image is located behind the eyepiece (Figure 1). The angle of view and the magnification are small, and the real intermediate image cannot be measured on a scale or photographed. Therefore, Galilean eyepieces are used infrequently, mostly in opera glasses.

Figure 1. Path of light rays in a telescope with a Galilean eyepiece. The real (intermediate) image E formed by the objective L1, is located immediately behind the focus F of the negative eyepiece L2. A beam of rays incident on L at an angle ω is observed through the eyepiece and reaches the eye of the observer at an angle ωʹ, which is greater than ω. This explains the magnifying effect of the eyepiece. () focal length of the objective, (f2) focal length of the eyepiece.

Positive eyepieces of a type still used today were constructed by C. Huygens in the mid-17th century and by the English scientist J. Ramsden in the late 18th century. Both types consist of two planoconvex lenses (Figure 2). Although their design is quite simple, for angles of view in the range of 35°–45° the correction of primary aberrations is good and the distance to the exit pupil is adequate. Their focal lengths are not less than 15–20 mm. In contrast to the Huygens eyepiece, a Ramsden eyepiece has a real first focus. As a result, the first focal plane (with the intermediate image) can be combined with a scale or crosshairs that can be used for measurement or with a photographic plate or film (if the intermediate image must be photographed). Satisfactory image quality in Huygens and Ramsden eyepieces is attained by correcting the chromatic differences of magnification, astigmatism, and coma. Correction is achieved by empirical selection of the ratio of the focal lengths of the lenses and the size of the air gap between the lenses.

Figure 2. Two-lens positive eyepieces: (a) Huygens eyepiece, (b) Ramsden eyepiece

Beginning in the late 19th century, the requirements for the field of view of telescopes became increasingly stringent, particularly for military optical devices, such as field binoculars and periscopes; wide-angle eyepieces with a field of view of 65°–70° were developed. The use of more complex designs, an increase in the number of lenses, and the use of lenses with nonspherical (for example, paraboloidal) surfaces subsequently made possible the production of eyepieces with fields of view of 100° or more (Figure 3). In addition to wide-angle eyepieces, high-power eyepieces came into use; their design is similar to that of wide-angle eyepieces, and the ratio between the distance to the exit pupil and the focal length is greater than 1.

“Compensating” eyepieces are used in combination with high-power apochromatic objectives, particularly in microscopes. These eyepieces are so designed that they correct the chromatic difference of magnification inherent in this type of objective. A commonly used type is the autocollimating eyepiece (Figure 4),

Figure 3. Modern multilens wide-angle eyepiece

in which a small prism P is located near the focal plane F. The prism directs the light rays that emanate from a weak source S to the crosshairs and from there to the objective and to a plane mirror located in front. The light is reflected from the mirror, again passes through the objective and is collected at the focal point of the eyepiece, where the crosshairs and their image are viewed simultaneously. Such eyepieces make possible a very accurate determination of the direction of the normal to the mirror, which is necessary for example, in telescope systems.

Figure 4. Autocollimating eyepiece


Tudorovskii, A. I. Teoriia opticheskikh priborov, 2nd ed., part 2. Moscow-Leningrad, 1952.
Sliusarev, G. G. Metody rascheta opticheskikh sistem, 2nd ed. Leningrad, 1969.
Optika v voennom dele: Sb. statei, 3rd ed., vol. 2. Edited by S.I. Vavilov and M. V. Savost’ianova. Moscow-Leningrad, 1948.



A lens or optical system which offers to the eye the image originating from another system (the objective) at a suitable viewing distance. Also known as ocular.
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