Eye pieces (Oculars) and their Cardinal Points

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1 Paper: Optics Lesson: Eye pieces (Oculars) and their Cardinal Points Author: Dr. D. V. Chopra College/Department: Associate Professor (Retired), Department of Physics and Electronics, Rajdhani College, University of Delhi Institute of Life Long Learning, University of Delhi Page 1

2 Objectives: After studying this chapter you should: 1. Be able to know various types of eyepieces such as Ramsden s eyepiece, Huygens eyepiece and Gauss eyepiece. 2. Be able to understand functions of eye lens and field lens 3. Be able to understand optical properties of and to study the cardinal points of Ramsden s eyepiece and Huygens eyepiece 4. Be able to know the construction and use of Gauss eyepiece in spectrometer telescope 5. Be able to work problems involving eyepieces and their cardinal points 1. Eye piece: The objective of a telescope as well as a microscope is a convex achromatic doublet which produces a real and inverted image of the object. Such an image is diminished in size in the case of a telescope and magnified in the case of a microscope. The function of an eye piece in the optical instrument is to magnify the real image formed by the objective. An eye piece is a specially designed co-axial system of two lenses, separated by a distance. It is also called compound eyepiece. (a) Constructions: An eye piece consists of two convex lenses placed co-axially with the axis of the instrument. The lens facing the objective is called field lens and the other lens placed near the eye is called eye-lens. Such a combination constitutes an eye-piece (also called an ocular). (b) Difference between an ey-piece and a magnifier: A magnifier is a convex lens or a lens system used to magnify a real object. An eye piece is used to magnify a real image (produced by an optical system) formed before it. (c) An eye piece consisting of a single converging lens suffers from the following defects: (i). In order to increase the magnification, the single lens of the eye-piece must have small focal length and it will have fairly curved surfaces. Such a magnified image suffers from defects such as chromatic aberration, spherical aberration, etc. (ii). The field of view is too small to see the outer parts of the image. Some of the rays from the image formed by the objective are not able to reach eye through the single lens of the eye-piece. This is shown in Fig.1, A B is the real image formed by the objective and E.L. is the single-lens eye-piece. Rays with the single arrow from A B are not entering the eye which is placed closed to the eye. Both these defects can be reduced by using two lenses in an eye-piece. Such a combination of two convex lenses is called an eye-piece (Fig.2). The lens nearer to the eye is called eye-lens (E.L) and the other which faces the real image formed by the instrument is called field lens(f.l): the combination of the two is so designed as to reduce the defects of images such as spherical aberration, astigmatism, distortion and chromatic aberration, this latte being by far the most important in the case of a single lens Institute of Life Long Learning, University of Delhi Page 2

3 Position of eye E.L Fig.1 A single-lens eyepiece Position of eye The image formed by the optical instrument lies infront of field lens (F.L) and all the rays from it are able to enter the eye, placed close to E.L the eye lens(e.l.). The eye lens is placed at the same position as an F.L eye piece consisting of single lens would do, but the position of the Fig. 2 A Compound Eye-piece field lens is either in front of, or behind, the image formed by the objective. But, it is required that the final image formed by the eye piece should be at infinity so that it may be seen without any strain to the eye. For this requirement, the image formed by the field lens must lie in the focal plane of the eye lens so that the rays are rendered parallel on passing through E.L. Function of eye lens (E.L.): Its purpose is mainly to magnify the image due to the field lens and to form it at infinity for normal vision. It is called eye lens because it is placed close to the eye. Functions of field lens (F.L.): (i). In the combination with the eye lens, it decreases sufficiently the focal length of the eye piece. This way, it increases the magnification of the final image seen by the eye. (ii). It increases the field of view because it bends the rays form the other parts of the image towards its axis and these rays enter the eye after passing through the eye lens. Hence, rays from outer parts of are not lost and the whole image is seen. It is called field lens because it increases the field of view. (iii). In combination with the eye lens, the eyepiece can be made wholly or appreciably free spherical and chromatic aberration. (iv). Eye can be placed at the centre of the eye lens, thereby increasing the angular image field and thus whole of the image is seen. Institute of Life Long Learning, University of Delhi Page 3

4 As stated above, as the final image through eyepiece is to be seen at infinity, the image as well as the field lens (Fig. 2) must coincide with the first focal plane of the eyelens. This is, theoretically, the best location for the field lens. This is so because in this case u = 0, and v = 0, and thus there is no change in the magnification and also, in addition, it will increase the field of view. The disadvantage of this location is that any scratches or dust particles on the surface of field lens or its other blemishes (like small air bubbles inside it, etc.) are observed magnified along with image and thus reduce the clarity of the image. In practice, the field lens is placed either a little in front of image (as in Huygens eye piece) or a little behind it (as in Ramsden s eye piece). Position of a cross wire: In order to make some measurements on the final image formed by the eyepiece, we require a cross-wire or a micro meter scale to be placed inside the eye piece. A crosswire must fulfill the following conditions: (i). It must be placed coincident and in focus with the final image. (ii). It must be magnified by both the lenses of eye piece. As the final image formed by the eye piece is at infinity, therefore it must lie in the first focal plane of the eye piece. Therefore, the image formed by an objective of any optical instrument like telescope and microscope must lie in the first focal plane of the eye piece. If the first focal plane of the eye piece lies outside the eye piece in the object space i.e. in front of the field lens, then real object (i.e. cross-wire) can occupy the position coincident with the final image formed by the objective of the instrument. Such an eye piece is called positive eye piece since this eye piece requires a real object (i.e. crosswire) to be presented to it, (i.e. since the first focal plane of the eyepiece is on the positive side of the field lens). If the first focal plane of the eyepiece lies within the two lenses of the eye-piece, than a virtual object or cross-wire can occupy the position coincident with the final image formed by the objective. Such an eye piece is called negative eye piece as the first focal plane of the eye piece is on the negative side of the field lens. Since this eye piece requires a virtual object (i.e. virtual cross-wire) to be presented to it, such an eye piece cannot be used with corss-wires as the positive eye piece can. The eye pieces which are commonly employed are as follows: (i). Ramsden s eyepiece (ii). Huygens eyepiece (iii). Gauss eyepiece These compound eyepieces have been discussed in the next sections. 2. Ramsden s eyepiece: Institute of Life Long Learning, University of Delhi Page 4

5 Construction (Fig. 3): It is consists of two thin plano convex lenses, F.L. and E.L., of some material and focal lengths, f, placed separated by a distance, as shown in Fig. 3 axis F 1 L 1 F.L f L E.L f L 2 x y z eye Position of eye They are placed coaxially with their convex surfaces facing towards each other. The lens E.L. placed close to the lens is eye lens while the lens F.L. placed Fig. 3. Ramsden s eyepiece away from the eye is fieldlens. is the image formed by the objective of the optical instrument. It coincides with the first focal plane F of the eye piece, as shown in Fig. 3. Since F 1 is on the positive side of field lens F.L., this eye piece is called positive eye piece. The F 1 or is also the position of cross wires. Only narrow beam passes through the eye piece. The various aberrations are reduced to tolerable amounts in the following way. Condition of achromatism: Chromatic aberration has to be eliminated in the sense that the size of the different coloured images the same. Condition of achromatism for two lenses of focal lengths f 1 and f 2 is given by the distances of separation, In the present case, f 1 = f 2 = f That is to say, the field lens F.L. should be placed in the focal plane of the eye lens E.L. Because eye lens is focused on the field lens and so any scratches, or defects, on its surface are seen and spoil the look of the final image. Therefore, instead of distance x = f, the distance between the two lenses of the eyepiece is kept. It causes slight departure from achromatism. chromatic aberration. Hence, Ramsden s eyepiece is not completely free from Spherical aberration is reduced by sharing the deviations as equally as possible among four refractions of the two lenses, F.L. and E.L. This helps to reduce coma as well. Spherical aberration is further reduced to minimum by taking each individual lens planoconvex (F.L. and E.L.). The radius of the circle of least confusion due to spherical aberration and astigmatism is reduced by the fact that only narrow beam from the objective is allowed to pass through the eyepiece. Curvature of the field and distortion are also small over fields of Institute of Life Long Learning, University of Delhi Page 5

6 Working : The, formed by the objective, will serve as real object to the eyepiece. For normal vision, this image should be situated at the first focal plane F 1 of the eye piece so that the final image formed by the eye piece, may lie at infinity. Actually, however, the final image at infinity is formed in two steps. In the first step, the real image formed by the objective serves as a real object to the field lens (F.L.) which forms its virtual image at which is also the first focal plane of the eye lens (E.L.). In the second step, serves as an object to the eye lens (E.L.) as is at the first focal plane of the eye lens, the image will be formed at infinity. Optical Properties of Ramsden s eyepiece: By optical properties of any optical system we mean those properties or characteristics of it on which its optical behavior depends e.g., the focal length, power, positions of cardinal points, angular field of view, aberration, etc. The various aberrations have already been described in this section. Other optical properties have been described below. Distance Focal length of the eye lens = f =L 2 Focal length F of the equivalent lens is given by Substituting f 1 = f 2 =f and x = 2f/3 Position of equivalent lens is shown by L with the Fig.3 Since field lens forms image, focal length f of field lens is given by of where u = L 1 and v= L 1 Institute of Life Long Learning, University of Delhi Page 6

7 This gives This indicates that the real image formed by the objective lies at a distance in front of the field lens: Position of cross-wires (or micrometer scale): The image of the object formed by the objective lies in front of the field lens, in the first focal plane of the eye lens, which is real, and cross-wires can, therefore, be used. For this reason it is called a positive eyepiece. Position of cross-wires coincides with at a distance in front of field lens of focal length f. This eye piece magnifies both image and cross-wires equally when seen through the eye lens. Hence accurate measurements can be taken. Cardinal Points of Ramsden s eye piece (Fig.4) Position of first principal Point (P 1 ) Distance of the first principal point P 1 from field lens L 1 is given by Eq It is Incident light F.L(f) L E.L(H) Equivalent lens where x = distance between the two lenses L 1 and L 2. axis L 1 L 2 = F 1 N 2 P 2 N 1 P 1 F 2 F = focal length of equivalent lens (from Eq. 2-2) f 2 = focal length of the eye lens L 2 = f Fig.4. Cardinal points of Ramsden s eyepiece Institute of Life Long Learning, University of Delhi Page 7

8 P 1 lies to the right of L 1, as shown in Fig.4 Position of second principal point (P 2 ): Using Eq. derived in chapter on cardinal points of a coaxial system, L 2 P 2 = = This P 2 lies to the left of L 2 ; as shown in Fig 4. The two principal planes through P 1 and P 2 are real (i.e. lie within the system), but crossed. Position of focal points (F 1 and F 2 ) Distance of the focal point, F 1 from the field lens L 1 is given by Eq. (3.9-11) Thus, F 1 lies to the left of the field lens L 1 at a distance from it f 2 = f is the focal length of eye lens. Distance of second focal point F 2 from the eye lens L 2 is (see chapter on Cardinal Points of a coaxial system) Thus, F 1 lies to the right of the eye lens L 2 at a distance from it where f 1 = is the focal length of the field lens L 2, as shown in Fig 4. Since the first focal point (and hence the first focal plane) is real here, the eye piece can be used to magnify a real object, i.e. it can be used as a simple microscope or magnifier. Position of nodal points: The medium on either side of the eye piece is same (i.e. air). Hence, nodal points N 1 and N 2 coincide with principal points P 1 and P 2 respectively. Dotted vertical lines through (F 1, F 2 ), (P 1, P 2 ) and (N 1, N 2 ) s how respective planes in Fig 4. These planes are normal to the axis of the eye piece. Position of Equivalent lens (L): Institute of Life Long Learning, University of Delhi Page 8

9 The distance of the equivalent lens (L) behind the first lens L 1 Thus the equivalent lens (L) should be placed coinciding with the first principal plane (P 1 ). From Eq(2-2), Focal length of the equivalent lens, Power of Ramsden s eye piece: where f is measured in metres. The power is positive. Since the eyepiece has the same medium on either side of it [i.e. on left of L 1 and right of L 2 ], the first and second focal lengths are both equal to each other, so that each is numerically equal to, with the first focal length negative and the second, positive. From Fig. 4, we have Angular field of view is about 30 0, but the correct field is smaller than in Huygens eye piece. When a Ramsden eyepiece is used in an astronomical telescope with an objective of focal length F 0, the magnifying power of the telescope is given by It is to be noted that the magnifying power of a Ramsden eyepiece when used as a magnifier Institute of Life Long Learning, University of Delhi Page 9

10 Importance of Ramsden s eye piece: It can examine a real object or a real image. Therefore, it can be fitted with a crosswire or a micrometer scale. It is used in optical instruments where accurate measurements are required. It is used in spectrometry to analyse each individual colour the spectrum, using white light. Although the eyepiece is not free from chromatic aberration; in spectrometry this aberration does not effect the measurements. Best position for the eye to be placed: From Fig 3, it can be easily gathered that the rays from the upper extremity of the objective pass through Z after emergence from the eye piece, those proceeding from its lower extremity pass through X and these through its centre pass through Y. Thus, XYZ is obtained as the image of the objective, as formed by the eyepiece, (shown in Fig 3) and all rays travelling ethrough the objective pass through XYZ. It is called the eye ring (or the exit pupil), with its centre Y, called the eye point. All rays which enter through the objective must emerge through the image of the objective formed by the eyepiece if they emerge at all. This image is called the eye ring or exit pupil. If the eye be kept at the eye-ring, the maximum number of rays emerging from the objective pass through the eye. In the case of normal magnification, the size of the eye-ring is the same as that of the eye-pupil, so that all rays travelling from the objective pass Cross-wire Incident light through the eye and the object appears the brightest. This is the best position of the eye, because this is the place where the rays on leaving the eyepiece come closet together. The aperture of the objective is called the entrance pupil. F 1 F.L E.L about 6mm B O Eye-ring Eye-pupil Ebonite cap Fig. Ramsden s eyepiece with cross section The position of the eye ring is usually marked by a small circular opening in the ebonite cap of the brass tube carrying the eyepiece. Such an eyepiece is shown in Fig. O is the small circular opening in the ebonite cap of the brass tube B which carries the field lens (F.L.), eye-lens (E.L.) and cross-wires, F 1, infront of field lens (F.L.). The distance between the eye-ring and the eye lens is called the eye clearance. This must be at least 6mm to allow free movement of the eye-lenses. For persons using spectacles, it should obviously be a little more. As the cross-wire are situated outside the eyepiece, infront of the field lens, the distance between the eyepiece and cross-wires can be changed and adjusted for person of different vision. Hence, persons of different vision can use the same eyepiece. Institute of Life Long Learning, University of Delhi Page 10

11 3. Huygens eyepiece: The Hygens eyepiece was introduced in order to improve the corrections for both spherical and chromatic aberration of the Ramsden s eyepiece. The astronomical telescope is fitted with a Huygens eyepiece. Construction: This eyepiece consists of two thin plano-convex lenses L 1 and L 2 of the same material but of different focal lengths. The lens L 1 is field lens (F.L.) of focal length 3f whereas the lens L 2 is eyelens (E.L) of focal length f. F.L(3f) F 1 E.L(f) eye L axis L 1 A A L 2 B f B 2f 3f Fig.6. Huygens s eyepiece These lenses are kept coaxially separated by a distance x = 2f, with their convex surfaces facing the incident rays, as shown in Fig.6. As the first focal plane F 1 of the eyepiece is on the negative side of the field lens L 1, this eyepiece is called negative eyepiece. Only narrow beam of light passes through the eyepiece. This eyepiece satisfies the conditions for both minimum spherical aberration and (lateral) achromatism. It is, therefore, known as a theoretically perfect eyepiece. Working : The image is the image formed by the objective of the optical instrument. It serves as a virtual object to the eyepiece. For normal vision, this image is to be formed at the first focal plane F 1 of the eyepiece, so that the final image formed by the eyepiece may be at infinity. Actually, the formation of final image at infinity takes place in two steps. In the first step, the converging rays from the objective, before they converge at, are further refracted by the field lens (F.L.) and a real image is formed at and not at. The focal plane of the eyelens (E.L.) coincides with. Thus, for field lens, acts as its virtual object while is its real image. In the second step, serves as an object Institute of Life Long Learning, University of Delhi Page 11

12 to the eyelens (E.L.). As is formed at infinity. lies at first focal plane of the eyelens (E.L.), the final image Let us apply the lens formula to the field lens of focal length 3f. distance The image is situated at a distance to the right of the field lens and hence a, to the left of the eyelens. Hence, it must lie in between the two lenses at a distance equal to half of its focal length from either lens. A field stop is usually placed in the position of to make the final image more sharply defined. Optical properties of Huygens eye piece: We shall describe below the focal length, power, aberration, cardinal points, angular field of view, etc. Focal length F of the equivalent lens is given by Substituting f 1 = 3f, f 2 = f, and x = 2f, we have Position of equivalent lens is shown by L. in Fig. It is situated at a distance from the first focal plane F 1. Now, distance,. It is so because the focal plane of L 2 coincides with Hence Since Institute of Life Long Learning, University of Delhi Page 12

13 For distinct vision, the image due to the objective must be formed within the first focal length LF 1 of the eyepiece (i.e. the image due to the field lens must be within the first focal length of the eyelens) so that the final image may be formed at the least distance of distinct vision. Position of cross-wires (or Position of micrometer scale): If a cross-wire or a micrometer scale is to be fitted, it should be placed coinciding with where the real image is produced after successive refractions through the objective (not shown in Fig.5) and the field lens (L 1 ). Thus, the cross-wires will be magnified by eyelens (L 2 ) only while the image is formed by both the lens L 1 and L 2 of the eyepiece. The magnification of the image and cross-wires will nto be same. Consequently, the image of the cross-wires will not be of a very much inferior quality, due to aberrations and distortions. Thus, cross-wires at cannot be used with this eyepiece to make measurements. In fact, since this eyepiece requires a virtual object to be presented to it, it cannot be used with cross-wires as the Ramsden eyepiece. It is often called a negative eyepiece to distinguish it from the Ramsden s eyepiece, which is called a positive eyepiece. Removal of aberrations: (i). Condition of achromatism: It is given by, In Huygens eyepiece, f 1 = 3f, f 2 = f This is in complete agreement with the distance of separation, L 1 L 2 = 2f, as shown in Fig.6. Hence, this eyepiece is completely free from chromatic aberration. (ii). Condition of minimum spherical aberration: The condition of minimum spherical aberration is, In the case of Huygens eyepiece, f 1 = 3f and f 2 = f, Institute of Life Long Learning, University of Delhi Page 13

14 This distance of separation is the same as L 1 L 2 = 2f, is shown in Fig. Hence, the Huygens eyepiece is free from spherical aberration. It follows from Eq(3-2) and (3-3) that spherical and chromatic aberration are simultaneously removed. (iii). It is mentioned above that the connection for chromatic aberration is as good as can be achieved, and the correction for spherical aberration and coma is better in this eyepiece than in the Ramsden s eyepiece. It is also free from astigmatism and distortion to the same extent, but it suffers from considerable curvature of the field, the curvature being convex towards the observer s eye. Cardinal Points of Huygens eyepiece: Position of principal points (P 1 and P 2 ) Distance of the first principal point P 1 from the field lens is given by (See chapter on Cardinal Points of a coaxial system) Incident Light F.L(3f) E.L. (f) L Axis L 1 P 2 F 1 N 1 P 1 N 2 L 2 F 2 f f f Fig.7.Cardinal points Huygens eyepiece 2f 3f Here x = distance of separation betwee the two lenses L 1 and L 2 = 2f F = focal length of equivalent lens = (from Eq.3-1) f 2 =focal length of the eyelens L 2 = f Institute of Life Long Learning, University of Delhi Page 14

15 Hence, P 1 lies on the right of L 1 at a distance 3f. Position of the second principal point P 2 from the second lens L 2 is given by Eq. L 2 P = = xf/f 1 where f 1 is the focal length of the first lens L 1 ; (f 1 = 3f) Hence, P 2 lies on the left of L 2 at a distance f. The principal points P 1 and P 2 have been marked in Fig. 7. The dotted (vertical) lines through P 1 and P 2 show respective principal planes. Positions of focal points (F 1 and F 2 ) Distance of the first focal point F 1 from the field lens L 1 is given by Eq.(3.9-11) Thus, F 1 lies on the right of L 1 at a distance, as shown in Fig. 7. Distance of the second focal point F 2 from the eyelens L 2 is given (See chapter on Cardinal Points of a coaxial system). Thus, F 2 lies on the right of L 2 at a distance. Positions of nodal points: Since the coaxial system of lenses L 1 and L 2 of the eyepiece has the same medium (air) on either side of it, the nodal points N 1 and N 2 coincide with the principal points P 1 and P 2 respectively. Dotted vertical lines through (F 1, F 2 ), (P 1, P 2 ) and (N 1, N 2 ) show respective planes in Fig. 7. Postitions of Equivalent Lens(L): Distance of equivalent lens L behind the field lens L 1 Institute of Life Long Learning, University of Delhi Page 15

16 Thus the equivalent lens L as shown in Fig. 7 should be placed coinciding with the first principal plane P 1. It must be placed at a distance f behind the eyelens. From Eq. 3-1, focal length of equivalent lens is Power of Huygens eyepiece is where f is measured in meters. The angular field of view is rather small about 20 0 Ramsden s eye piece. but the corrected field is greater than Discussion: (i) The first and second principal planes (P 1 and P 2 ) lie at distances 3f to the right of L 1 and f to the left of L 2 respectively (i.e. at distances f to the right and to the left of the eyelens respectively), as shown in Fig.7. The two principal planes are thus crossed, with the first principal plane, virtual (P 1 ) since it lies outside the system. (ii). The Huygens eyepiece cannot be used to see any real object. This is due to the fact that the first focal plane (and hence the first focal plane F 1 shown in Fig. 6) is virtual, lying in between the two lenses. This eyepiece cannot be used to magnify a real object but only an image. It cannot therefore, be used as a simple microscope or a magnifier. Since it can be used only to examine an image (and not a real object), it is called a negative eyepiece. Ramsden s eyepiece alone is used as a magnifier, its focal plane lies outside the eyepiece. Huygens eyepiece is often used in microscopes and in observational instruments using white light whereas Ramsden s eyepiece is used in telescopes or optical instruments with which measurements of distances and angles are to be made using cross-wires or micrometer scale. 4. Different Eyepiece used in different optical instruments: (i) Huygens Eyepiece in low power microscope: In low power microscope it is of utmost importance that the image should be completely free from the defects of chromatic and spherical aberrations. Hence Huygens eyepiece should be used in a low power microscope. (ii). Ramsden s Eyepiece in the spectrometer telescopes: In the spectrometer, measurements are to be made and hence chromatic and spherical aberrations are of secondary importance. Hence, Ramsden s eyepiece should be used in the spectrometer telescopes. (iii) Huygens eyepiece cannot be used in Fresnel s biprism experiment. A microscope scale for measurement purposes cannot be employed in Huygens eyepiece, because the image of the object is formed by both the lenses (field lens and eyelens) of the eyepiece while that of the scale is formed only by the eyelens. This leads to unequal magnifications of the image and the scale. Institute of Life Long Learning, University of Delhi Page 16

17 (iv) Huygens eyepiece cannot be used to see our palm. It is because this eyepiece cannot be used as magnifier. The first focal plane of the Huygens eyepiece falls within the eyepiece, where no real object can be placed. This eyepiece can be used only for viewing the images formed by objectives of microscope and telescope. Ramsden s eyepiece can be used for seeing the images as it can be used as a magnifier and its focal plane is situated outside the eyepiece. (v) Achromatic Ramsden s eye-piece: Silicate Flint Such an eyepiece is often used in prismatic binoculars. The lateral chromatic aberration of a Ramsden s eyepiece is slightly greater than that of Huygens eyepiece, but its longitudinal chromatic aberration is about half as great as that of Huygens eyepiece. Kellner used lenses as shown in Fig. 8. Such a combination improved the chromatic correction. field lens Eye lens Barium silicate crown Fig.8.Acrometric Ramsden eyepiece (vi) Compensating oculars: A compensating ocular is an eyepiece used to correct residual errors of the objectives of telescopes and microscopes. It is a combination of low power Huygens eyepiece and high power Ramsden s eyepiece. 5. Relative merits and demerits of Ramsden s and Huygens eyepieces: Huygens eyepiece Ramsden s eyepiece 1. It is completely free from spherical aberration 1. It is not completely free from spherical aberration. 2. It is compleely free from lateral chromatic aberration for all colours 2. It is not completely free from chromatic aberration. 3. It can be used with white light 3. It can be made achromatic for only two chosen colours. It cannot be used with white light. 4. The correction for coma is better 4. The correction for coma is less 5. It is free from astigmatism to the same extent 5. It is free from astigmatism to the same extent 6. Curvature of the field and distortion are not small. It suffers from considerable curvature of the field, the curvature being convex towards the observer s eye. 6. Curvature of the field and distortion are small over fields of Final image is almost flat. 7. It cannot be used with cross-wires since it 7. It can be used with cross-wires Institute of Life Long Learning, University of Delhi Page 17

18 requires a virtual object to be presented to it. It is often called a negative eyepiece. It is, therefore suitable for only visual or qualitative purposes. It is used with microscopes and telescopes working with white light. It is not suitable when measurements are required. It is used in microscopes required for biological work (no measurements) 8. It cannot be used as a magnifier or a simple microscope. This is so because the first focal plane is virtual and lies in between the two lenses. 9. The two principal planes are crossed but the first principal plane is virtual 10. The distance between the eye-ring and eye-lens is too small for comfortable use of the instrument to which the eye-piece is fitted. 11. There is considerable amount of longitudinal chromatic aberration since it requires a real object to be presented to it. It is called positive eyepiece. It is, therefore, suitable for quantitative measurements. It can be used with microscopes, telescopes and spectrometers working with monochromatic light. 8. It can be used as a magnifier or a simple microscope. This is so because the first focal plane is real and lies to the left of the field lens. 9. The two principal planes are crossed and real. 10. The distance between the eye-ring and eye-lens is greater; this makes it more comfortable for the eye to use. 11. It has comparatively less longitudinal Chromatic aberration Value Addition Christian Huygens ( ) Christian Huygens was born of a well-to-do and influenced family at the Hague in Holland. He published a book on optics entitled Traite dala Lumiere in He brought about great improvements in telescopes and microscopes by removing defects in images formed by lenses. According to him, the motion of light is in transverse waves. He thoroughly studied the phenomenon of reflection, refraction and rectilinear propagation of light and came to the conclusion that light consists of wave motion travelling in all pervading but hypothetical medium, called ether. However, Hooke believed that light travels in longitudinal waves but Newton discarded this view. It took more than a century for Young ( ) and Fresnel ( ) to show the wave nature of light. We now know that the phenomenon of interference, diffraction and polarization of light can be admirably explained on Huygens wave theory of light. 6. Gauss Eyepiece: It is often used in spectrometer telescopes. It is useful in focusing the collimator and telescope of spectrometer for infinity by Schuster s method. It is also helpful in adjusting the axis of telescope perpendicular to the axis of the instrument. C S Q 45 0 L 2 L 1 G It is just a Ramsden s eyepiece with a side opening between the two lenses of F.L. T E.L Institute of Life Long Learning, University of Delhi Page 18 Fig.9. Gauss Eyepiece

19 the eyepiece and is used in spectrometric measurements. It is shown in Fig.9. It consists of two lenses L 1 and L 2, each having equal focal length f and separated by a distance. However, the separation between the two lenses should have been in order to satisfy the condition of minimum chromatic aberration. For this separation, d = f, the field lens will be situated at the first focal plane of the eyelens. The objective lens forms the image of this focal plane. When seen through the eyelens, any scratch or defect of the lens (F.L.) surface is also magnified along with the final image. This difficulty is overcome by taking distance of separation instead of f. This will create small chromatic aberration. Such an aberration is further minimized by choosing achromatic doublets. A thin plate G of unsilvered glass is placed between the two lenses F.L. and E.L. inclined at an angle of 45 0 to the axis of the lenses which are placed in a tube T. The tube T has a small side opening to admit light form the source S of light. Light is reflected along the axis of the tube by G. Cross-wires (if used) are fixed at C. Sometimes this Gauss eyepiece is fitted in telescope of a spectrometer. For spectrometer fitted with a Gauss eye piece the following adjustment is made: Light from a source of light (e.g. a candle or a torch) is placed opposite the opening Q. Light is reflected along the axis of the telescope by glass plate G. These rays illuminate the cross-wires and proceed further till they emerge out of the objective of the telescope. If these rays are reflected back into the telescope by a plane reflecting surface, we shall see two images of cross wires, namely, one a reflected image and second a direct image when viewed into the eyepiece. The two images so obtained are used to focus the telescope for infinity. 7 Solved Examples: Example 1: 1. An eyepiece is made of two thin lenses, each of 20 mm focal length, separated by a distance of 16 mm. Find: (a). the equivalent focal length of the eyepiece (b). the distance of the focal plane form the nearer lens, and (c). the angular magnification provided,. Solution: (a). (b). This image is formed by first lens. distance of separation is 16mm. It is formed 4mm beyond second lens because Institute of Life Long Learning, University of Delhi Page 19

20 (c). Angular magnification or magnifying power of an eyepiece is Example 2: (a) Two thin plano-convex lenses of same material in an Huygens eyepiece are 10 cm apart. Find the focal lengths of the lenses and the equivalent focal length of the eyepiece. (b) Calculate these quantities for a Ramsden s eyepiece. Solution: (a) Huygens eyepiece consists of two planconvex lenses, namely, a field lens of focal length 3f and an eyelens of focal length f, and they are separated by a distance x = 2f. Its equivalent focal length is F. Because x = 10 cm Focal length of field lens = 3f = 3 x 5 = 15 cm Focal length of eyelens = f = 5 cm Equivalent focal length, (b). For Ramsden s eyepiece, Institute of Life Long Learning, University of Delhi Page 20

21 Example 3: An Huygens eyepiece has an eye-lens of 4 cm focal length. Sunlight is falling over the eyepiece. Find the position of the image in this condition and the distance of second principal point from the eye lens. Solution: Given In Huygens eyepiece, Equivalent focal length, Given object is sun which is situated at infinite distance. Its image is formed at the second focal point F 2 of the eyepiece. Distance of second focal point F 2 from the eyelens L 2 is Assuming light travelling from left to right, the image is formed on the right of eyelens at a distance 2 cm. Distance of the second principal point P 2 from the eyelens L 2 is Negative sign shows that point P 2 is on the left of L 2 at a distance 4 cm. Example 4: The focal length of each lens of a Ramsden s eyepiece is 4 cm. If light from the sun is falling upon this eyepiece, locate the positions of the image thus formed and also find the point from which the distance of the image is to be measured. Solution: Equivalent focal length, Institute of Life Long Learning, University of Delhi Page 21

22 Sun is at infinity. Rays coming from sun are parallel. Image will be formed by the eyepiece at second focal point F 2. Hence image is formed at a distance F 2 = 3 cm from the second principal point P 2. Distance of second principal point P 2 from the second lens (eyelens) L 2 is Second principal point P 2 lies at a distance 2 cm to the left of eye piece. Distance of the image from eyelens which is the distance of second focal point F 2 from the eyelens is Image is formed at a distance of 1 cm to the right of eyelens. Example 5: Find lengths of the lenses of Huygens eyepiece are 4 cm and 12 cm. Find the position of cardinal points and plot them in a diagram. If an object is situated 6 cm infront of the field lens, find the position of the image formed by the eyepiece. Solution : In a Huygens eyepiece if focal length of field lens (L 1 ) is f 1, then the focal length of eyelens (L 2 ) is f 2 such that Distance between them is Focal length of the Huygens eyepiece is Positions of Principal points (P 1 and P 2 ) Distance Institute of Life Long Learning, University of Delhi Page 22

23 P 1 is on the right of P Distance P 2 is on the left of L 2 System being in air, P 1 and P 2 are also nodal points N 1 and N 2 Position of Focal Points (F 1 and F 2 ) Distance Distance F 1 is on the right of L 1 F 2 is on the right of L 2 Cardinal points (P 1, P 2 ), (F 1, F 2 ), (N 1, N 2 ) have been shown in Fig. 10 Given object O lies at 6 cm in front of lens L. L 1 L 2 Let U and V be the distances of object O and image I from the first and second principal points P 1 and P 2 respectively. O 6cm N 2 N 1 P 2 F 1 F 2 P 1 8cm 5cm I 6cm 4cm 12cm 2cm 9cm L 1 O=6cm Fig.10 Hence, Thus, the image I is 5 cm behind the eye lens Example 6: Institute of Life Long Learning, University of Delhi Page 23

24 From the condition of no chromatic aberration and minimum spherical aberration of a combination of two separated thin plano-convex lenses, design a combination of equivalent focal length 6 cm. State the name of this eyepieces. Deduce the position of cardinal points of this eyepiece and show the path of a pencil of rays through this eye piece seen by an eye in relaxed accommodation. Solution : Let f 1 and f 2 be the focal lengths of field lens and eye lens respectively and x be the distance of their separation. For no chromatic aberration For minimum spherical aberration Focal length of equivalent lens is Given F = 6 cm Since, the given eyepiece is Huygens eyepiece. Cardinal Points: Principal Points (P 1, P 2 ) P 1 lies at 12 cm to the right of field lens L 1 P 2 lies at 4 cm to the left of eye-lens. Focal Points (F 1, F 2 ) Institute of Life Long Learning, University of Delhi Page 24

25 Distance of F 1 from L 1 is F 1 lies at 6 cm to the right of field lens Distance of second focal point F 2 from eyelens L 2 is L 1 in Fig. 11(b) L 2 N 2 N 1 P 2 F 1 F 2 P1 6cm 2cm 4cm 12cm 8cm Fig.11(a) Second focal point F 2 lies at a distance of 2 cm to the right of eye lens L 2. Nodal Points (N 1, N 2 ) Medium on either side of the combination being same, nodal points N 1, N 2 coincide with the principal points P 1, P 2 respectively. The six cardinal points (P 1, P 2 ), (F 1, F 2 ) and (N 1, N 2 ) are shown in Figs. 11(a). Path L 1 L 2 rays is shown eye Position of equivalent lens Fig.11(b) Example 7: A Ramsden compound eyepiece consists of two thin convex lenses of the same focal length f spaced apart a distance x, where. Prove that, for relaxed eye viewing, the object viewed (formed by the telescope or microscope objective) should be first lens. from the Institute of Life Long Learning, University of Delhi Page 25

26 Solution: Our eye is most relaxed when it is observing objects that are a long distance from the eye. Thus, for relaxed eye viewing, the image in the second lens L 2 (or eyelens) must be formed an infinite distance away from the second lens, L 2. For L 2, let the object be situated at a distance u 2 form L 2. Using thin lens formula, we get u 1 x This object lies to the left of the first lens L 1. In fact this is the image formed by first lens L 1 and this acts an object for lens L 2. Thus, the image formed by the first lens will then be virtual and at a distance v 1 given by A B v 1 L 1 Fig.12 Example 7 L 2 eye This is shown by B which is the image of object A. Distance of object A from L 1 is u 1 This distance is from the first lens L 1. Using lens equation, we get Since Example 8: Two converging lenses of focal lengths 4 cm and 5 cm respectively are placed 20 cm apart and used with the 4 cm lens as the objective and the 5 cm lens as the eyepiece of a microscope. Where must the object be placed, so that the final image may be 25 cm from the eye and virtual? Institute of Life Long Learning, University of Delhi Page 26

27 5.35cm 4cm 5cm Solution: We proceed to solve from the position of the final image which is at 25 cm from the eye. v = 25 cm, focal length of eyepiece (L 2 ), f 2 = 5 cm. L 1 L 2 Fig.13 20cm Using thin lens formula, For the objective (L 1 ) which gives where The negative sign shows that the object be placed before lens L, (which is objective). Summary An eye-piece is a spherically designed coaxial system of two lenses, separated by a distance. The lens facing the objective is called field lens and the other lens placed near the eye is called eye-lens. The combination of the two lenses is so designed as to reduce the defect of images such as spherical aberration, astigmatism, distortion and chromatic aberration. Function of eye-lens is mainly to magnify the image due to the field lens and to form it at infinity (for normal vision). Function of field lens is to increase the field of view and to increase the magnification of the final image seen by the eye. Institute of Life Long Learning, University of Delhi Page 27

28 In order to make some measurements on the final image formed by the eyepiece, we require a cross-wire or a micrometer scale to be placed coincident with the position of final image inside the eyepiece. Thus, as the final image formed by the eyepiece is at infinity, therefore it must lie in the first focal plane of the eyepiece. The eye-piece is called positive eye-piece when the first focal plane of the eyepiece lies outside the eyepiece in the object space (i.e. in front of the field lens). This eyepiece is called Ramsden s eyepiece. If the first focal plane of the eyepiece lies within the two lenses of the eyepiece, the final image will be formed on the negative side of the field lens. Such an eyepiece is called negative eyepiece or Huygens eyepiece. Such an eyepiece cannot be used with cross-wire as the positive eyepiece. Huygens eyepiece is used in low power microscope whereas Ram den s eyepiece is used in the spectrometer telescopes. Gauss eyepiece is just a Ram den s eyepiece with a side opening between the two lenses of the eyepiece and it is used in spectrometer telescopes. It is useful in focusing the collimator and telescope of spectrometer for infinity. Exercise 1. What do you understand by an eyepiece? What is its function in an optical instrument like telescope and microscope. Describe its construction. 2. State difference between an eyepiece and a magnifier. 3. Why does an eyepiece consists of two lenses instead of only one? What type of eyepiece is used in an optical instrument? What is meant by an achromatic combination of lenses? 4. Explain the importance of plano convex lenses used in eye piece. Explain the difference between the construction and working of Ramsden s eyepiece and Huygen s eyepiece? Why are cross-wires not fitted in Huygens eyepiece? 5. With neat diagrams discuss the theory and construction of Huygens eyepiece and Ramsden s eyepiece and trace the course of rays through them. Discuss their relative merits. 6. (a). State the function of an eyelens and field lens in an eyepiece. (b). State the position of cross-wires in an eyepiece. Explain its function. 7. A Ramsden s eyepiece is to have an effective focal length of 3 cm. Calculate the focal lengths of the lens components and their distance of separation. [Ans: 4 cm; 2.67 cm] 8. What are advantages of an eyepiece over a single lens of equivalent focal length? Describe the construction, theory and working of Huygens eyepiece and show that it satisfies the conditions of minimum spherical and chromatic aberration. 9. Can Huygens eyepiece be used to see our palm? State with reason. [Ans: No. The first focal plane of the Huygens eyepiece falls within the eyepiece, where no real object can be placed. This eyepiece may be used only for viewing the images formed by objectives of microscope and telescope. Ramsden s eyepiece alone can be used as amagnifier, its first focal plane lies outside the eyepiece. 10. Describe the construction, theory and uses of a Ramsden s eyepiece. Institute of Life Long Learning, University of Delhi Page 28

29 11. Deduce the positions of the cardinal points of a Ramsden s eyepiece and indicate them on a diagram. Find the position of cross-wire also. 12. Obtain and mark the position of cardinal points of a Huygens eyepiece. Find the position of cross-wires also. 13. Distinguish between positive and negative eyepiece. With the help of a neat diagram show that Huygens eyepiece is free from both spherical as well as chromatic aberration. 14. A Ramsden s eyepiece has equivalent focal length of 4.2 cm. Deduce its composition. [Ans: Plano-convex lens each of focal length 6 cm and their distance of separation 3.8 cm apart] 15. The lenses in a Huygens eyepiece have focal length of 2 cm and 4 cm. Find the distance between the lenses and locate the cardinal points. [Ans: 3 cm; Cardinal Points L 1 P 1 = L 1 N 1 = 2 cm; L 2 P 2 = L 2 N 2 = 4 cm; L 1 F 1 = 0.67 cm; L 2 F 2 = 1.33 cm] 16. What type of eyepiece would you recommend for (i) Spectrometer telescope (ii) Low power microscope (iii) Fresnel s biprism experiment 17. Discuss optical properties of Ramsden s eyepiece and Huygens eyepiece. 18. Distingush between a magnifier and an eyepiece. [Ans: If a converging lens, or a lens system, be used to magnify a real object, it is called a magnifier. If a converging lens, or a lens sysem is used to magnify a real image (produced by some other optical system before it) it is referred to as an eyepiece or an ocular.] 19. Why is Huygens eyepiece spoken of as a theoretically perfect eyepiece? [Ans: It is called so because it satisfies the condition for both minimum spherical aberration and (transverse) achromatism] 20. What is a compound eyepiece? What is its advantage over a single lens? Derive an expression for the equivalent focal length of a compound eyepiece. In relation to this expression discuss the eyepieces of Huygens and Ramsden explaining clearly the distinction between them. Also explain why Huygens eyepiece cannot be used for focusing on cross-wires and micrometer scales. 21. The equivalent focal length of an Huygens eyepiece is 0 cm. Calculate the focal length of the field lens. Locate on a diagram the position of focal points of eyepiece. [Ans: 10 cm] Objective Questions: 1. Newton s corpuscular theory of light could not explain the phenomenon: (a) reflection Institute of Life Long Learning, University of Delhi Page 29

30 (b) refraction (c) diffraction (d) rectilinear propagation Ans.: 1 (c). The theory could not explain the phenomenon of diffraction which proves that light is a wave motion. 2. Rectilinear propagation of light is only approximately true because (a) light consists of quanta (or photons) (b) light has very large velocity (c) light has very small wavelength (d) light exhibits the phenomenon of diffraction Ans.: 2 (c). Diffraction of light is bending of light round the corners of the edges of objects. Diffraction is possible when size of edge is comparable to the wavelength of light used. Due to diffraction sharp image of any object is not observed because some light inters the geometrical image (shadow) of the object. Diffraction is almost negligible if the size of the edges is very large as compared its wavelength of light. Hence light because of its very small wavelength travels approximately in straight lines. Fill in the blanks: 3. Monochromatic light of wavelength 6000 Å in vacuum enters a medium of regractive index 1.5. Its wavelength in the medium is and frequency is. Ans.: 4000 Å; Hz Solution: 4. The speed of light in water is than in glass, but than that in vacuum. Ans.: more; less. Speed of light is maximum in vacuum but lies in denser medium and greater in rarer medium. True/False 5. The speed of light in vacuum depends upon wavelength, frequency and speed of source. Ans.: False. Institute of Life Long Learning, University of Delhi Page 30

31 The speed of light in vacuum is independent of wavelength, frequency and speed of source; it remains constant in cacuum. 6. Match the theory of light mentioned in column I with the phenomenon mentioned in column II Column I Column II A Newton s corpuscular theory of light p Origin of spectra B Huygens s wave theory of light q Photoelectric effect C Maxwell s electromagnetic wave theory of light r Rectilinear propagation of light D Quantum of radiation s Laws of reflection and refraction t Polarisat Ans.: A s B r, s, t C r, s, t D p, q Question 7, 8, 9 are based on the paragraph given below. The figure shows a surface XY separating two transparent media, medium I and medium II. The lines ab and cd represent wavefronts of a light wave travelling of a light wave travelling in medium I and incident on XY. The lines ef and gh Medium represent wavefronts of the light wave in medium II after refraction 7. Light travels as a (a) parallel beam in each medium (b) convergent beam in each medium (c) divergent beam in each medium (d) divergent beam in one medium and converging beam in the other medium Ans (a) Light ray is defined as a line perpendicular to wavefront. Since wavefronts in each medium are parallel to each other, light ray travel as a parallel beam in medium. 8. The phases of the light wave at c, d, e and f and, and respectively. It is given that (a) a c X b d Medium e g f h Y Institute of Life Long Learning, University of Delhi Page 31