General Physics Experiment 5 Optical Instruments: Simple Magnifier, Microscope, and Newtonian Telescope Objective: < To observe the magnifying properties of the simple magnifier, the microscope and the Newtonian telescope. Equipment: < Optical bench with 4 carriages < Converging lens with focal lengtf about 6 cm (small lens with green dots) < Converging achromatic lens with focal lengtf about 13 cm (small achromat) < Converging achromatic lens with focal lengtf about 60 cm (large achromat) < Converging mirror with focal lengtf about 60 cm < Light bulb source < Telescope eye pieces, diagonal with eye piece mount < Meter stick < Screen and stand, prism screen < Projection screen < Object holders < Transparent rulers Physical Principles Simple Magnifier The closest distance of an object to the human eye at which there is a sharp image is called the near point distance N. An object of size h at the near point makes an angle of 2 o to the eye so that equation (1) is satisfied (see figure 1). h Near point N = 25 cm tan2 o h (1) N Figure 1 The near point distance of the human eye. If a short focal length converging lens is held up against the eye, a sharp image can be seen at a distance q from the lens when the object distance p is slightly less than the focal length. The object - image distance relation gives 1 o Eye Experiment 5 Page 19
1 p % 1 q 1 f Y 1 p 1 f % 1 &q (2) where q is negative because the image is virtual and -q is then positive. See figure 2. The angle that the image makes at the eye satisfies the following relationship, assuming that the distance from the eye to the lens is negligible. tan2 i h) q h p (3) For small angles, less than 10E, tan2 2 in radians. The magnification of this simple magnifier can be derived as follows Virtual image h' q Object h p Magnifier Figure 2 Image produced by a small converging lens. Eye 2 i 2 o h/p N/h N p N f % N q (4) M lin q p q N @ N p q N @ (5) Equation (4) is the angular magnification and equation (5) is called the linear magnification. When the image is at the near point (q = N), equation (4) becomes and the linear and angular magnifications are equal (see equation 5). N f %1 (6) Microscope A microscope consists of two short focal length lenses separated by a fixed distance, the tube length L, with the object placed just beyond the secondary focal point of the objective (see figure 3). Thus, the objective lens forms a real image at a distance from it that is large compared to its focal length. The lengtf the tube L is in such a way that the image formed by the objective is at the focal point of the eye piece. The linear magnification of the objective can be written as Experiment 5 Page 20 Object Objective lens q p Real image Eye piece Eye Figure 3 Optical structure of a microscope.
M o h) o &q o (7) The total magnification of the microscope is given by M h) e h ) e h ) o h ) o M e M o (8) where the subscripts o and e refer to the objective and eyepiece, respectively. Taking the distance between the two lenses to be L, the magnification M o and M e can be approximated as M o. L& f e f o M e. N f e (9) Knowing this, the magnification of the microscope is found to be M.& (L& f e ) N f o f e (10) Refracting Telescope A refracting telescope consists of a long focal length converging lens called the objective and a short focal length lens called the eye piece. For converging eye pieces and distant objects the distance between the objective and the eye piece is the sum of the focal lengths. Real object q o Objective h' q o p h' o Eye piece The angular magnification of the telescope is given by. 2 i 2 o (11) where 2 o is the angle of the object viewed directly and 2 i is the angle of the virtual image made by the eyepiece. For distant objects and small angles, 2 i h ) e h e and 2 &q e h ) o (12) e q o virtual image Figure 4 Optical structure of a refracting telescope. q Experiment 5 Page 21
Since p e = f e, q o = f o, and h e = N, these results give the formula for angular magnification 2 i 2 o f o f e (13) Virtual image h' Newtonian Reflecting Telescope Real object 50 cm q Objective A Newtonian reflecting telescope consists of a long focal length mirror called the objective, a flat diagonal mirror and a short focal length converging lens called the eye piece. The eye piece is placed so that the sum of the distances of the eye piece to diagonal mirror and diagonal mirror to objective is the sum of the focal lengths f o + f e. The magnification is defined in the same way as it is for the refracting telescope. Eye piece Real image Reflecting telescope Figure 5 Optical structure of a Newtonian reflecting telescope. Procedure: Measuring Focal Lengths Measure the focal lengtf the 3 lenses by focusing an image of an object at a distance of about 100 times the focal length. The focal length is the distance from the center of the lens and the image. Place the prism screen on the optical bench at the 0 cm position. Place a lens in a lens holder and mount the holder in the carriage. Move the carriage until a sharp image is visible. The scale reading on the bench by the carriage fiducial mark will be the focal length. For the mirror replace the prism screen with the projection screen, place the mirror in a carriage at 0 cm and the projection screen at about the 60 cm mark with the white side toward the mirror. Sight through a window on a distant object and move the carriage until the image is clearly focused. The scale reading at the screen is the focal lengtf the mirror. Record the four focal lengths. Simple Magnifier Mount the 6 cm focal length lens on the optical bench in a carriage at the 0 cm mark and mount a transparent ruler horizontally at right angles to the optical bench at a distance from the lens of slightly less than the focal length (at about 5 cm on the bench scale) as illustrated in figure 2. This is the object to be observed with this lens as a simple magnifier. Mount a second ruler parallel to the first and at a distance from the lens equal to your near point, N. 25 cm. Adjust the heights so that the tof rulers and the Experiment 5 Page 22
center of the lens are about 24 cm above the bottom of the bench track. Witne eye closed slide the lens carriage to focus while looking with the other eye through the magnifier so that the image appears sharp and superposed on the second ruler which is viewed with the same eye looking over the tof the lens. Record the left and right positions (x l and x r ) on the second ruler of a.5 cm portion of the first ruler. (The object size h =.5 cm). Calculate the magnification and compare this result with the value calculated from equation (6). Microscope Mount the small achromatic lens (eyepiece) in a lens holder and place it in a carriage at the 0 cm mark. Mount the 6 cm focal length lens (lens with the green dots, objective lens) in a lens holder and place it in a carriage at the 40 cm mark. Mount a transparent ruler horizontally at right angles to the optical bench and position it near the focal lengtf the objective at about the 46.5 cm mark on the optical bench. A 2 mm section of this ruler will be the object viewed through the microscope. Tape a second transparent ruler on a glass plate with the tof the ruler flush with the tof the plate. Secure the glass plate in the second holder. This ruler will be used to measure the size of the image. Position the second ruler parallel to the first and at the 25 cm mark on the optical bench. Adjust the heights so that the tof the object ruler and the centers of the lenses are about 24 cm above the bottom of the bench track and the tof the second ruler (on the glass plate) is 28 cm above the bottom of the bench track. Witne eye closed view the object ruler through the microscope while also viewing the gauging ruler. The eye should be about 10 cm in front of the eyepiece. Record the positions on the gauging ruler of the rulings marking a 2 mm section of the object ruler. Calculate the magnification. Calculate M o and M e from equation (9) and compare their product with the observed magnification of the microscope. Refracting Telescope Mount the 60 cm focal length achromatic lens (objective) on the optical bench at a position of about 73 cm. Mount the 13 cm focal length achromatic lens (eye piece) on the optical bench at the 0 cm position (with a separation of f o + f e ). Place a meter stick vertically on a wall at a distance of about 6 m. Consider the object to be a 10 cm segment on the meter stick. Witne eye view the meter stick directly and with the other eye view it through the telescope. Your eye should be about 15 cm from the eyepiece. Your lab partner should stand beside the meter stick and hold a pencil horizontally with the lead just above the meter stick fiducial marks. By moving the pencil up and down align the image seen by the top mark of the 10 cm interval viewed through the telescope. Record the position as x t. Repeat this process for the bottom mark of the 10 cm object interval and record the pencil position as x b. Calculate the magnification and compare with the predicted value given in equation (13). Newtonian Reflecting Telescope Mount the converging mirror in a carriage and position it at the 0 cm mark on the optical bench. Place the diagonal mirror and eyepiece holder rod in a carriage on the bench and position it at about the 67 cm mark. Experiment 5 Page 23
The mirror should be perpendicular to the bench and the diagonal should be at 45E to the bench. Place the 6 cm focal length lens in a lens holder and mount it in the eyepiece holder rod. The holder rod should be perpendicular to the bench. The centers of the converging and diagonal mirrors should be about 24 cm above the bottom of the track. With the lights out and the converging mirror pointed toward an illuminated light bulb hold an image screen in front of the converging mirror near the diagonal mirror. Rotate the converging mirror slightly and adjust its height so that the circle of light from the bulb is centered on the diagonal mirror. Then hold the image screen in front of the eyepiece toward the diagonal mirror and rotate the diagonal mirror and/or the lens holding rod slightly until the circle of light from the bulb is centered on the eyepiece. It may be necessary to raise or lower the eyepiece. With your eye about 5 cm from the eyepiece look into it and an image of the bulb should be visible. Move the diagonal carriage slightly until the bulb is sharply focused. Place a meter stick on the wall at a distance of about 10 x f o as in part 4 and observe a 10 cm section as an object. To measure the image angle lay a ruler on the table perpendicular to the optical bench with the 0 cm end directly under the eyepiece. Hold a second meter stick (image gauge) vertically at the 50 cm point of the meter stick on the table. View the image gauge meter stick directly witne eye and view through the telescope with the other eye the object meter stick on the wall. Record as x t the position on the gauge meter stick that is aligned with the image of the top mark of the 10 cm interval viewed through the telescope. Record the position as x t. Repeat this process for the bottom mark of the 10 cm object interval and record the position on the gauge ruler as x b. The difference #x t - x b # will also be about 10 cm. To measure the object angle use the 10 m tape to measure the distance D from the converging objective mirror to the object meter stick on the wall. Compute the object and image angles and the angular magnification. Compare this result with the predicted value given in equation (13). Experiment 5 Page 24