RESOLVING POWER OF A READING TELESCOPE

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1 96 Lab Experiments Experiment-255 RESOLVING POWER OF A READING TELESCOPE S Dr Jeethendra Kumar P K KamalJeeth Instrumentation & Service Unit, No-60, TATA Nagar, Bangalore , INDIA. Abstract Resolving power of a reading telescope is determined using a double slit and a micrometer adjustable single slit. The double slit placed in front of a white light source acts like two sources of light. A micrometer slit is used to control the light reaching the objective of the telescope. As the micrometer slit width is reduced, the two images of the light sources come closer and merge for a certain slit width. At this point the diffraction produced due to the two sources of light caused by edges of the adjustable slit is also seen in the field of view of the telescope. The first maximum of the diffraction pattern of one of the light sources falls exactly on to the second minimum of the diffraction pattern due to the second source of light producing a wide central fringe with reduced intensity in the field of view of the telescope which has been recorded using a digital camera. Introduction Invention of telescope was an accidental finding by a Dutch spectacle maker Hans Lippershey and his children in 608 []. Galileo (609) constructed a real working telescope, which has been used effectively till now. Invention of telescope gave impetus to research in Astronomy and Astrophysics. Magnifying power and the resolving power of the telescope are the two characteristic parameters of an astronomical telescope. Other than astronomical telescopes there is one more telescope, called reading telescope, which is frequently used in laboratory for making measurements. This telescope has magnifying power in the range of 0-5. Mounted on a stand these telescopes are used to count oscillations of pendulum or string. Using an eyepiece with scale marked on it measurements of number oscillations can be made. Reading telescope used in this experiment consists of an objective lens of 25mm dia and 20-25cm focal length. A 0X eyepiece is mounted at the end of the telescope tube for observation. A cross wire is also fixed inside as a reference frame. With this telescope one cannot make measurements but only qualitative observations can be made. Figure- shows an adjustable slit fixed on the objective of the telescope to control the light input. The amount of light entering the objective of the telescope can be controlled by opening the slit by fraction

2 97 Lab Experiments of a millimeter. The width of the slit opening can be measured using a micrometer screw gauge. Resolving Power Resolving power is the capacity of a telescope to identify two closely spaced sources or objects. Figure-2 shows two closely placed light sources. As one goes further away, the angle of observation becomes smaller and the source of light appears to come closer. At one point of the observation, the two sources merge and form a single source. At this point of observation, the human eye is not able to distinguish between the two sources or in other words the eye loose its resolving power. Figure-: Adjustable micrometer slit mounted in front of the telescope objective lens Similarly a telescope after a certain distance from a source or an object is not able resolve or identify two closely placed sources. The resolving power of the telescope is a measure of this identification. Since distance is quite difficult to measure, the angles that the two sources make with the field of view where the image is formed is measured from which the resolving power of a telescope can be calculated. World s largest refractive telescope at Yerkes Observatory has 4 arc seconds of resolving power. A normal human eye is said to have 47 arc seconds resolution based on size of the pupil. In fact, a human eye cannot resolve objects that are placed less than 60 arc seconds apart [2]. Resolving Power of a Telescope When light passes through a narrow slit or small circular hole, it gets diffracted and interferences fringes are formed [3]. The interference fringe pattern has the central maximum followed by secondary maxima and minima as shown in Figure-3. Two plano-convex lens (equivalent to a single double convex lens) illuminated by a rectangular aperture of vertical dimension, b, is shown in Figure-3. The narrow slit sources S and S 2 perpendicular to the plane in Figure-3 form the real images S and S 2 on a screen. Each image consists of a single slit diffraction pattern for which the intensity distribution is also shown in Figure-3. The angular separation of the central maxima is equal to the angular separation of the two sources. Each principal maximum of the diffraction pattern falls exactly on the second minimum of the adjacent pattern. As angle α is made smaller, the two images move closer to each other, the intensity between the maxima rises until finally no minimum remains at the centre. The

3 98 Lab Experiments resultant pattern is shown in Figure-4. At this close distance, the resolution between the two images is lost. Therefore the minimum angle of resolution [2] is given by θ λ =.22 D Where λ is the wavelength of the light used and D is width of the merged slit images S Light sources S2 Point of observation- Smaller angle of observation Point of observation-2 Figure-2: Two light sources and the angle of observation S' S b st Maxima due S2 2nd minima due S2 S2 st Maxima due S First minima due S2 S2' Angle Alpha Angle Alpha Figure-3: Light passing through small aperture producing a diffraction pattern

4 99 Lab Experiments Figure-4: Diffraction images of two slit sources (a) and (b) well resolved; (c) just resolved; (d) not resolved at all (Picture courtesy Ref-2) With a given objective in a telescope, the angular size of the image as seen by the eye is determined by the magnification of the eyepiece. By increasing the magnifying power of the eyepiece it is not possible to obtain minute details of an object. Hence the resolving power of the telescope is limited by the diffraction taking place at the edges of the lens of the telescope. In viewing a distant star the diffraction-taking place at the edges of the objective lens limits the resolution of the telescope. In this case D is nothing but the diameter or width of the objective lens. The resolving power of a reading telescope, if used to view a distant object, is given by λ 560nm 6 θ =.22 =.22 = 22.4x0 Radians = degree = minute (= 4.62 D 25mm arc seconds) Which is very small compared to the resolution of the human eye (being about 60 arc seconds). Apparatus used Figure-5: Experimental setup for measurement of resolving power of a telescope

5 00 Lab Experiments Experimental set-up of a telescope consisting of white light source on a stand, a resolving power double slit with about 2mm separation and 2mm width, Reading telescope and micrometer adjustable slit. Experimental Procedure. The resolving power double slit shown in Figure-6 is mounted on its frame in front of the lamp as shown in Figure-5 and Figure The reading telescope is placed at a distance of about to.5m from the slit along the line of the lamp. 3. Viewing through the telescope, it is focused on to the slit and the adjustment screw of the telescope is turned until the images of the two slit openings are observed clearly. The images seen in the field of view of the eyepiece are shown in Figure-8. Figure-6: Resolving power double slit and adjustable slit Figure-7: Resolving power double slit placed in front of the light source 4. Now the micrometer adjustable slit is mounted on to the telescope tube in front of the objective lens of the telescope as shown in Figure Micrometer slit is kept wide open and again the image of the objective slit is observed on the field of view of the telescope eyepiece. Two closed placed slit images are shown in Figure The micrometer screw is rotated so that the slit starts closing. As the width of the micrometer slit is progressively reduced, the slit images come closer and closer.

6 0 Lab Experiments Figure-8: Two identifiable slit images 7. Further reducing the micrometer slit width merges the images of the two slits and a single dull central image is observed as shown in Figure-9. At this position the micrometer width is noted from the micrometer as under: MSR =0, VSR=32 divisions (a) (b) Figure-9: (a) Merging of the two slit images and appearance of the diffraction pattern; (b) with fully closed slit the field of view becomes dark 8. The width of the micrometer slit is further reduced until the field of view becomes dark, as shown in Figure-9(b). The reading of the micrometer slit at this portion is noted. MSR = 0, VSR=3 divisions 9. The difference in the two readings gives the width of the merged slit images as D = 35-3 divisions = 32divisions = 0.32mm = 0.32x0-3 m 0. Resolving power is calculated using equation - 9 λ 560x0 nm 3 θ = = =.75x0 radian = 0.00 deg ree = 6 min utes mm 0.32x0

7 02 Lab Experiments. The trial is repeated by keeping the telescope at different positions. The readings obtained are tabulated in Table -. Note- Distance between double slit and micrometer slit Images just merged Table- Micrometer Slit Reading Field of view becomes blank Width of the merged image (D Divisions).3m m m Average D =32 divisions = 0.32mm Micrometer slit readings at different positions of the telescope As the width of the micrometer slit is reduced, the appearance of closely placed straightline fringes due to diffraction taking place at the edges of the micrometer slit is observed as shown in Figure-9(a). Colored (rainbow colored) straight lines fringes indicate the loss of resolution. These fringes are formed due to diffraction taking place through the edges of the micrometer slit. Once the diffraction pattern starts appearing, the resolution of the telescope diminishes. The telescopes fail to identify closely placed images. Results Resolving power of the telescope =.75 x 0-3 = radian = 0. = 6 arc minutes Note-2: References The reading of the micrometer slit when field of view becomes blank is taken because of the error of the micrometer slit. In fact, all micrometers have some zero error similar to a micrometer screw gauge. [] Dr. Jeethendra Kumar P.K, Space Explorations; the Foundations, LE Vol-6, No.2, P- 79 [2] Francis A Jenkins and Harvey E White, Fundamentals of Optics, 4th Edition, McGraw-Hill, Page 330 [3] Dr. Jeethendra Kumar P.K; Diffraction at the circular apertures, LE Vol 4, No-, Page-

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