Optics. Kepler's telescope and Galileo's telescope. f 1. f 2. LD Physics Leaflets P Geometrical optics Optical instruments

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1 Optics Geometrical optics Optical instruments LD Physics Lealets P Kepler's telescope and Galileo's telescope Objects o the experiment g Veriying that the length o a telescope is given by the sum o ocal lengths o the objective and the ocular g Determining the magniication o a telescope Principles The angle o vision determines the size o the image on the retina o the eye. Basically, there are two reasons why the angle o vision ϕ is too small (i.e. the object cannot be seen as a sharp image on the retina o the eye). Either the object size is to small or the object distance is too large. The irst case concerns to the observation o small objects with a magniier or microscope and is described in experiment P The latter case concerns to the observation o distant objects using a telescope. In the most simplest case a telescope is composed o two lenses: the objective and ocular. In an astronomic telescope (Kepler s telescope) a real intermediate image is ormed in the ocal plane P o the objective L1 (Fig. 1). This real intermediate image is observed through an eyepiece (ocular) L2 which is used as a magniier. A magniied virtual image is observed which is inverted in respect to the distant object. The magniication is the quotient o the visual angle with and without telescope. From Fig. 1 ollows or suiciently small angels (tanϕ ϕ): tan ϕ 1 V = = tan ϕ0 2 (I) ϕ: angle o vision with optical instrument ϕ 0 : angle o vision without optical instrument : ocal length o objective : ocal length o ocular Fig. 1: Schematic representation o the ray path o a Kepler s telescope: L1: objective L2: ocular, : ocal length o objective, : ocal length o ocular, P, ocal plane o objective, ϕ 0 and ϕ angle with and without instrument. ϕ 0 ϕ Bi 0309 L1 P L2

2 P LD Physics lealets The Kepler s telescope uses converging lenses both or the objective and or the ocular. Exchanging the ocular L2 by a diverging lens leads to the Galilei s telescope (Fig. 2). In contrast to the Kepler s telescope no real intermediate image is ormed. The convergent beam is made divergent by the ocular beore a imaged is ormed by the objective. The resulting virtual image is magniied and not inverted in respect to the distant object. The ocal points o the objective and the ocular co-incide in the direction towards the eye (Fig. 2). The length o a Kepler s and Galilei s telescope (i.e. the distance between objective and ocular) is given by the sum o the ocal lengths: = + (II) Apparatus 1 Optical bench, standard cross section 1 m Optics rider 60/ or 1 Optical bench S1 proile 1m Optics rider Lens in rame = Lens in rame = Lens in rame = Lens in rame = Lens in rame = Vertical scale, l = 1 m Saddle base Setup The experiments can be perormed with both the optical bench (460 32) or the optical bench S1 proile ( ). Fig. 3 (let) shows the principle setup o a telescope to determine the length o the telescope. The Kepler s telescope uses two converging lenses. The Galilei s telescope uses a converging lens or the objective and a diverging lens or the ocular. Fig. 3 (right) shows the vertical scale which has to be placed at a distance o approx. 10 m in ront o the optical bench to determine the magniication o the telescope. The experiment can also be perormed at smaller distances between objective and vertical scale. Fig. 2: Schematic representation o the ray path o a Galilei s telescope: L1: objective L2: ocular, : ocal length o objective, : ocal length o ocular, G: object at a ar distance, B: size o virtual image, : length o telescope. G B L1 L2

3 LD Physics lealets P Fig. 3: (let): Experimental setup o a telescope here with optical bench S1 proile ( ). L1 : objective, L2 ocular. (right): vertical scale as distant object. The recoended distance between scale and telescope is 10 m. Carrying out the experiment It is recoended to perorm the experiment in room which allows to observe distant objects through the window. a) Observing distant objects with a Kepler s telescope - Set up the lens L2 with = +50 at the end o the optical bench. The lens L2 corresponds to the ocular o the telescope (Fig. 3 let). - Position the lens L1 with = +100 at a distance o approximately 160 behind the lens L2. The lens L1 corresponds to the objective o the telescope (Fig. 3 let). - Lock through the ocular lens L2 and shit the lens L1 towards the lens L2 until a sharp image is observed. - Measure the length o the telescope. - Exchange objective = +100 by a lens = +200 and repeat the experiment. - Exchange objective = +200 by a lens = +500 and repeat the experiment. c) Determining the magniication o a Kepler s telescope - Set up the lens L2 with = +50 at the end o the optical bench. The lens L2 corresponds to the ocular o the telescope (Fig. 3 right). - Position the lens L1 with = +100 at a distance o approximately 160 behind the lens L2. The lens L1 corresponds to the objective o the telescope (Fig. 3 right). - Setup the vertical scale at a distance o approx. 10 m using the saddle base. Note: When the distance between the object (i.e. the vertical scale) and the objective L1 is smaller than 10 m the error o the magniication can be estimated approx. by: V 1 2 (III) 1 2 e.g. or the lens combination L1 ( = +200 cm) and L2 ( = +50 cm) and = 10 m the error is approx. 4%. For smaller distances, i.e. = 5, the error can be approximated by 10%. b) Observing distant objects with a Galilei s telescope - Set up the lens L2 with = -100 at the end o the optical bench. The lens L2 corresponds to the ocular o the telescope. - Position the lens L1 with = +200 at a distance o approximately 130 behind the lens L2. The lens L1 corresponds to the objective o the telescope. - Lock through the ocular lens L2 and shit the lens L1 towards the lens L2 until a sharp image is observed. - Measure the length o the telescope. - Exchange objective = +200 by a lens = +500 and repeat the experiment. - Lock through the ocular L2 and shit the objective L1 towards the lens L2 until a sharp image o the vertical scale can be observed. - Now look with one eye through the ocular and with the other eye directly to the vertical scale. Move the optical bench until the image o the scale o the direct observation and image o the telescope are close as in picture (Fig. 4) - Determine the magniication by the comparison o the graduations o the observed mages o the vertical scales. - Repeat the experiment or the objective with = +200.

4 P LD Physics lealets Measuring example In the ollowing tables the measuring results o the various experiments are suarized: Kepler s telescope Table. 1: Measured telescope length and magniication o the graduation o the vertical scale Fig. 4: Observation o the image o the vertical scale both with telescope (i.e. right eye) and without telescope (i.e. let eye) at the same time Galileo s telescope d) Determining the magniication o a Galilei s telescope - Set up the lens L2 with = -100 at the end o the optical bench. The lens L2 corresponds to the ocular o the telescope. - Position the lens L1 with = +200 at a distance o approximately 130 behind the lens L2. The lens L1 corresponds to the objective o the telescope. - Setup the vertical scale at a distance 10 m using the saddle base. - Lock through the ocular L2 and shit the objective L1 towards the lens L2 until a sharp image o the vertical scale can be observed. - Lock through the ocular L2 and shit the objective L1 towards the lens L2 until a sharp image o the vertical scale can be observed. - Now look with one eye through the ocular and with the other eye directly to the vertical scale. Move the optical bench until the image o the scale o the direct observation and image o the telescope are close as in picture (Fig. 4) - Determine the magniication by the comparison o the graduations o the observed mages o the vertical scales. - Repeat the experiment or the objective with = Table. 2: Measured telescope length and magniication o the graduation o the vertical scale Evaluation and results In the ollowing tables the measuring results are compared with values obtained rom theory, i.e. rom equation (I) the magniication V and rom equation (II) the telescope length. Kepler s telescope Table. 1: Measured telescope length Galileo s telescope Table. 2: Measured telescope length

5 LD Physics lealets P L1 P L3 L2 Fig. 5: Schematic representation o the ray path o a terrestrical telescope: L1: objective L2: ocular, L3: lens to invert the intermediate image, : ocal length o objective, : ocal length o ocular, 3: ocal length o lens L3, P, ocal plane o objective. Note: this setup can only be perormed when the ull experiment group P5.1.4 is available. Supplementary inormation I the light passes through the telescope in reverse direction the telescope can be used or expanding a beam o parallel light bundles and ocusing on a distant point. I the complete experiment group P5.1.4 is available, i.e. both experiment P and experiment P , two additional experiments can be perormed with the Kepler s telescope: First the real intermediate image can be viewed by using the translucent screen in the ocal plane P o the objective L1 (Fig. 1). I the translucent screen is placed in the ocal plane o the telescope an image is observed on the screen when locking through the ocular which is upside down. Secondly, a terrestrial telescope can be setup as depicted in Fig. 5. The additional lens L3 ( = +50 ) between the objective L1 ( = +200 ) and the ocular L2 ( = +100 ) is used to invert the real image observed in the ocal plane P o the objective. The length o the telescope is increased by 4 3. Thus the image observed with the ocular L2 is not inverted.

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