Laboratory Manual Physics_1. Index of refraction for solids

Transcription

1 AGH University of Science and Technology in Cracow Department of Electronics Laboratory Manual Physics_ Title: 009 r. Index of refraction for solids Experiment No. 9

2 . Goal To determine the index of refraction for transparent solids (glass, plexiglass). What to learn? Law of refraction. Law of reflection. Index of refraction. Total internal reflection. Chromatic dispersion of white light. Real thickness. Apparent thickness. 3. Equipment A microscope with a dial indicator. A micrometer screw. A set of glass and plexiglass plates with red and black lines marked with a sharply pointed marker on the bottom and the top side of the plates. 4. Introduction A beam of light traveling through a surface that separates two optically different media is both reflected and refracted at the boundary. Fig. shows an incident light ray, a reflected ray and a refracted ray. Each ray is oriented with respect to a line, called the normal, that is perpendicular to the surface at the point of reflection and refraction. The angle of incidence θ, the angle of reflection and the angle of refraction θ are measured relative to the normal. The plane ' θ containing the incident ray and the normal is called the plane of incidence. Fig.. Reflection and refraction of light Reflection and refraction is governed by two laws: Law of reflection:

3 A reflected ray lies in the plane of incidence and has an angle of reflection equal to the angle of incidence: θ = ' θ Law of refraction: A refracted ray lies in the plane of incidence and has an angle of refraction equal to the angle of incidence: n = sinθ n sin θ The symbols n and n are called the indexes of refraction and they are associated with media involved in the refraction. The index of refraction n of a medium is the ratio of the speed of light in vacuum to the speed of light in a medium: c n = v The index of refraction n in any medium except vacuum depends on the wavelength of the light. This dependence implies that when a light beam consists of rays of different wavelengths, the rays will be refracted at different angles. The light will be spread out by the refraction. The phenomena is called chromatic dispersion. Chromatic refers to the colors associated with the individual wavelengths and dispersion refers to the spreading of light according to the wavelengths or colors. For a pair of media we can introduce the concept of the relative index of refraction n : n n n = = = v c c v v v The relative index of refraction n the ratio of the speeds of light in two media. Vacuum or air is usually taken as the reference medium. Due to the refraction, objects situated in a medium of a larger optical density appear to be closer than in reality, when they are observed from air. A glass panel seems to be thinner than it really is, objects placed in water seem to be closer to the water surface. Those effects can be explained easily when we consider the way of the light ray traveling from point O, placed at the bottom of a glass slab, to the top of this slab (Fig. ). 3

4 Fig.. Light rays traveling through a glass slab. The beam OA, which is normal to the surface of a slab, travels straight on through the slab. The beam OB forms in glass an angle β to the normal at the boundary, and in air an angle α. The two beams leaving the glass slab diverge, appearing to originate in a point O. The distance OA = h constitutes an apparent thickness of the slab, and h < d, where d is the true slab thickness. 5. Measurements Index of refraction is determined in the experiment by comparing the real thickness with the apparent thickness of a plate. Real thickness is measured using a micrometer screw. Apparent thickness is measured using a microscope with a dial indicator.. Measure the real thickness D of a glass plate and a plexiglass 0 times using a micrometer screw.. Locate a glass plate on the table of the microscope. 3. Adjust the microscope tube to get a sharp image of the mark on the bottom side of a plate and read out the tube position d on the dial micrometric gauge (Fig. ). There are two pointers on the dial of the gauge. The small pointer indicates the whole millimeters, the big pointer indicates hundreds of a millimeter. Pay attention that these pointers move in opposite direction. 4

5 4. Adjust the microscope tube to get a sharp image of the mark on the top side of a plate and read out the tube position d on the dial micrometric gauge. 5. Repeat 0 times the measurements of d and d for the glass plate. 6. Locate a plexiglass plate on the table of the microscope and repeat the steps Write down the results in the table. Table Plate D [mm] d [mm] d [mm] d d h= d d σ d σ d σh n Δn Fig.. Dial indicator 6. Data handling. Calculate the average value of d and d. Calculate the uncertainties σ d and σ d.. Calculate the apparent thickness h = d d and then the uncertainty of σh which is the sum of uncertainties d and d. 3. Calculate the index of refraction n: the method of the logarithmic derivative. D n = and the uncertainty of the index of refraction Δn by h 5

6 Literature:. Halliday, Resnick Fundamentals of Physics - 8 th edition, John Wiley 007,. Zięba Pracownia Fizyczna Wydziału Fizyki I Techniki Jądrowej AGH, Uczelniane Wydawnictwo Naukowo-Dydaktyczne 999. Updated: by Teresa Kenig by Barbara Dziurdzia Appendix Using the vernier calipers and micrometer screw gauge The precision of length measurements may be increased by using a device that uses a sliding vernier scale. Two such instruments that are based on a vernier scale which you will use in the laboratory to measure lengths of objects are the vernier callipers and the micrometer screw gauge. These instruments have a main scale (in millimetres) and a sliding or rotating vernier scale. In figure below, the vernier scale (below) is divided into 0 equal divisions and thus the least count of the instrument is 0. mm. Both the main scale and the vernier scale readings are taken into account while making a measurement. The main scale reading is the first reading on the main scale immediately to the left of the zero of the vernier scale (3 mm), while the vernier scale reading is the mark on the vernier scale which exactly coincides with a mark on the main scale (0.7 mm). The reading is therefore 3.7 mm. Figure : The reading here is 3.7 mm. 6

7 Figure : The reading here is 5.8 mm. The vernier calipers The vernier calipers found in the laboratory incorporates a main scale and a sliding vernier scale which allows readings to the nearest 0.0 mm. This instrument may be used to measure outer dimensions of objects (using the main jaws), inside dimensions (using the smaller jaws at the top), and depths (using the stem). Figure 3: The vernier calipers To measure outer dimensions of an object, the object is placed between the jaws, which are then moved together until they secure the object. The screw clamp may then be tightened to ensure that the reading does not change while the scale is being read. The first significant figures are read immediately to the left of the zero of the vernier scale and the remaining digits are taken as the vernier scale division that lines up with any main scale division. 7

8 Examples: Note that the important region of the vernier scale is enlarged in the upper right hand corner of each figure. Figure 4: The reading is mm. In figure 4 above, the first significant figures are taken as the main scale reading to the left of the vernier zero, i.e. 37 mm. The remaining two digits are taken from the vernier scale reading that lines up with any main scale reading, i.e. 46 on the vernier scale. Thus the reading is mm. Figure 5: The reading is mm. In figure 5 above, the first significant figures are taken as the main scale reading to the left of the vernier zero, i.e. 34 mm. The remaining two digits are taken from the vernier scale reading that lines up with any main scale reading, i.e. 60 on the vernier scale. Note that the zero must be included because the scale can differentiate between fiftieths of a millimetre. Therefore the reading is mm. 8

9 Figure 6: The reading is mm. In figure 6 the zero and the ten on the vernier scale both line up with main scale readings, therefore the reading is cm. The micrometer screw gauge The micrometer screw gauge is used to measure even smaller dimensions than the vernier callipers. The micrometer screw gauge also uses an auxiliary scale (measuring hundredths of a millimetre) which is marked on a rotary thimble. Basically it is a screw with an accurately constant pitch (the amount by which the thimble moves forward or backward for one complete revolution). The micrometers in our laboratory have a pitch of 0.50 mm (two full turns are required to close the jaws by.00 mm). The rotating thimble is subdivided into 50 equal divisions. The thimble passes through a frame that carries a millimetre scale graduated to 0.5 mm. The jaws can be adjusted by rotating the thimble using the small ratchet knob. This includes a friction clutch which prevents too much tension being applied. The thimble must be rotated through two revolutions to open the jaws by mm. Figure 0: The micrometer screw gauge 9

10 In order to measure an object, the object is placed between the jaws and the thimble is rotated using the ratchet until the object is secured. Note that the ratchet knob must be used to secure the object firmly between the jaws, otherwise the instrument could be damaged or give an inconsistent reading. The manufacturer recommends 3 clicks of the ratchet before taking the reading. The lock may be used to ensure that the thimble does not rotate while you take the reading. The first significant figure is taken from the last graduation showing on the sleeve directly to the left of the revolving thimble. Note that an additional half scale division (0.5 mm) must be included if the mark below the main scale is visible between the thimble and the main scale division on the sleeve. The remaining two significant figures (hundredths of a millimetre) are taken directly from the thimble opposite the main scale. Figure : The reading is 7.38 mm. In figure the last graduation visible to the left of the thimble is 7 mm and the thimble lines up with the main scale at 38 hundredths of a millimetre (0.38 mm); therefore the reading is 7.38 mm. Figure : The reading is 7.7 mm. In figure the last graduation visible to the left of the thimble is 7.5 mm; therefore the reading is 7.5 mm plus the thimble reading of 0. mm, giving 7.7 mm. 0

11 Figure 3: The reading is 3.46 mm. In figure 3 the main scale reading is 3 mm while the reading on the drum is 0.46 mm; therefore, the reading is 3.46 mm. Figure 4: The reading is 3.56 mm. In figure 4 the 0.5 mm division is visible below the main scale; therefore the reading is 3.5 mm mm = 3.56 mm. Taking a zero reading Whenever you use a vernier calipers or a micrometer screw gauge you must always take a zero reading i.e. a reading with the instrument closed. This is because when you close your calipers, you will see that very often (not always) it does not read zero. Only then open the jaws and place the object to be measured firmly between the jaws and take the open reading. Your actual measurement will then be the difference between your open reading and your zero reading. (source: University of Cape Town Department of Physics)