120-lab-manual(1)

Contents Introduction page 3 Tutorial on Errors and Significant Figures 5 Tutorial on Graphs 7 Laboratory Exercises Electricity & Magnetism 21 Ohm's Law 9 22 DC Circuits 13 23 Force on a Current-Carrying Wire... 19 24 The Specific Charge of the Electron 23 25 The Oscilloscope 29 26 PN Junction Diode 35 Optics 27 The Speed of Light 41 28 Part I: Refraction 45 Part II: Focal Length 49 29 Mirrors and Lenses 53 30 Interference and Diffraction 57 31 The Grating Spectrometer 61 Radioactivity 32 Absorption of Radiation 65 1

This collection of Laboratory Exercises is the introductory physics laboratory manual used by Hunter College. The original exercises were developed by the Physics Faculty over thirty years ago. A number of revisions have since been made. In particular, the revision of 1994 led by Professor Robert A. Marino, introduced several new exercises involving modern optical and electronic equipment. We are indebted to the faculty and students who participated in the creation and revision of the manual over the years. Physics Faculty Hunter College July, 1999 © 1998, 1999 by Department of Physics and Astronomy, Hunter College of the City University of New York All rights reserved. 2

Laboratory Grade: The lab instructor will make up a grade 90% based on the average of your lab reports, and 10% on his/her personal evaluation of your performance in the laboratory. This grade is then reported to your lecturer for inclusion in the final course grade (15% weight factor). The list below will give you an idea of the criteria used by your lab instructor in grading your lab report: 1. Quality of measurements. Logical presentation of report contents. 2. Accuracy and correctness of calculations resulting from proper use of data and completion of calculations. 3. Orderly and logical presentation of data in tabular form, where appropriate. 4. Good-looking graphs, easiness to read, good choice of scales and labels. 5. Comparison with theory. 6. Answers to Questions; Conclusions. 7. Clarity, Neatness, Promptness. 4

TUTORIAL # 1 On Errors and Significant Figures Errors We could distinguish among three different kinds of "errors" in your lab measurements: 1. Mistakes or blunders. We all make these. But with any kind of luck, and some care, we catch them and then repeat the measurement. 2. Systematic Errors . These are due either to a faulty instrument ( a meter stick that shrank) or by an observer with a consistent bias in reading an instrument. 3. Random Errors . Small accidental errors present in every measurement we make at the limit of the instrument's precision. After blunders are eliminated, the precision of a measurement can be improved by reducing random errors ( by statistical means or by substituting a more precise instrument, i.e., one that yields more significant figures for the same measurement.) Accuracy can be increased by reducing any systematic errors as well as by increasing the precision. Significant Figures No measurement of a physical quantity can ever be made with infinite accuracy. As an honest experimentalist, you should relay to the reader just how good you think your measurement is. One simple way to relay this information is by the number of significant figures you quote. For example, 3.4 cm says one thing, 3.40 cm tells a different story. The last digit you write down can be your best estimate made between the markings of a scale, but it still represents a willfully reported number, it still is a significant figure. The placement of the decimal point does not change the number of significant figures. For example, 20.8 grams and 0.00208 grams each have three significant figures; each is assumed to be uncertain by at least ±1 in the last figure, i.e., ±1 part in 208, which is about ½ %. Normally, figuring out how many significant figures are in a stated number gives no problems, except when zeros are involved. For example, is it obvious how many significant figures are expressed in 5500 feet, 250 years, or $1,300,000 ? A good way to tell the reader which is, in fact, the last significant figure is by using scientific notation . For example, 5.50 x 10 3 feet, 2.5 x 10 2 years, and 1.300 Megabucks, telegraph that the number of digits in which any confidence can be placed was three, two, and four, respectively. Computations using raw data How do you combine your carefully gathered data with other numbers in an expression? With a little common sense, and a hand calculator, you can verify that the following rules should be followed:

TUTORIAL # 2 Making a Good Graph by Hand Start thinking about a nice title. e.g., " The Square of the Period (T 2 ) of a Simple Pendulum vs. its Length (L)" [ A shorter title would have been even better] Keep your axes straight: If you need to plot "A vs B", or "A as a function of B", then A is on the vertical axis and B is on the horizontal axis. vertical axis = y-axis = the "ordinate" horizontal axis = x-axis = the "abscissa" The crucial part is choosing the range and scale for each axis. Two examples: a) 0 to 5 sec; 5 graph boxes =1 sec. b) -300 to +200 degrees; 2 boxes =100 degrees The range must be: just large enough to accommodate all your data, yet allow a readable scale. The scale should be: spread out enough so your data take up most of the graph area, and labeled so plotting (and reading) is easy. Label the x and y axis with the appropriate magnitudes. These should be round numbers which cover the entire range of values that you will be plotting. A common mistake is to label too many boxes. If you are trying to show that one quantity is proportional to another, or if you are not told otherwise, zero is part of the range and must be located at the Origin. The numbers should be evenly spaced with the same number of boxes between the same increase in numbers including the space from zero to the first non-zero number. Choose an appropriate number of boxes between numbers. It is better to have 5 boxes between numbers than 4 since it is easier to interpolate in the first case than in the second. (Similarly 10 is better than 8, and 2 is better than 3.) Plot the results of your measurements on this graph. Where appropriate, you should include error bars to indicate the uncertainty in your measurements. These error bars are not of arbitrary size but should be of the size of your uncertainty on the scale dictated by the numbers on the axis of your graph.

When you draw the line that best fits your data, the line should be a smooth one that need not go through any points. In general, there should be as many points on one side of the line as on the other. If you have done your work properly, the line should pass inside of the error bars for each point. (If it does not, that may be an indication that there is something wrong with the point in question. Perhaps you miss-recorded a measurement, or your estimate of the error was too small, or there was something wrong with the apparatus, or with the technique you applied, etc.) If your graph shows that one quantity is proportional to another, it should be a straight line that starts at the origin and passes through the plotted data with as many points on one side as the other. If you are asked to find the slope of the line , choose two points on the line which are as far apart as possible. This will minimize the error that is introduced in reading the value of those points. The slope is the difference between the vertical values of those points divided by the difference in the horizontal values of those points. A common mistake is to measure the slope of the segment connecting two actual data points : this does not yield the slope of the straight line you fitted to your data! Note: Normally. the slope of your graphs has its own units. e.g., The slope of graph of velocity vs. time has units of (m/s)/(s) = m/s 2 . Here is a graph so messy, you can surely do better with . LABORATORY EXERCISE #21 8

Figure 1 In both methods there will be some error if the resistance is obtained by dividing the voltmeter reading V by the ammeter reading  . 1) In the figure on the left the voltmeter reads the potential difference across both the ammeter and the resistor. Hence, the ratio (V /  ) would equal R only if the ammeter resistance were exactly zero. In fact, ( V /  ) will more nearly equal R, the smaller the ammeter resistance in comparison with R. 2) In the figure on the right the ammeter reads the sum of the currents through the resistance and through the voltmeter. Hence, in this case, ( V /  ) would equal R only if the voltmeter resistance were infinite. So, ( V /  ) will more nearly equal R, the greater the resistance of the voltmeter in comparison with R. For the types of instruments used in your laboratory, the method of Figure 1 gives the smaller error unless R is very small. A rheostat is a device you will be using a lot. It is a three-terminal element, which we could label A , B and C , as shown in Figure 2. The resistance between the endpoints A and B is a constant, lets call it R 0 . However, C is connected to a sliding contact. Therefore, the resistance between C and either endpoint can be varied between 0 and the maximum value R 0 . The net result is that a rheostat can be used as a variable resistance, by connecting it from C to either A or B . Make sure you understand this point before continuing. Ask your instructor for assistance, if necessary. Procedure Note: All circuits MUST be approved by your instructor before connecting to the voltage source 10 V A Power Supply R V A Power Supply R

1. Diagram a circuit to measure the resistance of a fixed resistor R with a voltmeter and an ammeter by the method of Figure 1. Use a DC power supply for the voltage source. Include a switch and a variable resistance R' in series with the power supply. Including R' will enable you to vary the current through the fixed resistance R in a convenient way. A C A V B R’ Power Supply R Figure 2 2. Wire up the circuit you designed in Part 1. above. Do not turn on the power until your circuit has been approved by your instructor. 3. Adjust R' to its maximum value. Record the ammeter and voltmeter readings. Obtain nine more pairs of readings for currents between 0 and about 1.00 ampere. 11

LABORATORY EXERCISE # 22 DC Circuits Objectives Study series and parallel circuits. Equipment and supplies 6-Volt DC power supply, lamp sockets, rheostat, 1 A DC ammeter, 10 V DC voltmeter, wires with banana plugs. Discussion Resistors in series When two or more resistors are connected end to end as shown I Figure 1, they are said to be in series. Any charge that passes through R 1 will also pass through R 2 , and then R 3 . Hence the same current  passes through each resistor. We let V represent the voltage across all three resistors, and V 1 , V 2 , and V 3 be the potential differences across each of the resistors, R 1 , R 2 , and R 3 , respectively. By Ohm’s law, V 1 =  R 1 , V 2 =  R 2 , and V 3 =  R 3 . Because the resistors are connected end to end, the total voltage V is equal to the sum of the voltage across each resistor: The equivalent single resistance R eq that would draw the same current would be related to V by We equate this express with Eq. (1) and find Thus when we put several resistances in series, the total resistance is the sum of the separate resistances. Figure 1 Resisitors in series. 13 V = V 1 + V 2 + V 3 = IR 1 + IR 2 + IR 3 [ series ]( 1 ) V = IR eq R eq = R 1 + R 2 + R 3 [ series ]( 2 ) R 1 R 2 R 3 V { { { V 1 V 2 V 3 I

Another simple way to connect resistors is in parallel, so that the current from the source splits into separate branches, as shown in Figure 2. In a parallel circuit, the total current  that leaves the battery breaks into three branches. We let  1 ,  2 , and  3 be the currents through each of the resistors R 1 , R 2 , and R 3 , respectively. Because the electric charge is conserved, the current flowing into a junction must equal the current flowing out of the junction. Thus, When the resistors are connected in parallel, each experiences the same voltage. Hence the full voltage of the battery is applied to each resistor, so Figure 2. Resistors in parallel. The equivalent circuit R eq of the network must satisfy We now combine the equations above and obtain Procedure The lamp board contains three screw sockets for small incandescent light bulbs of various power ratings. 1. Set up a circuit to measure the resistance of a light bulb with a voltmeter and an ammeter by the method of Figure 3. 14 I = I 1 + I 2 + I 3 ( 3 ) V = I 1 R 1 = I 2 R 2 = I 3 R 3 [ parellel ]( 4 ) R 1 R 2 R 3 V I 1 I 2 I 3 I I = V R eq 1 R eq = 1 R 1 + 1 R 2 + 1 R 3 ( 5 )

R 1 R 2 R 3 V V I A Figure 4 3. Connect two light bulbs in parallel and the third one in series as shown in Figure 5. Set up the ammeter and voltmeter to measure the total current,  , the total voltage drop, V , of the circuit, and the current through and voltage drop across each of the light bulbs. R 1 R 2 R 3 V I 1 I 2 I 3 I Figure 5. Combination of series and parallel circuits. Calculations and Conclusions 1. For each set of readings ( V,  ) obtained from the parallel connection, compute R = V/  for each light bulb. Also compute the power P=  V. Draw a circuit diagram. Use the resistance value for each light bulb to calculate R eq . Then compare the calculated R eq and the measured value obtained from the ratio of the voltage drop and total current. 16

2. Draw a diagram for the series circuit. Use the measured resistance value for each light bulb to calculate R eq . Then compare the calculated R eq and the measured value based on the ratio of the total voltage drop and the current 3. Draw a diagram for the series-parallel circuit. Use the measured resistance value for each light bulb to calculate R eq . Then compare the calculated R eq and the measured value based on the ratio of the total voltage drop and the total current 17

LABORATORY EXERCISE # 23 Force on a Current Carrying Conductor in a Magnetic Field PURPOSE To show how the force on a current carrying conductor in a uniform magnetic field depends on the length of the conductor and on the current in it . Equipment and supplies 10 A DC ammeter, 20  Rheostat, vernier calipers, magnet, 4 current loops, Force on a magnet apparatus, 6-Volt DC power supply, rheostat, and current balance. Discussion If a current is sent through a straight conductive wire in a magnetic field, there is a force on the conductor which is perpendicular to both the conductor and the direction of the field. If the magnetic field is uniform and perpendicular to the conductor, this force is given by: where B is the uniform field in tesla , l is the length of the conductor in meters,  is the current in amperes, and F is the force in newtons. In this experiment, the magnetic field is supplied by a strong Alnico magnet. By Newton's third law, there is a force on the magnet equal but opposite to the force on the conductor. The magnet is placed on the pan of a balance, and the force on the magnet, rather than the equal force on the conductor, is measured. The validity of equation (1) will be studied in three ways. Note that B , the field of the permanent magnet, cannot be varied in this experiment. 1. The force will be determined as a function of  when B and l are constant (Procedure section 2). 2. The force will be determined as a function of l when B and  are constant (Procedure section 3). Procedure 1. Select a current loop, and plug it into the ends of the arms of the main unit with the loop extending down. 19 F = BIl ( 1 )

Figure 1 Current balance for measuring the magnetic force. 2. Place the magnetic assembly on the balance as shown in Figure 1. Position the lab stand so the horizontal portion of the current loop passes through the pole region of the permanent magnets. The height of the main unit on the lab stand can be adjusted by sliding unit along the pole. The current loop shouldn’t touch the magnets. 3. Connect the power supply, ammeter and rheostat as show in Figure 2. 4. First, set the current to zero. Measure the weight of the magnet assembly ( F 0 ) Then turn on the current, adjust it to the desired level, and measure the weight of the magnetic assembly with current flowing ( F  ). (Use the rheostat for fine adjustment of current reading) With current flowing, the reading will be higher or lower than before. The difference in weight ( F  -F 0 ) is proportional to the force exerted on the current- carrying loop. To investigate the relationship between the current and force, vary the current from 0 to 5 A for every 0.5 A and measure the weight at each current value. 5. To change the current loop: Swing the arm of the main unit upward to raise the current loop out of the magnetic field gap. Pull the current loop gently from the arms of the main unit. Replace it with a new current loop and carefully lower the arm to reposition the current loop in the middle of the magnetic field. Four current loops, SF 37, 38, 39, and 40, are supplied with the apparatus. Measure the length ( l ) of the horizontal segment of the current loop. 6. Repeat the measurement described in Step 4 and 5 for three other current loops. 20 Permanent Magnets Current Loop Banana Plugs Balance