Physics 202 Laboratory Manual

This manual gives instructions for completing the required labs forAthabasca University’s PHYS 202 course. It is designed for usewith the PHYS 202 Lab Kit available for borrowing from theAthabasca University Library. You should also consult the labguide from your course materials package and seek advice fromyour tutor. You will need some small household items also.

These labs involve a degree of hazard comparable to that inworking in a kitchen or office. Due care is needed in handlingvarious objects, including some which may become hot. Direct orreflected entry of LASER light into anyone’s eye must be avoided.No materials used are to be connected to electrical power outlets.Athabasca University takes no responsibility for injury incurredwhile performing these labs. If you do not feel able to do themsafely it is your responsibility to withdraw from the course and notbe required to perform them.

Contents

Kit Equipment ListLab 1 Basic Electricity and GraphingLab 2 Magnetic Fields of Magnets and SolenoidsLab 3 Earth’s Magnetic FieldLab 4 Geometric OpticsLab 5 Polarization of LightLab 6 Diffraction of Light

Athabasca University 2001 Author: Martin Connors Version: 1.1 Nov 2001

Physics 202 Kit Equipment List

Lab manual

Multimeter & leads & gripper clipsResistorsBreadboardPushbutton switchbattery clip9 V batterylarge value resistor (100 kΩ to 1 MΩ)electrolytic capacitorMagnetic SensorSensor plug/battery adapterMounted SolenoidMounted Permanent ‘Marble’ MagnetRuler (note rulings on magnetic sensor also)Stand (slotted piece of wood)power resistorLight SensorLaser Pointer2 pieces of polaroid material, slide mounted, plane of polarization marked by a barGlass slideLarge paper clipVisible (Green) LED with series resistorVisible (Red) LED with series resistor2 test leads with clips or grippers (separate from those with multimeter)Transmission Diffraction Grating mounted in slideDouble Slits mounted in slideStraw with black tapeRefraction BlockPlanoconvex lens on stand(weak) Biconcave lens on standLED array with series resistor________________________________________________________________________

Graph paper supplied in this lab manual was generated by the freeware program GraphPaper Printer by Dr. Phillippe Marquis of Metz, France.

You may obtain a copy of the program from:

http://perso.easynet.fr/~philimar/graphpapeng.htm

Although it is listed as being ‘adware’ and placing advertisements on your screen, in factit does not appear to do so.

Lab 1 Basic Electricity and Graphing

Introduction:

This lab is intended to introduce you to equipment used in this set of labs and to use ofgraph paper for analysis. It is also for review of basic electrical concepts.

The flow of electricity in a circuit will be studied here. The word circuit implies a loopand this is correct - charge flows around a circuit, and in the steady state (no timechanges) it does not accumulate at any given point in the loop (contrast Lab 18 wherecharge builds up in a capacitor and the voltage changes with time). The charge (by thiswe mean a small positive test charge, in fact it is usually negative electrons which carrythe current in wires) flows from regions of high potential to regions of low potential, i.e.from a higher voltage to a lower. The voltage is maintained steady by a source of so-called electromotive force such as a battery. We will not discuss how a battery does thisbut we will examine some properties of batteries. The fact that more charge moves in agiven time when the voltage difference is higher can be expressed as I V∝ , where I isthe current and V the voltage applied to the circuit. It is often convenient to talk about acircuit blocking the flow of electricity and it is common to talk of the resistance in acircuit; since more resistance causes less current to flow (for a given voltage), we can

refine the above relation to be IVR

= , where R is the resistance of the circuit or part of a

circuit. This is known as Ohm’s Law.

The ability to control current flow, and voltages within parts of a circuit, is important,and a common element in circuits is a resistor. These are available in various resistancevalues and in various power dissipation ratings. Higher dissipation resistors are usuallylarge enough that they have their resistance value printed on them. They often are in aceramic package.

Low power resistors often have colour bands aroundthem to indicate their resistance value (usually in ohms).Resistors have a resistive material inside them.

Generally, resistance RLA

= ρ , where ρ is a property

(resistivity) of the material and L its length, A its cross-sectional area. Wires, in general, may be thought of as having very little resistance, andalmost all of the resistance of most circuits comes from that of the components. Evencomponents such as batteries have resistance although this cannot be measured directly.The resistivities of materials vary enormously and we often speak of conductors,insulators, and semiconductors.

Reference:

Physics, D. C. Giancoli, Fifth Edition, Section 18-3 (Ohm’s Law). See p. 534 for anexplanation of the resistor colour code. Also see Sections 18-1 about batteries and 18-2about currents, and 19-1 and 19-2 about combining resistors and battery resistance.Sections 17-7 (Capacitance), and 19-7 (Circuits containing resistor and capacitor).

Equipment:

Multimeter & leads & gripper clipsResistorsBreadboardPushbutton switchbattery clip9 V batterylarge value resistor (100 kΩ to 1 MΩ)electrolytic capacitor

You must supply

a coina timepiece (watch or clock with second hand or display)an assistant would be handy although you can do this alone if you are dextrous

Procedure

Read the instructions included with your multimeter. Voltage is measured from point topoint in a circuit, but current is measured by placing the meter into the circuit in series.Note that there are separate plugs in the multimeter to be used for resistance and voltage,and current readings. Do not attempt to measure anything else when in resistance mode,and ensure that there is no voltage in any circuit when measuring resistance. Do notplace the meter probes across a voltage drop when in current mode. Do not attempt tomeasure the current flow by placing the meter across the battery. If the meter stopsworking you may have blown the fuse and should contact the Science Laboratory.

For this and the following Lab, the battery may be separated from the sensorplug/battery adaptor. Please store the temperature probe and the adaptor so that thebattery is never brought into contact with them, which could damage to probe.

A separate battery clip is supplied to supply power to the circuits which you will build ona ‘breadboard’ as described below.

This procedure is mostreadily done using the‘breadboard’ supplied. Ithas arrays of holes behindwhich are conductingstrips with small clampswhich hold in place anywires placed into them.Holes form columnsparallel to the long axisand rows perpendicular toit. The columns are joinedonly in the outside twocolumns, which arelabelled + and -. We willmake more use of theholes of the innercolumns. As columnsthese are marked asa,b,c,d,e,f,g,h,i, and j. Asrows they are numbered as1 to 63 from the top. Someof these numbers can beseen in the picture at left.The most useful aspect ofthe breadboard is that

these rows are electrically connected. Anything inserted into a row is connected toanything else in that side of the same row. Connecting elements to form circuits is thusmade very easy.

The photo shows the circuit whose schematic diagram is atleft. The battery is not shown in the photo but the wire fromthe negative terminal enters the picture near the bottom andis plugged into row 46, where the bottom end of thepushbutton switch is also plugged in. The wire and this sideof the switch are thus now connected. One resistor isconnected to the other side of the switch in row 44. The two

resistors are joined at row 38, and the return connection to the battery is made at row 33.Use of a breadboard allows rapid construction of electrical circuits. By use of apushbutton, the circuit may be activated only when needed and the battery is not drainedunless it is pushed.

Parallel Resistors

Select about 10 resistors of the same value. Starting with one resistor connected betweenrows, add resistors between the same rows, recording the number of resistors and theresistance as measured with the multimeter. Use wire to ‘jump over’ the gap in themiddle. Leave this section of breadboarded circuit in place for later use.

Series Resistors

Select about 6 resistors of differing values if available (but not enormously different).Use a free area of the breadboard to build a circuit to which you add resistors in series(connected end to end) one at a time. Measure and record the resistance of each, and ofthe chain of resistors as you add them.

Current in Parallel Resistors

Connect a battery plug (without the battery attached) into the breadboard across yourparallel resistor set. Measure the total resistance of the parallel resistors. Change themultimeter to voltage measuring setting, transferring the test probe. Insert the battery andmeasure the voltage across the resistors. Calculate the current which must flow in each.How is current divided among parallel resistors? Change the multimeter to currentsetting, transferring the test probe. Remove one leg of one resistor from the breadboardand connect it to the battery lead through the multimeter. Verify that the current flowingis as expected.

Current and Voltage in Series Resistors; Battery Resistance

Connect the battery plug to the series of resistors. Measure the voltage drop across eachresistor and record this along with the resistor value. Remove the battery from the circuitand directly measure the voltage across it. You will find that the battery voltage is nowslightly higher than it was before. Consider the battery to place an extra resistor into thecircuit when it is there. What would its value have to be so that all the voltages measuredbefore would add up to the battery voltage if the drop across this battery resistance wasadded in?

Analysis

For the parallel resistors, make a graph of the overall resistance versus the number ofresistors. Use the linear graph paper supplied. Explain your result using the rules forcombining parallel resistors. You should be able to manipulate the rule for parallelresistors of equal value into a ‘law’ which involves a power law fit. Make a second graphusing the log-log graph paper supplied. Measure directly in cm the slope of this graphand determine what index this corresponds to. (Hint: the equation is log R = m(log N) +b.)

Part 2 - Introduction

A capacitor is a device which stores electrical charges. Capacitors are important parts ofmany electronic circuits, particularly those in which the voltage changes with time. Thevoltage across a capacitor depends on its geometry but is proportional to the charge on it.The constant of proportionality between the charge and the voltage is called thecapacitance: Q=CV. Changing the voltage results in a change in the charge stored. Sincethe charge must come through the circuit, and moving charge is a current, a changingvoltage in a circuit with a capacitor causes current to flow. The opposite is also true:when current flows in such a circuit, the voltage on the capacitor will change. We canstudy capacitor circuits by measuring the voltage across the leads of the capacitor.

Procedure

The capacitorsused in this labare electrolyticcapacitors. Thiscommonly usedtype has theadvantage that alarge capacitancecan be placedinto a smallcontainer. This isbought at a price- the capacitorsare polarized andmust be placedinto the circuitcorrectly or theycan be damaged.The photo showsthe capacitor(left) correctlyplaced into thecircuit. Thebattery is ofcourse also

polarized and has a + and - terminal. The battery clip is designed to attach to the batterysuch that the black wire is connected to the - terminal. The capacitor has a negative sideindicated by a band of – signs (not visible in image). This side must always be closest inthe circuit to the - terminal of the battery, even if the two wires are not directly connectedas shown.

This schematic diagram shows the circuit you shouldassemble on the breadboard. The capacitors supplied aregenerally about 470 µF. You may be used to seeing aslightly different capacitor symbol in the book. The oneused here is used for polarized capacitors likeelectrolytics, and the circular part is the negative side. Asa reminder, a + has also been put into the diagram. Use the

supplied resistor of several hundred kΩ to get a reasonable time constant. You shouldcheck the resistance but after doing so remember to move the red cable to the V socket onthe meter. Attach the voltage probes from the mulitmeter, with the grippers attached,across the capacitor, again observing the convention that red means + and black means -.The probes should be in the proper jacks to measure DC voltage and the setting on themeter on “DC V”. The initial reading should be very near zero (see below aboutdischarge if you are repeating this part).

Charging of a capacitor

Press and hold the pushbutton, and the voltage will startto slowly rise. You should record it at regular intervalsof about ten seconds. Make a graph on linear graphpaper. A graph should result looking somewhat similarto that shown at left. In the meantime, even after thepushbutton is released, charge is stored in the capacitor.

Discharge of a capacitor

Remove the battery from the its clip and thus from circuit. Press a coin across theterminals of the battery clip (not of the battery!) creating a ‘short’. You now have acircuit consisting of only a charged capacitor, a resistor, and a pushbutton switch. Notethe voltage and shortly thereafter push and hold the pushbutton. The capacitor willdischarge through the resistor and the shorted out battery clip. Record the voltage atregular intervals of about ten seconds. Make a graph on linear graph paper, which shouldshow a curve for the regular decline of the voltage. Make a graph on semilog paperrecording with the time on the horizontal axis (abscissa) and the voltage on the vertical(ordinate). Interpret the graph starting from log V = mt + b.

Analysis

When you have finished these steps measure the resistance of the resistor used, changingthe position of the leads from the multimeter as needed to do this. If the value is too highto be measured by the multimeter, 1000 with a flashing 1 will appear. In this case, use theresistor colour code chart to decode the value of the resistor.

In the textbook it is mentioned on page 570 that the expected form of the chargingvoltage is

V Vt

RC= − −0 1( exp( )),

and for discharging (see p. 571)

V Vt

RC= −0 exp( ).

Compare these equations to your equations, noting that K is one over the ‘RC timeconstant’. Knowing the values of the capacitors and resistors, verify that the RC timeconstant had the ‘correct’ value, based on the slope of the semilog graph.

Report

Prepare your report and submit it at the suggested time with the other reports. Keep acopy for yourself.

Unless you have arranged otherwise with your tutor, keep your lab report and submitreports for Labs 1,2, and 3 together.

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Regular graph paperLog-Log graph paperSemilog graph paper

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Lab 2 Magnetic Fields of Magnets and Solenoids

Introduction

This lab will allow you to determine the direction and strength of the magnetic field ofsolenoids and permanent magnets by measuring it with the magnetic sensor. From thetheory giving the field of a short solenoid the magnetic permeability of free space (µ0)can also be determined.

Reference:

Physics, D. C. Giancoli, Fifth Edition, Section 20-1 (Magnets and Magnetic Fields),Conceptual Example 20-6 and Figure 20-19, Section 20-2 (Electric Currents ProduceMagnetism), Section 20-7 (Definition of the Ampere and Coulomb), 20-9 (Torque on aCurrent Loop; Magnetic Moment), 20-11 (Hall Effect).

Equipment:

From Physics 202 lab kit

Multimeter & leads & gripper clipsMagnetic SensorSensor plug/battery adapterMounted SolenoidMounted Permanent ‘Marble’ MagnetRuler (note rulings on magnetic sensor also)Stand (slotted piece of wood)30 cm rulerpower resistorbreadboardswitch

You must supply

6V lantern battery (do NOT substitute any other voltage of battery – hazard of burns!)a small amount of sticky tape (‘Scotch’ tape, masking tape, etc.)thin book, magazines, etc. for height adjustment.

Procedure

Read the instructions included with your multimeter. Voltage is measured from point topoint in a circuit with power applied, but resistance is measured across a component withno power applied.

Please ensure that the sensor is not plugged into the sensor plug/battery adaptor whenyou attach the battery to the battery clip. Reversal of the battery contacts, evenmomentarily, can damage the sensor. Please store the probes and the adaptor so that thebattery is never brought into contact with them, as this could damage the probe.

Sensor setup

The sensors used in this lab are Hall effect sensors. They feature a current forced to flowthrough a medium which shows a strong Hall effect. This results in a voltage output fromthe sensor which is proportional to the magnetic field. The sensor chip itself is located atthe end of the small board supplied. The board also features an amplifier and a powerconditioning circuit which allows both + and – voltages to be developed from a single 9V battery. The board is coated for its protection but please do not subject it to staticelectricity, excessive heat, mechanical strain, or moisture.

Ensure that the battery is properly attached to the battery clip of the sensor plug/batteryadapter. Locate the magnetic sensor and note (write down) the sensor type (HAL400 orAllegro) and the Gain of the onboard amplifier. Plug the black plug from the sensor pluginto the centre –COM socket of the multimeter. Plug the red plug of the sensor plug intothe V+ socket of the multimeter (also labelled DC 1000V). Turn on the multimeter andturn the dial to the DC V setting. At this point a very small reading should appear on themultimeter, likely varying and with the mV (millivolt) scale indicator at upper rightactive.

Plug the sensor into the sensor plug/battery adapter. Now some larger voltage (possiblynegative) should be indicated. This is the sensor output in volts. If you have the HAL400sensor there will likely be some variation in the number displayed but that should befairly small. Most of what you are seeing is due to an offset voltage of the sensor, itsoutput relative to the a voltage reference, and some signal due to the magnetic fieldaround it. In what follows we must take account of the offset of the sensor. It generallydoes not read 0 when in zero magnetic field.

1. Field of permanent magnet

Locate the permanent magnet ‘marble’, attached to a base, in your lab kit. Align itcarefully so that the midpoint of the magnet (as indicated by the colour divide) is lined upwith the 15 cm mark on the ruler, yet that you can still see the numbers on the ruler. Tapeit in place.

The HAL version of the magnetic sensor gives a more positive reading when themagnetic field direction is upward through the board (from the label side to thecomponent side). Bring the magnetic sensor near one of the ends of the magnet.Depending on orientation you should find the voltage to go to about +7 V or –7 V. Thisis the saturation level of your sensor in a strong magnetic field. Deduce whether the poleyou are near is a S or N pole. Move to the halfway point between the poles but very closeto the magnet. Note what happens to the magnetic field and make sure this makes senseto you. Make a sketch showing the direction and strength (voltage reading) of themagnetic field at a few points near the magnet. Label the N and S poles and the colourareas of the magnet.

The strength of a permanent magnet is well indicated by its dipole moment M. As youhave seen in the reading, a current-carrying coil also can be characterized by this value(actually a vector). In fact, on the axis (line joining N and S poles) the magnetic field Bof a small magnet is given, if far enough away, by the equation

30

2 rMB

πµ

= .

If we take the logarithm on both sides we find

rMB log32

loglog 0 −=π

µ .

On log-log graph paper, this will produce a straight line of slope 3. The equation wouldthus be verified if we measure that slope. Further, if we put r=1, log r is 0, so that then we

would have π

µ2

loglog 0MB = , and knowing µ0 we could determine M.

This assumes everything is measured in SI units. In this lab it will be easier to measure r,the distance from the centre of the magnet, in cm. If we call the measurement in cm rc,then r=0.01rc, or

cc rMrMB log362

log01.0log32

loglog 00 −+=−=π

µπ

µ .

Finally, we must be able to convert our voltage measurements into the units of magneticfield, which are Teslas. The Hall sensors produce a voltage of 45 V/T for the HAL400and 50 V/T for Allegro. This is multiplied by the gain G of the amplifier as marked onyour sensor probe. Thus the magnetic field in T is given by 45VM/G for HAL400 sensorsor 50VM/G for Allegro. VM is the measured voltage due to the magnetic field. Asmentioned above, much what we see for small fields can be a spurious offset voltage.

We are just about ready to start. All that we need to remember is that our measuredvalues will have an offset to be subtracted, and that if we measure too close to the magnetour sensor will saturate. We also should ensure that no other magnets are near our workarea to affect our results.

Place the sensor into the slot of the stand, ruled side down. Be careful not to damage thesensor board. Use a small amount of paper to wedge the sensor in place securely if theslot is a bit too big. Place a book or other objects under the ruler/magnet to adjust theirheight so that the sensor is at the same height as the centre of the magnet.

Starting from near the magnet, move the sensor away along the ruler, until the readingstarts to change systematically. Then record at least 10 distance/reading values on thetable supplied. Take the last reading very far away to use to remove offset.

Place reading from ruler (estimate will suffice for very distant last value) in x column. rcis distance from centre of magnet. V is the voltage reading from the multimeter. VM is Vminus the offset value as measured far away. B is VM*45/G for HAL400, or VM*50/G forAllegro. Take readings on opposite side of magnet to fill in lower table.

Unplug the sensor from the adapter, and turn off the multimeter, while you proceed to doanalysis. This will help with stability and preserve battery life.

Use the log-log graph paper supplied to plot rc on the horizontal axis and B on thevertical (label these and give a title). Obtain two lines and fit an average line down themiddle. By measuring rise over run directly in cm measured from the plot, determine theslope in this plot. Compare to the –3 value expected.

For rc=1 (the left edge of the plot) we have

62

loglog 0 +=π

µ MB i.e. π

µ2

10 06 MB = .

From this and the known value of µ0 determine the value of M. In turn, estimate thestrength of B at the magnet poles, a value which was too strong for us to measure withour very sensitive probe.

x on ruler (cm) rc (cm) V (V) VM (V) B (T)

x on ruler (cm) rc (cm) V (V) VM (V) B (T)

2. Field of wire coil

The procedure for magnetic field measurement is very similar in this part to that in part 1.

Remove the permanent magnet from the ruler and replace it with the coil, with its centrelined up with the 15 cm mark and its axis along the ruler.

Unplug the sensor adapter from the multimeter. Plug the multimeter leads into the –COM(black lead) and DC mA/kΩ sockets of the multimeter. Place the grippers on the ends ofthe multimeter probes. Turn the multimeter on, turn the dial to the kΩ setting, and a largenumber with flashing 1 should appear to indicate an open circuit. Join the leads togetherand 0 or a very low value should appear for the resistance. Now locate the power resistorwhich may be marked with a value between 10 and 20 ohms. Measure its resistanceaccurately and record the value in ohms. Currents over 200 mA will flow in the circuitwe will build. Since the mulitmeter cannot measure currents this large we will use Ohm’slaw V=IR to determine the current I by measuring the voltage drop V through the nowknown resistor of value R. Rearranging, we get I=V/R.

Turn off the multimeter, place in the V setting, and change the red lead into the DC voltplug.

We now must construct the circuit to pass a relativelylarge current through the coil to make a magnetic field. Aswitch is used so that the coil or other circuit parts do notget too hot. In addition, since resistance changes withtemperature, we do not want changes in the resistance ofthe resistor used to let us determine the current. The circuitis very similar to that used in Lab 1 but with the coil

replacing the capacitor, and is built on the breadboard supplied. Place the resistor into thebreadboard along columns (parallel to the long axis). Take a test lead from the battery toone side of the resistor, connect the coil into the same row and side of the breadboard asthe opposite end of the resistor. Connect the other end of the coil to the same row as oneside of the switch. Use a test lead to connect the switch back to the battery (you may needto use a small bit of wire or the lead from a component stuck into a hole to clip the testlead onto).

With the multimeter connected to measure voltage across the resistor, press the button.Where previously there was no current through the resistor and thus no voltage dropacross it (or vice versa, chicken and egg fashion!), there should now be a voltage acrossit. Measure this voltage accurately (holding the switch down long enough for a stablereading). Calculate the current using I=V/R and the R measured earlier. The result shouldbe about 500 mA or so. If you get no voltage drop check the connections.

Now remove the multimeter probes and connect the magnetic sensor as before. With it inthe stand, place the sensitive part near the coil axis. Note the reading on the meter. Sincethe current is not flowing, this is the bias value. Press the button and hold long enoughfor the reading on the multimeter to stabilize (perhaps with some fluctuation if a HAL400is in use). Note the distance from the centre. Repeat, moving out taking at least 10readings as before and fill in the following tables. Record the bias at each reading ratherthan once at the end as before. This should help compensate for the weaker field. Repeaton the other side of the coil. Convert to B as before.

x on ruler(cm)

rc (cm) V (V) VB (V) VM=V-VB (V) B (T)

x on ruler(cm)

rc (cm) V (V) VB (V) VM=V-VB (V) B (T)

As for the permanent magnet we expect a dipole field with falloff along the axis

30

2 rMB

πµ

= .

The analysis to verify the –3 exponent and use the rc=1 cm value to obtain

πµ2

10 06 MB = proceeds identically to the case of the permanent magnet. However, here

we now know M and thus can detemine µ0. Simply M=NIA, where N is the number ofturns which is marked on the bottom of the coil mount. I was determined above, and Amay be determined using the effective diameter of the coil as marked on the bottom ofthe coil mount and A=πr2 where r is half the diameter. Do the algebra, then with thenumbers obtained in the experiment, determine a value for µ0. Include the units and makesure that they can be worked through to be equivalent to those in the book.

Prepare your report and submit it at the suggested time with the other reports. Keep acopy for yourself.

Unless you have arranged otherwise with your tutor, keep your lab report and submitreports for Labs 1,2, and 3 together.

Following pages: two sheets of 2 cycle by 3 cycle log-log graph paper.

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Lab 3 Earth’s Magnetic Field

Introduction

This lab will allow you to determine the direction and strength of the Earth’s magneticfield by measuring it with the magnetic sensor in different directions.

The Earth’s magnetic field is a vector field, that is to say that there is a vector value ofthe magnetic field at each point in space. Although the magnitude and direction changeas one moves from point to point, at any given point there is one vector value and thiscan be projected onto a set of axes as can any vector. Most people know that a compassaligns with the field and thus points to magnetic north (which actually is a S polemagnetically!). That is not true north and the difference is called the declination (asmarked on maps to provide compass corrections). The field is also at an angle to thesurface called the inclination. In Canada the inclination is usually fairly large, in excessof 45°.

By measuring the projection of the Earth’s field onto the measuring device while movingit around, the vector field can be determined.

Reference:

Physics, D. C. Giancoli, Fifth Edition, Section 20-1 (Magnets and Magnetic Fields),Conceptual Example 20-6 and Figure 20-19.

Equipment:

MultimeterMagnetic SensorSensor plug/battery adapterStand (slotted piece of wood)Paper protractor (glue sheet supplied to cardboard)

You must supply

a small amount of sticky tape (‘Scotch’ tape, masking tape, etc.)thick book, small piece of furniture, etc. to provide a movable vertical surface

You should also know the local direction of true north by reference to local streets (oftenaligned N-S or E-W) or maps. Be careful, since even in areas with a very regular streetgrid, that grid may not be aligned with the cardinal directions (NSEW).

Note that an amazing amount of map information may be had at www.mapblast.com.

Procedure

Locate the printed protractor sheet supplied and glue it to a piece of cardboard of roughlythe same size. We will call this a protractor.

Horizontal Field

First we will find the direction of the horizontal field. The horizontal field componentalways does generally point northward. If the angle between the normal (perpendicular)to the sensor and north is θ, then we will measure a voltage proportional to BHcos(θ−δ),where BH is the maximum value of the horizontal component.

It follows that (see diagram) if we measure the anglefrom the North (N) then the sensor (grey bar) with itsnormal shown toward the bottom (component side)would give an output proportional to BHcos(θ−δ) sincethis is the angle between from the sensor normal beingaligned with the field.

Place your protractor flat and away from any magnetsor magnetic material (iron, etc.) with its top toward thenorth. Tape it in place. Place the sensor in its stand andattach it to the multimeter as you did in Lab 2. Set thesensor on the protractor with its component side facing

north and align it so that its normal faces north exactly by using the markings on theprotractor. Record the value of the voltage shown on the multimeter averaging smallfluctuations (mentally) if necessary. Next rotate the sensor clockwise 30° (note that thismay not be the basic interval on the protractor) and repeat. It is not necessary that thesensor be centred on the protractor but the angle should be carefully lined up, at eachposition, so that the sensor is parallel to the appropriate angle marking on the protractor.Continue for the whole circle. Verify that the 360° value is the same as the initial valuebut do not record this value again. Leave your protractor in place for the moment.

Using ordinary graph paper supplied make an appropriately scaled graph with the angleon the horizontal axis and the measured voltage on the vertical. You should obtain asinusoidal curve with an offset due to bias. Take the average of all values recorded andplot a horizontal line at that ‘y’ value. This line should bisect the curve and provide itszero value.

Although the curve should have its maximum value for θ−δ=0, i.e. when θ=δ sincecos(θ−δ) is then cos(0)=1, this is not an easy position to find on the graph since the coscurve is flat there. It is best to find when the debiased curve goes through 0 and subtract90°. Use your graph to determine δ, the declination at your location. This is a purelygeometric exercise and we do not need to convert the voltages to magnetic field values.We now proceed to find the total field.

N

BHδ

θ

Vertical component

Without going into fancy trigonometry, it should be clear that the overall field directionlies in the vertical plane where the horizontal component of the field has its maximum.That vertical plane is at the angle δ from the north that we just determined. If we measurethe field in that plane, it will vary much as the horizontal field did, but the maximumvalue will be along the overall field. We can also measure that maximum value todetermine the strength of the Earth’s field.

Note by marking in some way what the direction ofthe declination is. Take your protractor and tape it toa book, small piece of furniture, or similar objectwhich will allow it to be held steady and vertical. Inthis picture the total field is shown in the plane yourprotractor is now in (i.e. the vertical plane at an angleδ from the north). The angle from the vertical to thesensor normal is labelled as ω. The angle between thevertical and B is not labelled here but we will refer toit as β. So the sensor output should, similarly tobefore, be proportional to Bcos(ω−β). In this case Bwill be the magnitude of the Earth’s magnetic field atthe location of measurement. This is often referred to

as the intensity.

Put the sensor against the protractor with its component side facing upward and align itso that its normal faces upward exactly by using the markings on the protractor. Recordthe value of the voltage shown on the multimeter much as before. Similarly, obtain awhole rotation’s worth of values spaced by 30°, and verify that the 360° value is the sameas the initial value but do not record it. You now have all the information you need.Disconnect the magnetic probe from the adapter.

Make a graph of the voltage versus angle ω much as you did before, and similarly debiasit. Find the value of ω for which the corrected voltage was maximum, again using theproperties of the cos function for best accuracy. This angle should be greater than 90° ifyou live in the northern hemisphere.

We now know not only the two angles to specify the field, but can go further. We knowthat the maximum value of the voltage from the graph we have just made for the verticalplane corresponds to that of the total field. Determine this maximum voltage and use theconversion factors from the previous lab to convert it to a magnetic field value. Youshould expect a value of order 50 µT if you live in Canada.

Prepare your report and submit it with the other reports. Keep a copy for yourself.

Next pages: Protractor sheet Linear graph paper (2 sheets)

up

B

ω

Lab 4 Geometric Optics

Introduction:

In this lab you will investigate geometric optics, which is based on the approximationthat light travels in straight lines except when it bends at interfaces. You will investigatethe index of refraction and total internal reflection. You will set up a small ‘opticalbench’ and determine some properties of lenses and images. Optical surfaces may beplanar, convex, or concave. You can remember that concave means going inward (like acave). A laser beam can be used to determine the straight line travel of light. Aninexpensive laser pointer provides a convenient source of laser light (see the next lab formore discussion of the physical nature of laser light).

DO NOT LOOK INTO THE LASER BEAM OR ITS DIRECT REFLECTIONS!

Reference:

Physics, D. C. Giancoli, Fifth Edition, Chapter 23 “Light: Geometric Optics”.

Equipment:

Planoconvex lens on standBiconcave lens on standGlass rectangular prism (a.k.a. Refraction Block or glass slab)LED array with series resistorStandRed LED with series resistorLaser pointerLarge Paper ClipRulerStraight pinsmillimeter graph paper (from this manual)2 test leads with clips or grippers (separate from those with multimeter)

You must supply

6V lantern batterycardboard (heavy corrugated type) and/or small piece of wood (2 by 4 or similar, ca. 10 cm length)paperdrawing triangletack (thumbtack or similar)

Procedure

1. Snell’s Law and Index of Refraction

Set up the refraction block on a piece ofpaper. Tape the paper to a piece ofcardboard into which pins may be stuck.Find the ‘on’ button on the laser and putthe large paper clip onto the laser in sucha way that it both holds it steady andholds the button in so that the laser stayson. Set up the laser point to shine throughthe glass as shown. BE CAREFUL NOTTO LOOK INTO THE BEAM OR ANY

REFLECTIONS OF THE BEAM. Place straight pins in the transmitted beam starting atthe far end (beyond B) as shown, so as to be able to trace the beam back. Place straightpins in the weaker reflected beam as shown at lower right. Finally place pins in theincident beam starting from A. You will be able to tell when the pins are in the beam asyou will see the beam on them. Trace the refraction block onto the paper. Remove thesetup and turn the laser off. Trace the incident and reflected rays. They should intersect atpoint A on the surface of the glass block. Draw the perpendicular at A carefully to reachpoint C and continue line AC on the incident side.

By using trigonometry and the furthest pin marks from point A on the incident andreflected light lines, determine the angle of incidence and the angle of reflection.Compare.

Trace the transmitted beam and determine point B. Determine the angle from theperpendicular at which the beam left the glass. Using the distances BC and AC determinethe angle of refraction at point A.

Since the index of refraction of air is essentially 1, use Snell’s law to determine the indexof refraction of glass based on the angles you have determined.

AC

B

2. Total Internal Reflection

Setup up the equipment on paper muchas before but this time shine the lightnearer a corner of the block as shown.Adjust the angle of incidence. Whenthe angle of incidence (measured fromthe normal) is large enough, light willemerge from the block at point C.When the angle of incidence declines

to a certain value, there will be a point when no more light emerges at C and total internalreflection takes place. DO NOT LOOK ALONG THE BEAM TO DETERMINEWHETHER LIGHT IS COMING OUT AT C, LOOK ONLY FOR A SPOTCAUSED BY THIS LIGHT STRIKING AN OBJECT (SUCH AS A FINGER).Using pins as before determine the angle of incidence at A when this happens. UsingSnell’s law to get the angle of refraction at A. Figure out what that gives as an angle ofincidence from glass to air at C. Again use Snell’s law to figure out the what the angle ofrefraction (in the air) would be at the angle where total internal reflection starts to occur.

3. Focal Length

Find the planoconvex converging lens among your materials. Form an image of a distantobject (Sun or distant scenery) onto a sheet of paper (with this small lens there is littlerisk from the Sun's heat). Using a ruler estimate the focal length of the lens.

Locate the LED array which is on a small circuit board. Place the circuit board in a standand connect to the 6V lantern battery using the test leads with clips. The LEDs are solidstate lamps. They are also diodes, which means that they pass electric current only ifhooked up in the proper direction. If they are reversed they pass no current and give offno light. If the LEDs give off no light they are simply connected to the battery backwardsand this does them no harm. In that case reverse the leads connected to the battery andthe LED array should light up in a nonsymmetic pattern.

Take the 1 mm ruled graph paper supplied and attach it to cardboard or a piece of woodin such a way that it stands on its own and is vertical, with the ruled area centred aboutthe same height at the LED array. This is the ‘target’.

Set the lens on its stand on a level surface between the LED array and target. It shouldhave its centre at roughly the height of the LED array and the LED light should shine inits direction. Place the ruler alongside it. Line up the target and LED array with the ruleralso to give a straight line to move things along and be easily measured.

Dim the room lights and move the target back and forth until an image of the LED arrayis seen on the target and is in the best possible focus.

ABC

Determine the distance do between lens centre and the LED array face, and the distance difrom the lens centre to the image. Record in the table. The spacing of dots on the LED is1.089 mm in the vertical distance and 1.013 mm in the horizontal (there are 7 dotsvertically and 5 horizontally but only a subset light up). Determine the spacing of dotsvertically in the image and record . If the image is inverted record the height as a negative

value. Use the lens equation fdd io

111=+ to determine f and the magnification formula

o

i

o

i

dd

hhm −== to fill in the f and m column values. Repeat for at least 5 positions.

Disconnect the LED array from the battery when you have finished.

di do hi ho (mm) f m1.089

Comment on the values of f and m which you have found.

4. Diverging Lens

A diverging lens usually has at least one concave surface. Since it does not form realimages by itself, the simple method used to estimate its focal length by forming an imageof a distant object cannot work. The easiest way to find the focal length of a diverginglens is to use it in combination with a converging lens. If it is placed between theconverging lens and its image, and is of a focal length larger in magnitude than theconverging lens, the image will reappear further from the converging lens. Thus theoverall focal length will be longer. This effect is used to increase the magnification of atelescope with a “Barlow” lens, or with cameras in a “tele-extender”.

Since focussed light no longer passes through the image initially formed by theconverging lens, insertion of the diverging lens converts it into a virtual image. Thisvirtual image is then used as the object point for the diverging lens but with a negativedistance from that lens.

The diagram below shows the path of light leaving a point on the object at left, passingthrough the lens, and forming an image at the distance di from the lens.

The right hand side of this diagram is copied below, but with the diverging lens in thelight path leading to the original image, which now would be a virtual image.

That virtual image is now at a distance do’ from the diverging lens and the new image isformed at a distance di’ from the diverging lens. We can measure both do’ and di’ and usethe lens equation (remember do’ is negative) to determine the focal length f’ of thediverging lens (which should also come out negative).

Set up the converging lens as in the previous section and determine the position of thereal image formed. Mark this in some way, and place the diverging lens not too far aheadof the real image but toward the converging lens. Place the target screen to focus the newreal image, which should be behind the original one (i.e. farther from the converginglens). Measure do’ and di’ and determine the focal length of the diverging lens supplied.

do di

di

do’

di’

5. Lensmaker’s Equation

The final exercise in this lab is to verify that the lensmaker’s equation applies to aplanoconvex lens. In this case one side of the lens is flat and thus has an infinite radius ofcurvature. The lensmaker’s equation then can be re-formed as

1121

111)1(11)1(1R

nR

nRR

nf

−=

∞

+−=

+−= .

If we regard R1 as simply R, the only radius of curvature in the problem, we get f=R/(n-1). This makes sense since if R is large then the lens is not very curved and the focallength is long. Typically lenses are made of glass with index about 1.5, so a planoconvexlens should have a focal length roughly twice the radius of curvature of the curved face.

We will use a subtle method to determine the radius of curvature. Lenses are in practicespherical surfaces since that is the easiest shape to grind. If we rotate a sphere about itscentre its appearance does not change. The same is true about reflections from the sphere:due to its symmetry any reflection will not change if the sphere undergoes any rotationabout its centre. The same is true of any part of a sphere as long as the reflection remainson it. We will simply rotate a piece of paper carrying the lens about a fixed point andmove the lens around on the paper until a reflection does not change as we rotate.

Take a piece of paper and place it on a piece of cardboard. Place a thumbtack near oneend and into the cardboard below. The paper should rotate freely about the tack. Take theplanoconvex lens and place it on the paper. Take the Red LED with series resistor andhook it to the 6 V battery much as you did for the LED array (again there is only onedirection which will make it light up). Set the LED up so that you can see its reflection inthe convex face of the lens. There will likely be two reflections visible, and the one fromthe convex face alone is the smaller. It is helpful to line the two reflections up to ensurethat you are looking along the axis of the lens. Move the paper to rotate around thethumbtack and in general the small image will move. Move the lens holder around on thepaper and there should be a position where the small image does not appear to movewhen you move the paper. Measure the distance from the thumbtack hole to the front ofthe lends when in this position. This is the radius of curvature of the lense.

Assume that the index of refraction of the lens glass is the same as that of the glass prismused in the first section. From that verify that the result of lensmaker’s equation is correctfor the planoconvex lens, given the focal length you have alredy determined. Describethe size of any possible discrepancy and suggest a reason for it.

Prepare your report and submit it at the suggested time with the other reports. Keep acopy for yourself.

Unless you have arranged otherwise with your tutor, keep your lab report and submitreports for Labs 4,5 and 6 together.

Lab 5 Polarization of Light

Introduction

Our eyes are not in general sensitive to the orientation of electric fields in light waves,and for much of the light in nature this orientation is random in any case. However,reflection from certain objects or interaction with certain materials can favor a certainpolarization. For example, light reflected from a nonmetallic surface like a highwayreflects best if its electric vector is parallel to the surface. Thus, highway glare ispreferentially polarized parallel to the ground. If one wears Polaroid sunglasses whichpass only vertically polarized light, this glare reflection will be largely stopped whileother randomly polarized light will pass (at reduced intensity). Some light such as laserlight is produced polarized.

Reference:

Physics, D. C. Giancoli, Fifth Edition, Sections 24-10 (Polarization), 28-11 (Lasers)

Equipment:

Multimeter & leads & gripper clipsLight SensorLaser PointerSensor plug/battery adapter9 V battery2 pieces of polaroid material, slide mounted, plane of polarization marked by a barGlass slideCardboard Protractor

You must supply

Area in which to work, where ambient light level can be varied easilyFlashlightMasking or similar tape and/or sticky labelSmall scissors

Note: please avoid touching any optical surfaces, they are adversely affected by dirt.Also please do not attempt to clean them as you may scratch them; we clean them.

Procedure

Take the cardboard protractor used in the previous labs and cut a small (less than 1 cmdiameter) hole near its centre.

1. Randomly polarized light

An ideal polaroid would transmit half the light falling on it. Commercial polaroids suchas we use transmit less since they also contain dyes.

Connect the light sensor (sensitive area is under the clear 1 mm hemispherical lens on theIC package at the end of the sensor) to the sensor plug/battery adapter. Connect to themultimeter with the black lead to –COM and the red lead to DC V, and turn on themultimeter. Note that the sensor responds sensitively to changes in light level and that innormal to bright room light it saturates at roughly 6.5 V output. When not saturated thesensor gives a voltage directly proportional to the light intensity (for a constant colourbalance) falling on it. The sensor detects light from a wide range of directions and canpick up shadows which you might not notice, so be careful moving around it when doingmeasurements.

Place the sensor in an area where there is light falling on it from a fairly small source(like a ceiling lamp) yet it is not saturated. Tape it in place. Record the voltage level.Place the glass slide gently touching the sensor and between the light source and sensor.Record the voltage level. Remove the slide. Find the transmission of the glass slide bytaking the ratio of the voltage level with the glass slide in place to that with it absent.Explain the major sources of light loss when the glass is present.

Tape one of the polaroids to the back of the protractor cardboard, so that it may be seenthrough the hole. Align it with the 0 degree direction. Place this over the light sensor.Note the original voltage level and that with the polaroid covering the sensor. Computethe transmission of the polaroid. Rotate the polaroid and see whether the voltage levelchanges. Explain in terms of the polarization properties of normal room light. When youhave finished, tape the polaroid and protractor in place over the sensor.

An ideal polaroid would pass 0.5 of the light intensity, but due to the presence of dyethese polaroids pass less. If I=I0*TD*0.5 then compute TD. TD includes losses due to thedye but also due to reflection.

2. Transmission of polarized light

The light coming through the polaroid is now linearly polarized. If we place a secondpolaroid over it, the light from that will be linearly polarized and then will have to passthe second polaroid to get to the sensor. As explained in the text, the amplitude (ofelectric field vector in the light) passed is proportional to the cosine of the angle betweenthe two polaroids. This is because it is the projection of the field of the first onto thepolarization direction of the second which can pass. However, the light intensity whichwe detect is proportional to the amplitude squared, so that we expect a variation I=I0cos2θas we rotate one polaroid with respect to the other.

Place the second polaroid with its axis parallel to that of the first. Note the new voltage.At this position, linearly polarized light from the first polaroid enters the second parallelto its axis. From a polarization perspective, no light is removed from the beam. Onlylosses due to dye come in. Contrast this to the case of placing the first polaroid over thesensor. In that case, a 0.5 reduction in intensity came from rejecting light not properlypolarized, and in addition a factor TD multiplied in due to the dye. Verify here that thereduction in placing the second polaroid is only by a factor TD.

This should make it clear that the polarized beam referred to above and in the text is ofamplitude 0.5TDII if II was the original unfiltered incident intensity. Thus I0=0.5 TD II .Due to the second passage through dye, a further factor TD is introduced as we have justverified. Thus we expect the overall effect of rotating one polaroid with respect to theother to be I = 0.5 TD

2 II cos2θ . Since neither TD nor II depend on the angle we can defineI|| = 0.5 TD

2 II to be the intensity when the two polaroids are parallel. We then expectI=I||cos2θ as we rotate one polaroid relative to the parallel position. Since I is proportionalto the voltage V, an identical form holds for measured voltage: V=V||cos2θ.

Rotate the top polaroid through a full circle in 15° increments and record the voltagevalues. Unplug the sensor when you have finished the measurements. Remove thepolaroid taped to the back of the protractor so that you will not forget to return it.

Plot the voltage on graph paper as a function of the angle. Verify that the curve resemblesthat expected.

To show quantitatively that the curve is proportional cos2θ, plot your data on the verticalaxis but on the horizontal axis place cos2θ, rather than the angle. When you have donethis verify whether the resulting graph shows the expected result, and state your argumentin your lab report.

3. LASER Polarization

LASER* light is produced by ‘cloning’ photons. Not only is the intensity high since allthe photons are identical and in phase so that their electric vectors add (to square theintensity) but they are identically polarized. Modern laser pointers use transitions insemiconductors and produce a slightly ‘lower quality’ laser light than the types describedin the book. Nevertheless all of the important qualities of laser light are present includinga high degree of polarization.

It is easy to show that laser light is highly polarized. We could do it by takingmeasurements as we did in the previous section but a filter would be needed to reduce theintensity, and the geometry would be a bit complicated. So we will settle for seeing thevariation in the brightness of a beam projected onto a wall.

DO NOT LOOK INTO THE LASER BEAM!

Locate the small laser pointer in your lab kit. Point it at a painted wall and press thebutton. You will see a bright red spot. There is no danger in looking at such scatteredlaser light. Place a polarizing filter between the laser and the spot on the wall, beingcareful that the reflection from the surface of the filter does not enter anyone’s eye.Rotate the filter and you will find that the brightness of the spot varies. Describe thebrightness variation of the spot as you make one full rotation of the filter and explain whythis is consistent with the beam being highly polarized.

The eye has trouble detecting changes in bright things but can detect small changes inless bright light. Rotate the laser pointer and filter with respect to one another until thespot is at minimum brightness. At this time the axis of polarization of the laser beam andthe filter are at right angles. Place a small piece of tape on the laser pointer and make amark to indicate its direction of polarization, bearing in mind that it will be 90° from thatof the filter (which is marked on it).

* LASER = L.A.S.E.R.=Light Amplification by Stimulated Emission of Radiation. Wewill use this as a common noun ‘laser’ rather than an acronym, from this point on.

4. Brewster’s Angle

The text explains that there is an angle, called the polarizing angle or Brewster’s angle, atwhich reflected light is 100% polarized. It is relatively easy to demonstrate this using theglass slide and a polarizer. Hold the glass slide nearly horizontal in one hand and thepolarizer in the other with its axis vertical. When Brewster’s angle is made with a lightsource the reflection will be 100% polarized horizontally and will not be able to pass thepolarizer. Find a light source such as a ceiling lamp where you have some room to moveback and forth. Align the glass slide and your eye so that you can see the reflection of thelight souce. Move the polarizer into your line of sight and the reflection will get dimmerin comparison the dimming of the slide frame, since the reflection has a lot of polarizedlight in it. By moving the glass slide around and moving the polarizer in and out of theline of sight you should be able to find a position at which the reflection disappearscompletely. In this case the angle from the light to the slide normal, which is the same asthe angle from the slide normal to you eye, is the Brewster angle.

To measure the Brewster angle, we will use the opposite effect. If the reflection is 100%polarized parallel to the glass surface, that means that light polarized perpendicular to theglass surface is not reflected at all. We have a source of polarized light in the laserpointer and we know in which direction it is polarized. If we shine the laser pointer ontohorizontal glass with the plane of polarization vertical, there should be a point near theBrewster angle where very little light will be reflected. Further, if we rotate the laserabout its axis while holding it there, the brightness of the spot should vary dramatically.If we rotate the laser beam’s axis of polarization by 90°, we will come to a position notonly where the reflected light is 100% polarized, but where it is 100% reflected. This issince the incident light is already 100% polarized. For the right polarization, Brewster’sangle allows 100% reflection or transmission!

Place the glass slide on a horizontal surface such as a floor. Tape a piece of paper on anearby vertical surface such as a door. Place the mark on your laser pointer, whichindicates the plane of polarization, at the top and turn on the pointer. Reflect a spot fromas close to the centre of the slide as possible onto the paper. Move the pointer arounduntil the spot becomes as weak as you can find. You can test that you are near theBrewster angle by rotating the laser pointer on its axis: the spot should brightenconsiderably. When you are as near the Brewster angle as possible, mark on the paper theheight of the spot. The distance from the reflecting point (centre of the slide) to the wall,divided by the height of the spot, is the tangent of the Brewster angle. Since the mediumis air, we know that tan θp = n, where n is the index of refraction of the glass. Determinethe Brewster angle and the index of refraction of glass based on your measurements.

Prepare your report and submit it at the suggested time with the other reports.

Unless you have arranged otherwise with your tutor, keep your lab report and submitreports for Labs 4,5 and 6 together.

Lab 6 Diffraction of Light

Introduction

This lab is intended to demonstrate some of the wave properties of light. Although on thelarge scale we regard light as travelling in straight lines, its wave properties becomeimportant when it interacts with objects similar in size to its wavelength.

Reference:

Physics, D. C. Giancoli, Fifth Edition, Sections 24-3 (Interference), 24-5 (Diffraction), 24-6 (Diffraction Grating).

Equipment:

Multimeter Light SensorLaser PointerLarge paper clipVisible (Green) LED with series resistorVisible (Red) LED with series resistorPushbutton switchSensor plug/battery adapter9 V battery2 test leads with clips or grippers (separate from those with multimeter)RulerTransmission Diffraction Grating mounted in slideDouble Slits mounted in slideStand for slideStraw with black tape

You must supply

Dark area in which to workFlashlightTape measure or meter stick6 V lantern batteryObjects such as books or magazines on which to place items and vary their height

Note: please avoid touching any optical surfaces, they are adversely affected by dirt.Also please do not attempt to clean them as you may scratch them; we clean them. Thediffraction grating is relatively fragile.

Procedure

Locate and identify the optical components needed. The diffraction grating resembles theglass slide but is lighter and shows coloured fringes around lights when they are viewedthrough it. The double slit slide has a number of pairs of clear bars on a dark background.The Red and Green LEDs are red and clear (with greenish tinge) respectively.

1. Wavelength of light

A transmission diffraction grating consists of many finely ruled parallel lines with aspacing close to the wavelength of light. The rulings on inexpensive gratings are notopaque and so the performance deviates from the ideal described in the book. The 0order, corresponding to direct transmission, is very bright compared to the m=1 order andthe other orders are much fainter yet. In practice only 0 order and the two m=1 orderspectra are visible.

The grating supplied has the separation d marked on it. By holding it up to a lightdetermine in which direction it disperses light. The light should show zero order in whitelight with the dispersed first orders beside it in the direction of dispersion. Place thegrating in the slide stand so that it will disperse in the horizontal direction. Place thestand on a horizontal surface about 10 cm from a wall or other vertical surface. Shine thelaser through the grating toward the wall. In addition to the spot corresponding to the 0order transmission, two other spots should appear horizontally separated from it. Theseare the first order spectra. Since laser light is basically monochromatic these spots are notlarge. DO NOT LOOK INTO THE LASER EITHER DIRECTLY OR THROUGH THEGRATING.

Carefully align the grating to be parallel to the wall. Place the laser in the large paper clipprovided in such a way that the clip clamps its on button and holds it on. The clip willalso permit the laser to be placed on a flat surface without rolling. Place it carefullyperpendicular to the grating so that the laser beam shines through onto the wall. Tape apiece of paper to the wall so that the 0 order beam is roughly centred.

In the diagram (showing the viewfrom above) the distances from thezero order spot to the first orderspots are Y1 and Y2. The distancefrom the grating to the wall is X.Mark the 0 order spot and the twofirst order spots with a pen. Notebeside each what it is. Leave thepaper on the wall but remove thelaser pointer and remove it from thepaper clip so that it turns off. Donot move the grating.

Y1

Y2

X

LASER

Grating

Light Emitting Diodes (LEDs) are solid-state light emitters which are widely used inmodern electronic devices. They come in several colours (and infrared) and most arefairly monochromatic. A diode passes current with near-zero resistance only when it ishooked up in one direction; in the opposite direction it has extremely high resistance andallows virtually no current to flow. In the conducting (forward) sense the resistance is solow that current through the device could become very high and lead to thermal damage.A series resistor is thus used so that the resistance of the diode-resistor combination ishigh enough to limit the current. The value of the series resistor has been chosen so thatroughly 20 mA of current flows. This results in about 0.1 W of heat dissipation in theresistor, which does not seem like much. However, since the resistor is relatively small itdoes heat up noticeably in order to dissipate that heat.

We will use a tube made of a straw in order to have a narrow beam from the LEDs andthus be able to distinguish 0 and first order light when the beam passes through thegrating. Locate the tube and firmly insert the Red LED into one end. Use jumper wires toconnect each end of the LED to the 6V battery. If the LED does not light, reverse theconnections. Place the straw in about the same position as the laser was, perpendicular tothe grating. You will likely see the 0 order with the room lights on. Adjust the zero orderto be centred on the same position as the marking for the 0 order spot from the laser.Tape the straw in two places so that it is securely held in this position. Dim the roomlights and you should see the first order spots. Mark as best you can their positions andlabel.

Disconnect the red LED from the battery. Use caution if the resistor and/or LED becamehot and remove the red LED from the straw. Firmly insert the green LED in its placebeing careful not to move the straw. Connect the green LED to the battery to obtain lightoutput. The 0 order spot should line up with the previous ones. Dim the room lights andthe first order spots for the green LED should become visible. Mark their positions asbest you can and label.

Disconnect the green LED from the battery. Use caution if the resistor and/or LEDbecame hot and remove the green LED from the straw. Remove the paper from the wall.

Measure the distance X from the grating to the wall.

Analysis

Measure Y1 and Y2 for each light source from the paper. Average these to obtain Y, thedeviation of the beam. Averaging should reduce the effect of measuring error or possiblemisalignment. Clearly Y/X is the tangent of the angular deviation of the beam. Find θ,the angular deviation. We know that sinθ = λ/d in first order. Determine the wavelengthof the laser beam, the red LED, and the green LED. Compare these to known values forthe appropriate colours.

2. The Real Double Slit

As for the diffraction grating (and for the same reason) the maxima in the ideal doubleslit interference pattern occur when d sinθ = m λ, with m=0,1,2,… the order and d thespacing between the slits. A real double slit, however, is made of two single slits and foreach of these there is a diffraction pattern with minima when D sinθ = n λ, withn=1,2,3,… and D the width of the slit. Usually D<d since the distance between slitswould be larger than their width. The real double slit thus has a diffraction patternderived from both the interference between slits and the diffraction from each slit. In factto a good approximation the two patterns can be multiplied together to give the overallpattern. That pattern features closely spaced maxima because λ/d, which is their spacing,is smaller than λ/D which is the spacing of the diffraction minima. If we know λ and thespacing of the maxima, we can determine the slit spacing d. From λ and the spacing ofminima of the larger diffraction pattern, we can determine the slit width D.

Since the laser source is bright it is possible and useful to use a large baseline and workwith large diffraction patterns. Place the double slits slide in the slide stand and set up thelaser in the paperclip to be on and pointing through the smallest double slit onto a distantwall (3 m or more). Tape some paper to the wall centred on the beam. You will likely seesome maxima with room light on, but dimming the light will allow many more to beseen.

Mark on the paper the position of the beam centre, and with different symbols the closelyspaced maxima and the positions of the overall minima with larger spacing.

Measure the distance from the slide to the wall.

For several of the maxima use d sinθ = m λ in a similar analysis to that done to find thewavelength, only now determine the slit spacing d. You will need to keep track of m.

Repeat the analysis using the minima and D sinθ = n λ, to obtain the slit width D. Youwill need to keep track of the minimum count n.

Do this again for one of the other slits with larger spacing.

Comment on your results.

3. Complementarity and the Width of Small Objects

We have not included an experiment with a single slit. A surprising result in optics is thata small obstacle creates exactly the same diffraction pattern as does a small slit of thesame dimension! This is known as the complementarity principle of optics.

A slit of the width of a human hair and a human hair will produce exactly the samediffraction pattern, described by the D sinθ = n λ equation.

Obtain a piece of human hair and suspend it in the laser beam, projecting across the roomas in the previous section. You will see scattered light from the surface of the hair when itis in the beam. The hair will create a diffraction pattern around the main spot, but due toits small size (equivalent to a very narrow slit) the pattern will be faint. You will need todim the room lights to see it.

As before mark the positions of minima in the pattern on a sheet of paper and record thedistance from the hair to the wall.

Use several minima to determine the value of D, which is the width of a human hair.Average these results and comment on the value you obtain.

Prepare your report and submit it with reports 4 and 5. Keep a copy for yourself.

Congratulations! You have now finished the laboratory portion of Physics 202. Pleasereturn all borrowed laboratory materials to the university library. Pack carefully and referto the packing list as this kit contains many small parts. You do not need to return this labmanual. If you encountered any difficulties with the materials in the lab kits pleaseenclose a note describing the problem.