Physics72.1 Laboratory Manual

ilI

tr

li F

rp

$ffirffiWIWr

Es= G

ea

iD

C' CD

*'

PHYSICS 72.1,

LABORATORY MA}{TJAL by'

Rommel C. Gutierrez Maricor N. Soriano Rumelo Amor Marie Ann Michelle Calix

Edmundo Casulla LizaDavtla Michelee Patricio PetetJohn Rodrigo Miguel Yambot

-(a

z

.?

Cooer design b1: Codeon

U. Toralba

NrP-0 0 6 t

6fl

qc

3r

fsqt ).ool

,t.ft

Vair+

s.t\nu

Fitst Edition, June 2000 Second Edition, Jun e 2001, Edited by: Edmundo Casulla

LizaDavtla Christine Ison Jonathan Palero PeterJohn Roddgo Miguel Yambot

--

w

-- E6"&? ^;U 1L^2I"7

Policies and guidelines

i

EXPERIMENTS

1. Electric field and field potential

1

2. Ohm's law 7

3. Resistors in series and parallel 19 4. Ktrchoff's rules 25 5. Electromagnetic induction 33 6. Introduction to alternating current (ac) circuits 43 7. Optical disk: reflection and refraction 57

8. Image formation using thin lenses 67 References 74

1.

Grading System Laboratory Reports Practical Exam N-ritten Final Exam Recitation, Quizzes, etc

TOTAL

60% 1,5% 1.50

10% 1,00%

Grade Equivalent

>x 92 >x 88 >x 84 >x 80 >x 76 >x

100

Z.

72 >x 68 >x 64 >x 6o >x 50 >x

> > > >

68 +2.50 64 +2.75 60 -+3.00 5o +4'oo > 0 ->5.00

Laboratory Report Guidelines I.

Data sheets (or the manual itself) are collected by the instructor at the end of each experiment, and ate returned during specified periods for wdting the report. II. Laboratory reports are accomplished individualty and only during r.port-*riti.rg sessions. They are collected at the end of these periods. References (textbooks and journals only) are allowed during these sessions.

3.

Genetal Guidelines

I.

If a student misses an experiment, he has to present a medical certificate (in cases where applicable) from the UP Infirmary within.seven (7) days of the absence, or within the first day he is able to come to class. Failure to do so forfeits the student's right to a make-up experiment. Only two experiments are allowed for make-up. II' In the event a student misses the final exam or practical exam, a grade of "INC" is given with the tematk "missed the final exam" or "missed the practical exam." III. A grade of "DRP" or dropped is given upon the initiation of the student, and provided he submits a copy of the dtopping slip to his instructor. The same rule applies to students who file a leave of absence pOA). fV' A grade of "4.0" impJies that the student should retake the course as there is no

v.

A student who

has not submitted at least 4 experiments by the droppingdate automatically be given a failing grade of "5.0" if the student has not dropped.

National Instirute of Physics, Up Diliman

will

I}iTRODUCTION The electrostatic force on charge qo due to charge 4 is given by (Coulomb's law):

F-

kq!,,

r

i

per charge qoin moving the charge berween rwo

points

potential difference AZbetween the points: (1

.1)

LVu,

where r is the distance between the charges, i is the unit vector pointing from q to ,q, and the consrant ,€ is 9.0 x 10e N-m2 /cz. The direction of the force on a charge may be determined :sing the law of charges. Like charges repel and ';ilike charges attr^ct.

(unit is N/C).

-Vz-V, -vru =it Ot 40)

where

Q.4)

dl is thepath from A to B.

For a finite path length Ad the magnirude the electric field is given by:

lal=+

The electric field is defined as the electrical :orce per unit charge, or

-tr lr-_

in an electric field, E is called the

of

(1.s)

If a charge is moved ilong a path at right (1.2)

4o

na the case

of the electric field associated with a s:agle source charge Q, the magnitude of the sectric field a distance r away from the charge q :s

angles

ot perpendicular to the field, there is no

work done M=0), since there is no force

component along the path. Then along such p

path,

LVru =Vt -Ve

=Y=g.

(1.6)

4o

E

r =9r =L=\!r?= r Qo q,r'

If

(1.3)

a free charge, 4,, is released in the vicinity :i a stationary soufce charge, it would move .{ong a line of force. Since a free charge moves '- an electric field by the action of the electric iorce, work is done by the field in moving the 'd:arge from one point to another. The work IV

Vu

=Vn'

(1.7)

Hence, the potential is constant along paths peqpendicular to the field lines. Such paths are called equipotential lines (or equipotential surfaces in three dimensions).

oBIECTT\rE To determine the equipotential surfaces in an electrolytic ank and estimate the direction and the snitude of the electric field.

\Ea.uJ

Institute of Physics, UP Diliman

1.

Electric Field and Field Potential

MATERIALS

Fig. 1.1 The experiment set-up, Two cylindrical electrodes ate immersed in a shallow pool of watet of constant depth. The elecrodes ate Placed at (0r8) and (0,-4).

PROCEDURE

1.

Pour water on the electtolytic tank. Put two disc electodes at coordinates (0,8) and (0,-4). Attach the connectors to the probe, pov/er supply and voltmeter as shown in Fig. 1.1.

4.

of values, instead plot the coordinates

on Graph 1.1 in the data sheet. The symmetry of the gtven electrode

/

configuration allows you to limit the plot to

the first and fouth quadrants. It convenient to make eithet x- or

3.

field

:I

uolt/cm. Show sample calculations the magnitude and draw the E vectors

cm

is

for

y-

on Graph 1.1.

coordinate an integer when locating a point in an equipotential line. Choose the points such that they span the whole area of the tank. Trace the equipotential line fot a potential of 1.0 V.

of the electric

(magnitude and dkection) at the points of intersection of the equipotential Line V(*,1) = 3,0 V 'nth x = 0, 2, 4,6. Get the values of Alby measuring the perpendicular distance ftom each of these points to an adjacent equipotential line and AV from the difference in potential between *re 3.0 V line and this adiacent equipotential line. Represent the electric field vector, -E at these points by arrows using a scale of

2. !7ith the probe tip on the electrolytic tank, determine 5 to 10 coordinates with a potential value of 1.0 V. Do not make a table

Obtain an estimate

5.

in (0, 8) with a long rod oriented peqpendicular to the yaxis. Repeat steps 2 to 4 and Plot Replace the disc electrode

coordinates on Graph 1.2.

Perform step 2 fot potentials of 2.0 V, 3.0 V, 4.0 V, 5.0 V and 6.0 V.

National Institute of Physics, UP Diliman

1. Electric Field and

\-ame:

Date Performed:

Partners:

Date Submitted:

lrsrructor:

Section:

Gruph

l.l

Electric Field and Field Potential for Two Disc Electrodes

dd

of ine

tre rlar an dre d're

dal E

rof ons [ors

ftra

fltt Calculations

\i:'r::l


Fidd Potc*id

1. Electric Field and Field Fotential

Graph L.2 Electric Field and Field Potentid for One Disc Electrode and One Rod Electode

Calculations

National Institute of Physics, UP Dilirnan

Physics 72.1

1.

Electric Field and Field Potcrtid

QUESTTONS

1.

The direction of the electdc field is indicated on field lines. \Why are there no directions indicated on equipotential lines?

Use the equipotential lines to explain why the surface charge density Lt each electrode is not uniform.

Use the equipotential lines and associated lines edge of the tank.

+

of force to show that there are excess charges at the

For the electrode configurations in Graphs 1.1 and1,.2, comment on the electric field (a) between the electodes, and (b) near the edges of the electrodes. In what region(s) does the electric field have the greatest intensity? How is this determined from the plot?

l5nel

lostin:te of Physics, UP Dilirnan

1,

ElectricField arld Ficld

Iflstitteof

Physics, UP Diliman

t,

INTRODUCTION Ohm's Law states the linear relationship between the voltage ar-rd current of an electrical &cuit that contains resistors only. It is stated in the following way: 'If t])e Empqdture and otbq fiiyical conditions ofa ntewllic confucnr is unclnngd,

The resistance of an ohmic conducting wire is found to be proportional to its length and inversely proportional to its cross-sectional area. Its constant of proportionality is called resistivity of the conductor, p. The SI unit of p is the ohm-meter (O-*).

the ratio oftbe potential dffirence to tbe current is constant."

*: r1

This onsant is knovrn to be the resistane of the @ndrctor. Nlarhernatically, Ohm's law may expressed as:

The resistivity, p of any metal varies almost linearly with temperature. It is usually given in tables in tenns of its value pa x 2ffC and the temperature coefficient, o. The produa pao is defined as the slope of th. p vs. T curve. The raistivity at some other temperature T fC), is:

(2.r) AV:IR where AV is the potential difference (also called voltag.) across the metal conductor measured in volts (V), I is the current through the conductor measured in amperes (4, ,nd R is the resistance of the conductor meazured in ohms (O).

Although the definition

Q.2)

p(T)=p,[t+o(T-20)]

of

resistance for nonohmic materials is the same as that for ohmic materials, the resistance R, defined for non-ohmic materials is currentdependent. Nonohmic materials will not give us a linear voltage ns. Errrent behavior.

Q.3)

Table 2.L below shows raistivity values at 200C and temperature coefficients of resistance based on the resistance of some corlmon conductors at

OoC.

German (nickel), silver

Table 2.1Resi$ivities and temperature coefficients of common metals

IoBIECTTVE

To determine the behavior of an ohmic material

!{riood

Iostitute of Physics, UP Diliman

as a

function of vol

, current and resistance

2. Ohm's Law

Physics 72.1

MATERIALS materials we will use fot this experiment ate enumerated below and are illustrated in Figure 2.1.. The circuit diagrams in

Variable power supply. Its output voltage

The

is0Vtoabout6V. 2-m wire. This will be our resistor. The

the Procedure makes use of the symbols below.

Multimeter. This

will

wire is

serve as the

made of

German-nickel.

voltmeter, ammetef and ohmmeter.

l'l-

power supply re s isto r

connectors

Multimeter

voltm eter

Variable Supply Power

am m eter

ohm m eter

2-M Resistance wire Fig 2.1 Equipment used in the experiment.

Fig2.2 Symbols used in the citcuit diagtams.

PROCEDURE Read and undetstand the general instructions experiments.

in the text box below before proceeding with

the

To avoid damage to the meters, always start rilrith the metet on its least sensitive scale. Increase the sensitilty of the meter only as needed fot accurate measurementr and temembet to retuflr the meter to its least sensitive scale before proceeding. (tacfoss" so, voltmetets afe connected patallel to the citcuit element. Voltages afe measured Culents are measured ,,through', so ammeters are connected in series with the circuit element.

Tum off the power supply when not measuring. Before using the ohmmeter to measure the resistance of the resistance wire, always disconnect the tesistance wire ftom the powet supply and othet metefs. A. Variation of voltage with current

1.

the following quantities: the resistance of the 2-m wire using an

Measute

ohmmetet, the room temPerature duting the experiment and the diameter of the wite.

Recotd these values in Data Table 2.1. Perfotm 5 trials in measuring the room temperature and the diameter of the wire.


ta'eh'l wc a(c in am?re reXiro<' {\c'

!

ZOhmtkt

2.

Set up the apparatus as shown in Figure 2.3.

2-m wire and the potential difference

3.

Set the output current

between points A and B.

of the power supply to a minimum. Turn the knob of the powet supply to vary the output current.

4.

Take five readings of curtent and voltage for uniformly increasing values of current

The

suggested increment

step

is

apptoximately 0.1 A. Measure and record in Data Table 2.2 the currenr supplied to the Fig.2.3 Citcuit fot A.

B. Variation of Curent with Resistance

l. Use the sarne affangement as shown in Figure 2.3. 2.

Set the voltage from the power supply

to

a

5.

Remove all the wires connected to the 2-m wire. Measure and record its resistance at different lengths using an ohmmeter.

minimum. Increase the voltage from the power supply until current is read in the ammeter. Record this current irData Table 2.3. 3.

Decrease the length of the wire by increments of 40 cm (Figure 2.4). At each length, measure the current. Take five different lengths.

4.

Keep the voltage constant throughout

Fig.2.4 Citcuit fot B.

this part of the experiment.

C. Variation of Potential with Resistance I. Connect the apparatus

as shown in Fig. 2.5. Make sure that the terminal A is the zero end of the 2-m resistance wire.

z 3.

Measure the voltage and recotd Table 2.4.

Increase the length of the wire between terminals A and C by increments of 40 cm. Take the voltage at 5 diffetent lengths.

{. Keep the current constant this part of the experiment. [HDl

it in Data

Iostitute of Physics, tlP Diliman

throughout

Fig. 2.5 Circuit for C.

Physics 72.1

National Institr-rte of Physics,

2.

Physics 72.1

Law

Name:

Date Performed:

Partners:

Date Submitted:

Data Table 2.1 Theoretical values of resistivity and resistance

COMPUTED PARAMETERS

: :=:

*i:+!J.

1

0.4

Cross-section area:

====+tr :,".,===..1I.?#

Resistivity (from Eq. 2.3):

3:.

Resistance (from Eq. 2.2)z

:,'. :i:l::'.r:..;i:;i

=r:.'r!:.i-f,'

=.*.# :::::::t:-.r,ri

Resistance (ohmmeter):

.-,5

ToerrOr:

+

::::::::t::irri

Calculations

\^cond

Institute of Phpics, UP Diliman

OhEt

Data Table 2.2Yoltage vs. Current

LINEAR REGRESSION

Resistance (ohmmeter)z

Au')

Calculations

Nationd Institute of Physics, UP Dilimao

2.

Phpics 72.1

Irw

Data Table 2.3 Current vs. Resistance

LINEAR REGRESSION

Slope:

y-intercept: Constant voltage (voltmeter): o/oettOti

Calculations

lkhoal

lnstitute of Physics, UP Diliman

l.v

Ohn'r

2. Ohm's Lew

Physics 72.1

Data Table 2.4 Voltage vs. Resistance

TINEAR REGRESSION

Slope:

y-intercept: Constant current (ammeter): o/oettOfi

Calculations

Netiond Iastitute of Physics, UP pilimrn

Physics 72.1

2.

Ohmt Law

QUESTIONS

1'.

Use the data in Data Table 2.2 to plot a curve in the gridlines provided below.

Voltage (V)

Cunent (A)

Inteqpret the significance of the shape and intercept of the curve. !7hy is the slope of the curve the resistance of the 2-m wire?

Account for any discrepancies among the values of the resistance in Data Table 2.1, and Data Table 2.2.

lPiml

ln5dhrle of Physics, UP Diliman

2. Ohm's l-aw

Physics 72.1

4.

Use Data Table 2.3 to plot the variation of current with the reciprocal of the resistance.

Gurrent (A)

1/Resistance

5.

(o'')

Compare the slope with the constant V used fot this procedure. Account for orry discrepancy.


2. Ohm's

6.

Iaw

Use Data Table 2.4 to plot voltage vs. resistance alld resistance vs. length, L.

Voltage (V)

Resistance (Q)

Resistance (Ct)

Length (cm)

Compare the slope of the V vs. R plot with the constant discrepancy

hl

Institute of Physics, UP Dilirnan

I

used for this procedure. Account for any

2 Ohm'sLaw

8.

Calculate the tesistivity, p ftom the slope of the resistance vs. Iength graPh. (Show yout calculations belovr) Compate this result with the p inData Table2'7'


I

i

Ili

I

INTRODUCTION For resistors connected in series, the current passing through each resistor is the same, but the voltage depends on the value of the resistor. The totai potential difference of resistors in series is the sum of the potential differences acfoss each resistor.

For resistors connected in parallel, the potential difference across each resistor is the same, while the total current of the parallel resistors is the sum of the individual currents passing through each resistor.

For

resistors connected

ifi

series, the

effective resistance of the whole circuit is: Run

=& +& +&

+...+&

(3.1)

For resistors connected in patallel, the effective resistance of the whole circuit is:

11111

R"n= & R2 & -

1-...-r-

R,

(3.2)

To learn how to implemeht a circuit diagram and to be able to compute the effective resistance of resistors in series and MATERIALS

-flItrBreadboard

6V Power Supply

-{IITfF Resistors

lrARNING To avoid damage to the meters, always start with the meter on its least sensitive scale. fncrease the sensitivity of the meter only as needed for accurate measurement, and remember to return the meter to its least sensitive scale before proceeding. Voltages are measured ((across" (in parallel). Currents are measured ttthtough" (in ueries). lirimat


3, Resistors

in

Series sfld

Pan[el

PROCEDURE

L.

Table 3.3. ComPute and tecord

the individual tesistances (Rr) using Ohm's law.

Using the color bandsx of the resistots, tabulate the values of the rcsistances (R) in Data Table 3.1.

4.

Black Brown Red Orange Yellow Green Blue Vioiet Gray White

4 5 6 789

0123

Remove the power supply, then measure and the effective resistance, Rqfr using an ohmmeter and record it in Data Table 3.5. Compare this with the value in Data Table 3.2 md get the percentage effor'

Table 3.1 Numerical equivalents of resistot color bands

From the above values, comPute and record the theoretical effective resistance 6"n) "t each circuit (Data Table 3.2).

to

Set up R,,

&, and R3 according diagram for circuit 1. Use a S-volt Power supply to drive the circuit, then measure the voltage across, and the current passing through each resistor, and tecord in Data

3.

the

From the values in Data Table 3.3, compute and record the effective resistance pata Table 3.4). Compare this with the value in Data Table 3.2 and get the percentage error.

6.

Measure the effective voltaqe and cutrent for circuit L and tecord them in Data Table 3.6. Ftom these values calculate the effective tesistance and compare with the value in Data Table 3.2. Get the percentage error. Repeat steps 3

to 6 for circuits 2,3, and 4;

ffisofresistots,followthediag,umbelow,withthebandsasA,B,CandD.Thevalueofthe resistance ls

values of AB, and C ate read accotding to .an b. sitv.r iTOo/o) or.gold (570). Fot exarnple, a resistor with bands' C-ted, D-gold, has resistancs f,=(45x1@ O t snQ, o. 4'! ]9 lj%'

ft=(10A+B) x 10c]A + D. The

Table 3.1, while

b

CIRCUIT DIAGRAMS Circuit

Circuit 2

1

V=5.0V Rr = 1.0 k(l = 1'2Id) Rr = 1'5 k(l

Rz

Cirodt 2A

3

Circuit 4 Natiural Institute of Phpics, UP Dilirnan

Phvsics 72.1

3. Resistors

in Series and Parallel

=EI the lw.

Name:

Date Performed:

Partners:

Date Submitted:

)ute

)ata

ein

lnstructor:

rof. sure

lafl 3.5.

abie

Data Table 3.1. Theoretical values of resistance

Erent

lable

ctive

ein )r.

4.

j f

rhJ Data Table 3.2, Theoretical values of effective resistance

I["o:tal lnstitute of Physics, UP Diliman

3. Resistors in Series and Parallel

Data Table 3.3. Experimental values of resistance from voltage and current measurement

Data Tabl e 3.4.Effective resistance from Data Table

3.3

W

usc'

brN^'lq

Data Table 3.5. Effective resistance from ohmmeter

Circuit

Experimental Effective Resistance, &n

o/oettot

1

2 3

4

Nationd Institute of Phpics, UP Dilim.n

r..lr{- g O 6

t 65 Qt zg fgq> ?

&rrl

3. Resistors in Series

aadPardlcl

DataTable 3.6. Experimental values of effective resistance from effective voltage and current

llt 7" c((or

cor{\OanJ 'ol

National Institute of Physics, UP Dilimen

Tebte I ' 2-

3. Resistors in Series and Patallel


i i I I

;

h

F i

INTRODUCTION

In the analysis of circuits, Gustav Kirchhoff (1824-1,887) formulated two empirical rules which can be observed to be theoretically consistent w-ith the principles of conservation of energy and charge.

o

o

The Voltage Rule (or loop rule) states that the algebraic sum of the voltage changes around a closed loop is zero.

IV, = 0 o

The following sign convention is recommended:

(4.1)

The Current Rule (or lunction rule) states that the sum of all currents entering a junction must equal the sum of all currents

lWhen going around

a loop and passing through a bafre\, the voltage change is taken to be positive when the battery is

ffaversed toward the positive terminal, and negative when traversed toward the negative terminal.

o

\ff/'hen passing through a resistor, the voltage change across the resistor is taken to be

negative ("voltage

positive

leaving the junction.

if

drop') if it is traversed in

of the assigned

the direction

traversed

current, and opposite

in the

direction.

I l"rt

ri.g = E It.u'irg

(4.2)

oBJECTT\rE To be able to analvze multi-looo circuits usins Kirchhoffls Rules.

MATERIALS Two power supplies, multimeter, resistors, breadboatd and connectors.

PROCEDURE 1. Examine the resistors. Compute the rate of resistance from the color bands and their actual resistances using an ohmmeter. Record your data in DztaTable 4.1.

2. Set up the fitst circuit (nvo loop network). Switch on the voltage sources (adjust each power supply as closely as possible to the values specified in the figute). Measure I,, I, and I, using an ammetef. Measure V,, V, using a voltmeter. Record your data in Data Tzble 4.2.

3. Using Kirchhoffs Rules (and the measured voltages and the theoretical resistances), solve National Institute of Physics, UP Diliman

for the currents I,, I, and I, passing through the resistors R,, R, and \ respectively. Show your solution cleady on your answer sheet. Indicate also the directior of the currents through each resistor. Compate these cuffents with the measured cuffents obtained in step 2 by computing the percentage error of each current. Account for these etfofs. 4. Now take each loop and measure the volage

across each element in the loop. Add these voltages (taking note of our sign convention). What value shouid you obtain?

25

4.

Physics 72.1

Kirchhoffs Rules

as indicated above aod measuring the voltage across each resistor. Recotd your data in Data Tzble 4.3.

lyzing the nvo-loop network, add a After ^flto the original citcuit usihg a fourth third loop resistor, Ro = 3.3 kQ. Answer questions 2-4, solving fot and measudng Ir, 12, 13, In, Iu, and Iu 5.

CIRCUIT DIAGRAMS

Vt=5.0v Rt = 1.0 kO

V2=4.5V R2 = 1.2

kC)

R3 = 1.5 kO

Three-loop netwotk R+

v2

1,, I6 Vz=4'5V

Vt=5'0V Rt = 1.0 kO

R2 = 1.2 kO

RS

= 1.5

kO

R+ = 3.3 kQ

National Institr:te of Physics, UP Diliman

i

Physics 72.1

4. Kirchhoff's Rules

Name:

Date Performed:

Partners:

Date Submitted:

I

lnstructor:

Data Table 4.1. Resistance values

Data Table 4,2. Two-loop network


Physics 72.1

4. Kirchhoffs Rules

Calculations


4.

Data Table 4.3. Three-loop network

Calculations

National Institute of Physics, UP Dilimen

NA

NA

NA

NA

NA

NA

Kirchhofft Rules

Physics 72.1

4. Kirchhoffs Rules

QUESTIONS

1. Do the measured values of the resistances fall within

the range indicated by the last band ofl the resistor label? (tolerance values: gold t5%, silver *1070, no band !20tA

Refet to step (4) in the procedrre. What rule does it explicidy verift? What is the significance of this rule?

What would be the effect of using the same voltage level for the two Power supPlies in the thteeloop network (e.g. V,=Vr=$.Q !))

T1a

30

o


Physics 72.1

4.

4. Kirchhoffs Rulcs

The direction one goes around a circuit loop makes no difference in the Voltage Rule equation obtained for the loop. Show this explicidy by going around the loops (in circuit diagram 1) in the opposite directions.

Apply the loop theorem to the big outer loop (travesing Vr, &, R" and V) of circuit 1 and show that it is redundant or unnecessary if you are already using the trro inner loop equations.

National Instinrte of Physics, UP Diliman

Physics 72.1

4.

Kirchhoffs Rules

National Institute ofPhysics, UP Diliman

INTRODUCTION Hans Oersted discovered that a magnetic field is associated with an electric current. He further established a relationship between the direction of the cuffent and the direction of the magnetic field. The magnetic field lines are found to be closed circles around the currentcarrying wire.

The direction of the magnetic field is given

the number of field lines, peqpendicuiar to and through a loop is given by the rate of change of the magnetic flux, LQ I Lt = (AB I Lt)A. The result of this wotk was Faraday\ law of inductioz, which relates the induced voltage or enf rn a wire to the time rate of change of flux:

by a rigbt-band rule:

l/=

If o current-carrying

uire is grasped u)itb tbe rigbt band witb tbe thumb extended in tbe direction of the conoentional canrent, the curled fingers will indicate tbe circular sense of tbe tndgneti.c fr.eld line.

The direction of the magnetic field point is then tangential to the circle.

^t

any

Faruday investigated the possible tevetse effect of a current being produced by a magnetic field in the viciniry of a wire. No effect was found with a stationary magnet or magnetic field. Howevet, it was discovered that a cuffent is induced when there is relative motion or a changlng magnetic field. Thus, elecftomagnetic induction involves a timevtryingmagnetic field. Investigations led Faraday to the conclusion in electromagnetic induction was the time rate of change of the magnetic field B thtough a loop. The total magnetic field through a loop of wire can be characteized by what is called magnetic flwc @:

that the important factor

O=B

l

t-

t

.A= BAcos9

(5.1)

where A is the cross-sectional arca of the Ioop and 0 is the angle benveen a normal to the plane of the loop and the magnetic field. Hence, the time rate of change of the rnagnetic field, or National Institute of Physics, UP Diliman

AO

Lt

(s.2)

where V is r}.e a'verage value of the induced voltage over the time interval Ar. Note that

Ao

Lt=r44u.8144) tarJ l.ar./

(s.3)

That is, a flux change can be due to a change in the magnetic field through a loop of constant area, andf ot due to a coflstant magnetic field and a change in the area of the loop.

In either case, the number or density of field lines through the loop changes. The latter effect is commonly obtained by rotating a loop of wire

in a constant magnetic field so that the efectiue of the loop exposed to the field, and hence the flux, changes. area

The negative sign in equation (5.2) expresses

another important law of elecuomagnetic induction, Lenz's law, wlichgives the direction of the induced current:

An induced current is in sucb a direction tbat its ,ff at oppose the cbange tbat produces it. Essentially, this means the induced cuffent gives rise to a magnetic field that opposes the change in the odginal magnetic field.

Physics 72.1

5, Electromagretic

Still another way to produce a timevarying magnetic field, and an induced vokage in a stationary wire loop, is to vary rhe current in a current-carrying loop. If there are a number of loops N, the flux change through each loop contributes to the induced current or voltage, and F araday's law becomes

Y=-NA@

3 = ltonl

Induction

(s.s)

where z is the linear turn densiry of the coil (i.e., the number of turns per unit length N/L, where I, is the length of the coil).

The constant Uo is called

(5.4)

Lt Similarly, if loops of wire are wound in a tight helix so as to form a coil (solenoid), the magnitude of the magnetic field would be increased, and near and along the axis of the

the permeability of free space, and indicates that the solenoid has an air core. If a material with a magnetic permeability 1t is used as a solenoid core, p.o is replaced by ll in equation (5.5).

solenoid, it is given by

oBJECTT\rE To studv electromagnetic induction in a simple circuit usins Faradav's law and knz's law.

MATERIALS

Pair of insulated cylindrical coils (many turns on secondary relative to pdmary)

Iron and brass or aluminum-cote rods Two bar magnets of different pole strengths Low-voltage dc powet supply or dry cell Magnetic compass

Iftife

switch

Galvanometer

Metdc ruler or meterstick

Conne.

wires


Physics 72.1

5. Electromagnetic

Induction

PROCEDURE g;./ctmiqe poletr'fo a( gdvqwr{rc,lrr 1.. In this experiment, is important to know the direction of the induced current in the circuit. This is related to the positive and negative deflections of the galvanometer. To establish the direction of the galvanometer deflection to a known current direction, connect one terminal of the dry ceil (or dc pov/er supply at 1.5-3.59 to one terminal of the galvanometer and the other source terminal tbrougb a large resistance to the other galvanometer terminal. €rg"re 5.1a). Use yourself as the large resistance.

2. From the known polarity of the source, relate the galvanometer deflection to the direction of current flow. For conventional curtent, this flows from the positive source terminal. Galvanometer deflections to the dght are usually labeled as positive and deflections to the left as negative. It is convenient to have a conventional current entering the positive galvanometer terminal to give a positive direction.

3.

Connect the galvanometer to the terminals

of the secondary coil (the larger coil with the greater number of turns) as shown in Figure 5.1b. Use the compass to determine the relative strengths of the bar magnets. Then, using the stfonger magnet, move the magflet in and out of the coil, noting and recording the effects (relative magnitude and direction of the galvanometer deflection with (a) the speed at which the magnet is moved; and (b) the change of the magnet's polariry). Record your results. Repeat using the other magnet and record the results.


4.

Set up the primary coil circuit as shown in

Figure 5.1c with the switch S open. ( A secondary coil circuit is not needed in procedures 4 and 5). Close the switch and with the compass, investigate the magnetic field atound the coil. Make a sketch of the field pattern. 5.

Open the switch and insert the stronger bat magnet into the pimary coil almost the fuil Iength of the magnet. Close the switch and

slowly remove the magnet from the coil. Note, record, and explain afly observed effects. 6.

Open the switch and insert the pdmary coil

into the secondary coil, which is connected to the galvanometer @igure 5.1c). Close and open the switch, noting and recording the

magnitude and direction of galvanometer deflection in each

the case.

Repeat using each of the two metal cores. 7.

Measure and record the lengh of the pdmary coil. -$7ith the switch open, insert

the primary coil with the iron

core completely into the secondary coil. Make a series of observations of the magnitudes of the deflections as the switch is opened and closed, withdrawing the primary coil 1 cm between the observations. Record the length of the primary coil still inside the secondary coil in each case. Find the a-verage magnitude of the plus and minus deflections for each observation, and plot a graph of the average deflection magnitude (ordinate) versus the length of the pimary coil inside the secondary coil (abscissa). Intelpret the results of the data.

35

physics

72.1

5. Electromagnetic

E

Induction

masnet

primary coil

secondarY coil

c)

Figute 5.1 Electomagnetic induction setups and citcuits.

National Instin:te of Physics, UP Diliman

Physics

72.1

5. Electromagnetic Induction

Name:

Date Performed:

Partners:

Date Submitted:

Instructor:

Section:

Data Table 5.1 Galvanometer deflections from motion of magnet.

Motion touard coil v1

vz ) vr

Cfaskr raka( ,han1l-)

Motion auaryfrom coil v1

vz )vt

Motion tozoard coil v1

vz )vr Motion aroay from coil v1

vz )vr

ANALYSIS lau' [n ktms o1 {o'tadagts \ el ( lar Xcr ) sl'o n cr ma4rt 1

lenz la'u

cu'rcof-'cJ'(luhon "


Physics 72.1

5. Electrornagnetic

Induction

Sketch of Magnetic Field (from Procedute 4)

Observed effects (ftom Ptocedure 5)


Physics72.l

5. Electromagnetic

Data Table 5.2 Galvanometer deflections for different primary coil core materials.

ANALYSIS


Induction

5. Electromrgnetic Induction

Physics 72.1

Data Table 5.3 Galvanometer deflections for different primary coil lengths in secondary. :11

H*Y'ffi.,,t.' ..

:.:

!:=

NDARY

flot

:

|,"

^;:*^Y-ANALYSIS


Physics

72.1

,

QUESTIONS 1'. Suppose that a bar magnet is dropped through

5. Electromagnetic Indgcrion

a hoizontal loop of wire

connected

galvanometer. Explain what would be observed on the galvanometer as the magnet enters, as the middle, and as it leaves the loop, and why.

2.

to

a

it is in

Describe the change of flux through and the induced current in a loop of wire rotated in a uniform magnetic field (rotational axis of loop peqpendicular to field.).


Physics'72.1

5. Electrornagnetic Inductio,n


INTRODUCTION

A.

The instantaneous potential difference vo, is thetefore:

Resistor in an AC circuit

An AC source is a device that supplies

t)

(6.7)

,^ (r)= v* cos(ar t)

(6.8)

v^ (r) = /R cos(ar

a

sinusoidally varying voltage or current. The voltage a and current i at any ldme t are:

,Q)=v cos(at)

(6.1)

iG)= t cos(ar t)

(6.2)

whete V is the maximum voltage amplitude, I is the maximum current amplitude and o is the angular frequency of the AC source.

A convenient way of describing these types of quantities is the root-mean-square (r*0 value. Most multimeters provide readings for tms values of AC voltage (V-) and current

(I*J,

rz - V mr Jz

,-mt

I

f_

Jz

Therefore, the maximum voltage amplitude across the resistor is

B. Inductor in an AC citcuit The inductor is basically a piece of wire wound closely together to form a helix. There exists a potential difference across the inductor

because the alternating current source produces a self-induced electromotive force. For an inductor, the potential is given by:

vL

(6.3)

(6.4)

V=V*=IR.

,"Q)=

L*,O

(6.e)

Hence, the potential at any instant i'; proportional to the time rate of change ol' cuffent. Using 8q.6.2, the potential is expressed as:

,

rQ)= -IaLcos(at + 90')

From the previous equation, the voltage and cufrent are "out of phase" by a quartet cycle (90') and the potential is given a "head start" of 90" relative to the current. The maximum voltage of the inductor is give as:

Figure 6.1.

Consider Figure 1. Using Ohm's Law, the instantaneous potential vo across the resistor is:

,^Q)=

iQ)R

(6.10)

(6.s)

Vr = IaL The inductive teactance is defined

Since the instantaneous curfent is assumed

to be:

(6.11) as:

Xr=@L

(6.1,2)

V, = IX,

(6.13)

Hence,

iQ)= t cos(ar t)

National Instjtute of Physics, UP Diliman

(6.6)

))hysics 72.1

6. Introduction to Altemating Current

C. Capacitors in an AC circuit The potential across a capacitor in an AC circuit may be written as:

/\ I v.(/)= ^cos(@t-90")

(6.14)

OL

The maximum voltage therefore written

use the phasor diagram to remind us that the total instantaneous voltage is equal to the sum :. of the proiections of the phasors Vo,Vr, and V.. Also, note that the total instantaneous voltage is the same as the source voltage. Therefore,

=w

V = tlV o' + (V L -Vc)z

ampJitude

is

as:

I

VC

1

v

,LC -

(6.1.9a)

(6.1eb)

R'+(x,

(5.15)

@C

The capacitive reactance is defined

(AQ Circuits

(6.19c)

Impedance, Z is given by:

as:

(6.16)

CN,

.-V I

R' +(X,

- Xc)'

$.20)

Equations 6.1,8,6.19 and 6,20 are valid oniy

such that

V,

= IX,

(6.1,7)

for an LRC series circuit. Equations fot different circuit configurations would be derived differently.

D.

Resonance in AC circuits

For an inductor, capacitor and resistor connected in series to an AC soufce, the sum of the instantaneous potential across each device is equal to the potential of the source at the same time t, or v(t) =

u^ (r) +

vr(t) +v"(t)

(6.18)

As the angalar ftequency {o is varied, the combination of minimum impedance Z and maximum current I may be obtained. The phenomena of current at the pinnacle at a certain frequency is called resonance angular frequency ot . At this frequency the inductive and the capacitive reactance are equal. Therefore: frl

1

" Jtc =-

(6.21)

oBJECTT\rE Determine the response of different electrical devices such as inductors, capacitors and resistots to sinusoidally varying voltage and current signals.

MATERIAI,S AC circuit apparatus, multimeter and wires.

PROCEDURE

WARNING The following experiment is ditectly connected to the 110 V, 60Hz mains supply. To prevent electrical shock, please be sure that the main switch 5L is set to OFF when conirecting the setup. Do not touch the open terminals wtren operating. Show your setuP to your instructor before collecting data. National Institute of Phpics, UP Diliman

Physics

72.1

6. Introduction to Altemating Cutrent

A.

Resistor in an AC circuit

1.

Close Switch 54 and leave opefl.

2.

Connect the ammeter across "I,*0". Be sure the ammeter is set to AC mode. Connect the variable resistor such that the solenoid is omitted as shown below. Set to any value from 50 to 100Q by turninq the knobs.

-1.

D. a1l

other switches

(Aq

Circuils

Resonance in an AC circuit

Resonance in an LRC Series Circuit fwo parallel capacitors are connected in series with the inductor and the lamp) 1.. Close 52, 53 and 55. Leave 51, 54 and 56 oPen.

2.

Connect the ammetef across a iumper across

"Iro1".or6tt. Place

"I,,*".

3. Move the iron-core to the

outemost

position.

4. Variable feslstor

h i

ic

6. 4. Plug the apparatus to

6. t d

110VAC, 60 Hz

mains.

5.

7.

E

Close switch 51. Draw the pertinent circuit dtagnm Record the current and measure,the voltage across the resistor and the lr-p.l Increase the resistance. : Observe what I

happens.

E

B. Inductot in an AC circuit

Close switch 51. Draw the pertinent circuit diagram Move the iron-core at constant intervals and record the current and the voltage drop across each device. Record the current and voltage of each element when the lamp intensity is at the maximum.

Resonance in an LC Parallel Circuit

parallel capacitors are connected in with the inductor and this combination in series with the lamp) 1,. Close 52, 53, 54 and 56 with 51 and 55

G*o

open.

E

t

110 VAC, 60 Hz

parullel

I

,a

to

mains.

5.

D

h

PIug the appararus

1,. Close 54 and

leave other switches open. ttl".,"..,.", Place Connect the ammetef acfoss .il iumpers across "f ,u-ott. 3. Move the iton-core to its outermost position. 4. Connect apparatus to 110VAC, 60 Hz

2,

2.

Close 51. Draw

the pertinent

circuit

diagram.

6. Move the iton-core position ^t regular intervals and record the currents and the voltages of the solenoid and the lamp.

C. Capacitors in an AC circuit 1.. Close 52, 53 and 56 and open 51, 54 and 55.

2. 3. 4. 5.

Place ammetef across "I,^-0". Plug apparatus to 110VAC, 60 Hz. mains. Close 51. Draw the pertinent circuit diagram

Record the current and voltage effective capacitor and lamp.

National Institute of Physics; UP Diliman

of

the

"Iro,"no,ut'. Plac'e

3. Move the iron-core to its 4. 5.

mains. 5.

Connect the ammeter acfoss a jumper across 'I,u-'".

6.

outermost

position. Plug apparatus to 1 10VAC, 60 Hz mains. Close switch 51. Draw the pertinent circuit diagram Move the iron-core at constant intervals and record the current and the voltage drop across each device. Record the current and voltage of each circuit element when the lamp intensity is at the minimum.

6. Introduction to Altemating Curent

(Aq

Circuits

E

N

APPARATUS

PI

I

Ir

I

solennoid

L

[}

110 Vac

(t


Physics

72.1

6.

Name:

Date Performed:

Partners:

Date Submitted:

Instructor:

A.

Resistor in an AC Circuit

Data Table 6.1 Current and vol

Observations

in

Introduction to Alternating Current (AC) Circuits


and resistor

Physics72.l

,

,

6.

lntroduction to Alternating* Current (AC) Circuir

!

(

B. Inductor in an AC Circuit Data Table 6.2 Dat* for solenoid and lam

Calculations


Physics 72.1

6.

C. Capacitors in an AC Circuit Data Table 6.3 Data for

r';l:r:iai::i'::',:ii:iar:::,,:rri':.r::ll;ll: ,::!rr:::rjl?t:,!j:,,:t r,ir:rl

ir::.ij:

i:it ,:::l .li

,rirr:l;l'l.i*l::l{iril:l

Calculations


i:'r:,riti:ir:i:tr!::i :::i

l::i r,ir:::rr i|i:r:,,iil:i..::a:":ri:::.lar:i'a

Introduction to Ahernating Current (AC) Circuits

Physics

72.1

6.

Introduaion to Alternating Current (AC) Circuits

D. Resonance in an AC Circuit Data Table 6.4 Resonance in an LRC series circuit

Calculations


Data Table 6.5 Resonance in an LC

Calculations


6.

Physics 72.1

Inugduction to Altemating Curre"t

(49 t{94t

!

J

I

QUESTIONS

1

Answer questions 1 to 3 using your data in Table 6.1 1. Compute fot the following: (a) V and I, O) T and

cD.

Draw the voltage and cuffent as a function of time for the resistor and lamp combined. Label yout plots completely.

Voltage (V)

Cunent (A)

Time (s)

Dtaw the phasot diagram for the combined resistor and lamp. What are the proiection of the voltage and current phasors called?

National Institr.rte of Physics, UP Diliman

Physics 72.1

6. Introduction to Altemeting Current

(Aq

Circuits

Answer questions 4 to 6 using your data in Tab\e 6.2. 4. tU7hat is inductive reacance? From your data, compute forftr. Show sample calculations.

5. Compute for the impedance of the circuit

6.

at each core position. Show sample calculations.

What happens to the interrsity of the lamp as he core goes in? Draw the phasor diagram at this

position.

Answer questions 7 oad 8 using your data in Table 6.3 7. What is capacitive reactance? From your data, compute foryr. Show sample calculations.



Physics 72.1

8. Compute fot Xc using Eqs.

(AQ Cirarits

6.16 and 6.17. Compare the results.

Answer questions 9 to 12 using your data from table 6.4 9. At what core posirion is the intensity of the lamp maximum in the sedes LRC citcuit?

10. Compute for the impedance at each core position. Show sample calculations.


11. why does the lamp intensity increase? what brings about this condition?

f

Z. Vrnat

t ,t. irrdr.tance at maximum lamp intensity?

Answer questions 13 to 16 using your data from Table 6.5 13. At what core position is the intensity of the lamp at a minimum?

14. Derive an expression fot the total impedance in the circuit.


Physics 72.1

15. Compute


(Aq

Circuits

for the impedance at elch core position. Show sample calculations.

IN Ai solt

r$ 16. What happens

to the lamp intensity

as the

iron core is moved in? Explain.

ori

rlcd

aq

PCq

atd tcE firri

su .rl

t

lEq 7:t:

rl

rd

efi,

*{ icl

r!i

d

*d

Pr$

fiq

ffi r€f,i

nct B.'llx

I

ri

rPd


INTRODUCTION

A.

Reflection

\When light strikes the surface of a material, some light is usually reflected. The reflection of light rays from a plane surface like a glass plate

or a plane mirror is described by the law of

0r

Normal------,-

reflection:

The angle of incidence is equal to the angle of reflection

0,=0,

(7.1)

These angles are measured from a line perpendicular or normal to the reflecting surface at the point of incidence. Also, the incident and reflected rays lie in the same plane with the normal.

The rays from an object reflected by a smooth plane surface appear to come from an image behind the surface, as shown in the Figure 7.1. From equal triangles it can be seen that the image distance d, fuom the reflecting surface is the same as the object distance do . Such reflection is called regulat or specular

I

.\i,,

)@, Obiect

Figute 7.1 Law of Reflection. The aagle between the incident tay and a notrrral to the surface O is equal to the aagle between the teflected tay and the normal 0, , i,e., & = 0r.

notmal to the surface, it is "bent" or undergoes a change in direction. This is due to the different velocities of light in the rwo media. In the case of refraction, the angle of incidence and the angle of refraction are denoted by 4 and 0r, respectively.

reflection. The law of reflection applies to any reflecting surface. If the surface is relatively rough, like the paper of this page, the reflection wili become diffused or mixed, so that no image of the source

or object wiil be produced. This type of reflection is called irregular or diffuse reflection.

sinO,

u.I

sinl,

u,

_

_^

t'12

(7.2)

where the ratio tt,, of the nvo velocities (a, in medium 1 and a, in medium 2) is called the

relative index

of tefraction and the above

equation is known as Snell's law.

If

B. Refraction \Mhen light passes from one medium into an optically different rnedium at an angle other than

h


ur(u,, the tays are bent toward the normal in the second medium. And if ur)a,, the rays ate bent away from the normal.

For light traveling initially in vacuum (medium 1), the ratio of the speed of light in vacuum and its speed in medium 2 is called the index of refraction of medium 2 denotedby n,

Physics 72.1

7. Optical Disk: Reflection and Refraction

Ptt

Snell's law can then be written as:

ltr= L a

sinO,

where r is the speed of light in vacuum and z the speed of light in medium 2. Hence, the index of refraction for vacuum is t = cf c = 1, and for ur, u

ac,sona1.

OBJECTIVE To study by means of

sinO,=r,_c/h t)2 c/nz

Q.3)

_L fll

Q.4)

of

n,sin9, = nrsin9,

(7.s)

where n, and nrate the indices of the refraction of the medium 1 and medium2, respectively.

D.

an optical disk the fundamental principles of reflection and refraction of light.

MATERIALS Optical disk and accessories,light source.

E. PROCEDURE Place the optical disk @ig. 7,2) so that the

beam of parallel rays from the illuminator strikes the edge of the disk. Turn the screen so that it is beween the illuminator and the disk. Adlust the illuminator until the beam covers most of the opening in the screen and traces its path across the face of the disk. Adjust the disk and screen until a single beam of light coincides with the 0'-0' axis of the disk.

A.

Reflection by a plane mirtot

Fasten the plane mirrot to the disk so that the face coincides with a segment on the 90'-90' axis. Tum the screen qntil the ray strikes the mirror exactly at the center of the disk. Leave the screen stationary and turn the disk to sevetal

different positions, increasing the angle of incidence as shown in Fig. 7.3a. Record the angles of incidence and the corresponding angle

of reflection in Data Table A.

B.

Reflection and refraction by glass

1.

Place the semicircular glass plate in the path of the light ray so that the ray hits the center of the flatfice, Fig.7.3e.

2. Set the ny at diffetent angle of incidence by slowly rotating the disk between 0o and 90o about c as the axis and record the angles of teflection and refraction in Data Table B-1. Choose incident angles that result to noticeable reflection and refraction of light. Compute for the coresponding values of the index of refraction.

3.

From Fig. 7.3e, rotate the disk exacdy 180' about c axis (obtaining Fig. 7.3f. Using the angle of refraction from 2 as the angle of incidence, record the angles obtained in Data Table B-2.

C. Total intemal reflection 1.. Place the semi citcular glass plate in the path of the light ray so that the ray enters the curved face and travels along

the radius to the center point c in Fig. 7.3f. Slowly rotate the disk until it is 90' about the c axis. Record your observations about the uansmitted intensity.

National Institute of Physics, UP Dilirnan

l.Ir

Physics 72.1

2. 3.

7. Optical

Record the critical angle ec in Data Table C and compute for the index of refraction of glass.

Draw the complete ray traces for the two rays indicated in Figs. 7.3g, 7.3h, and 7.3i. In each figure, one line is dravrn as a broken line to differentiate

point of the emergent rays. This point Qetrveen the light source and lens) gives the focus of the concave lens.

2,

two incident rays.

D. Refraction through

a parutleL/

trapezoidal plate

1.

in Fig. 7.3i. Note the relative direction of the Place the ruy as shown

incident and emergent beams. Repeat for several angles of incidence and comment on the results.

E.

Refraction thtough lenses

1,. Open the other slits to increase the number of incident parallel rays of light. Construct traces for parallel rays through the center section of the diverging or concave lens, Fig.7.3m.Trace backwards the intersection


Disk Reflection and Refraction

Attach the convex lens in place of the concave. Send a single ray along 0"-0' axis passing through the center of the Iens. Rotate the disk through a small angle on either side of the initial position (such that the ray still passes through the center of the lens) and observe the incident and emergent rays.

3.

Return the disk to its initial position with a single incident ray along the optical axis of the convex lens (0"-0'

axis). Slowly rotate the disk by large angles (<90") and note that the reftacted

rays intersect about one point in space. Note this location on the disk when at

initial position as a tentative

(or

approximate) focus of the convex lens. Veri$r or correct this focal point with the intersection of parallel rays, Fig. 7.3n, used in 1.

59

Phvsics 72.1

Figure

7.

7.2. Optical disk

Opticd Disk Reflection and Refraction

and

optical elements

faJ

==4 <1 ftt

{al

=

_{__+>_n

---\r -/ {d)

I

a :-

-\ AJ

-€5 -----*{'7 ftn)

{i)

-t

f*j

-----+l --:-{ b)

,

--.=T/\

=:=t.r_ (ol

a

Figute 7.3. Expetimqrt coafigurations of optical elemeats

Netional Institute of Physics, UP Diliman

l

-

Disk: Reflection and Refraction

ics 72.1

Name:

Date Performed:

Partners:

Date Submitted:

Instructor:

Section:

Data Table7.1. Reflection by a plane mirror

Data Table7.2. Reflection and refraction by glass

B-1. Normal Orientation

Calculations

National Institutc of Physics, UP Diliman

61

T

D

t

c

B-2. Semi-circular plate rotated 180'

Nationd Institute of Physics, LIP Diliman

Physics 72.1

7. Optical


Data Table 7.3. Internal reflection

Critical angle, 0p

Index oftefttcaon,n:

Calculations

Data Table 7.4. Reftaction through lenses Focal leirgth

f

Focd

-(concave)


length/-

(convex)

7. Optical Dislc Reflection and Rcftaction

Physics 72.1

QUESTIONS

1.

Do your results in Part A obey the law of reflection?

2. What happens to the ray transmitted by the glass in Part B?

3.

.4.

Comment on the index of teftaction obtained in B-1 andB-2.

Is the $y t^ce reproduced itt-B? Does the ditettion of the

ny affectthe path?


Physics

721

5.

In part c, eirplain why the ray is not transmitted beyond a definite angle?

6.

Does the intemally reflected ray obey the law of reflection?

7. Optical

Disk Reflectjon and Refractiqr

7. Draw the complete my traces for the two rays indicated in Figures 7.3g,7.3h and 7.3i.

National Institute of Physics, UP Dilimrn

Physics 72.1

8.

7. Optical


Comment on the results of Part Dtof the experiment.

9, When a single ray passes through the optical center of the lens, how does it emerge? Construct a ray trace for the concave and convex lenses with seneral incident rays parallel to the opticd axis.

INTRODUCTION

A

lens

is a

simple optical instrument that produces a change in the direction of a light beam that passes through it. If an object is placed in front of a lens, the position and size of the image can be determined by graphical and algebraic means.

The image position, s', is related

to

the

object position, s, by the equation

111 srsf

(8. 1)

The magnification of the object is given by the equation:

=+=-'' bs

thin lenses. One needs only two rays to locate an image: The ray from the tip of the object, parallel to the optical axis, which after refraction passes through the far focal point of a convex lens or seems to come from the near focal point of a concave lens. A ray, from the tip of the

object, passes through the center

of the lens

unchanged.

where/is the focal length of the lens. The above equation, sometimes called the lens-maker's equation, was derived on the assumption that the lenses are very thin, and that the rays are close to the optical axis.

M

s : object distance Just like the mirrors, ray-tracing method could very well define the images formed by

(8.2)

: height of the image D : height ofthe object s' : image distance

where b'

The

quantities above obey

the

sign

conventions in Table 8.1.

The thinJens equation is used to calculate the focal length of a lens from the known object and irnage distances from the lens. Furthermore, the equivalent focal length of lenses (in contact) combined may be obtained by treating it as a single lens. So, if the individual focal lengths, /, fz, are known, th,: equivalent focal length,f,* y be calculatedusing the following equation:

two thin

111

f,f,

f

Focal length

Convex lens

Concave lens

Object distance

Real object

Vinual object

Image distance

Real image

Virtual image

Object/image height

Erect object /image

Inverted object/image

Magnification

Erect image

Inverted image

(8.3)

Table 8.1 Sign convention in lensmaker's equation

OBJECTIVE

Ill

To be able to determine the focal len$hs of a convex and a concave lens. National Institute of Physics, UP Diliman

67

8. Image formation using thin lenses

l)hysics 72.1

APPARATUS

r:fr:,1,,li SLAr}I ,ryIIH d{}-€$$f$'rE+

l-fi.ffi

Arr*

Hr,q^#EF

e*#fR

,,Ltt.,{,SfE

PROCEDURE

1. Look fot a

2.

convex-concave

lens

Arrange convexl in such a way that only

a

virtual image of the obiect would be formed. This virtual image will become the

convexl. Put both convexl and concave lenses in contact. Obtain a sha{p image and record the observations in Data Table 8.1. !(/hat is the equivalent focal length of the combined lenses? After obtaining the focal length of convexl from step 3 below, calculate the focal length of the concave

real object of convex2. Place convex2 in front of convexl (the t'wo lenses should not be in contact) and obtain a final real image (from convex2) with a magnification of thtee. Draw and ptoperly label the ray diagram using a convenient scale in Figure 8.2. Recotd measurements in Data Table

lens using Eq. 8.3.

8.3.

Obtain another convex lens and label

it

as

convex2.

3.

4.

combination that will produce an image if they are in contact. Label the convex lens as

Determine the focal lengths of the two convex lenses (convexl and convex2) by using the lensmaker's equation (Eq 8.1). Use each lens individually to form a shaqp image.

Draw and properly label z ey diagram, using a convenient scale, for one lens in Figure 8.1. Record your measurements in Data Table 8.2a and8.2b.

5.

To detetmine the focal length of a concave lens, use convexL lens to fotm a reduced image of the object on the screen. Next, place a coflcave lens before this image. This image will become the virtual object of the

concave lens. Move the screen to get a sharp final image. Draw and propedy label the ray diagram using a convenient scale in Figure 8.3. Compare the calculated focal length of the concave lens to that obtained fromData Table 8.1. Record measurements in Data Table 8.4.

National Institute of Physics, UP Difiman

tt

[.,,

8. Image

Physics 72.1

Formation Usiag Thia

Name:

Date Performed:

Partners:

Date Submitted:

I

Instructor:

Data Table 8.1. Concave-convex lens combination (in

contact) l"* L

(

rcq,s)

Distance of screen from the lenses ,

'::, ,t,.::,: :

tlr:: lu:r:- !:t-t:u:l:rr.:::i].:f::.i:,l.:t,rrithU,i::,,iit:tt..r,,.'r'at.:t

:

:

I

:

Equivalent focal lolgth:

rt hc

({r^' ,-,

Calculations

bE

ln

ft EF

of

!r llc

& I

hE Ed I

Iq

[s he i.

e,

b.l

in cel Ed I

Lts I

I

i I

F i

I


Focal length of the concave lens:

tl *l.lr

Las

Physics 72.1

Data Tabl e 8.2-a.Convrx lens #1

8. Imrge formation usiae

thir LoG

(f -')

Average focal length of convexl: Data Table 8.2-b. Convex lens #2

0r'-)

Average focal length of convex2: National Institute of Physics, UP Diliman

Physics 72.1

8. Image Formation Using

Data Table 8.3. Two convex lens combination

Calculations

*t- ,*s?*rq-e
Data Table 8.4. Convexl-concave lens combination (not in contact)

Calculations

National Institute of Physics, UP Dilimea

Thin Lenses

8. Image formation using thin lenses

Physics 72.1

QUESTIONS 1,. Draw the ray diagrams for the experiment procedures 3,4

and 5.

Figure 8.1 Ray diagtam of convex- lens

Figure 8.2 Ray diagtam of conv-ex1-convex2 lins combination National Institute of Physics, UP Diliman

physics

72.1

8. Irnage Forrnation Using

Thin Ia|ses

Figure 8.3 Ray diagtam of convexl-concave lens combination

2.

Compare the results for the focal length of the concave lens obtained from experiment procedures and 5.

National Instin:te of Physics, UP Dilirnan

1

Navarro, P. ed., Compilation of Elementary Physics Experiments (unpublished).

Tipler, P., Physics for Scientists and Engineersr

4tr

Ed., W.H. Fteeman & Co. USA (f999).

White, M. and Manning, K., Experimental College Physics 3d Ed., McGraw-Hill Book Co.

usA

(1e7e).

\Urilson, J. Physics Labotatory Expedments, 3d Ed. DC Heath and Co. USA (1990).

Young, H., Univetsity Physics 8n Ed., Addison-Wesley Publishing Co. USA (1992),


Physics72.1 Laboratory Manual

Recommend Documents