phys 1412 manual_2011

7/30/2019 Phys 1412 Manual_2011

1/36

The Universit

WAVES, OPT

Department of Ph

(Revised 2011)

of the West Indies

HYS1412CS & THERMODYN

sics

MICS

7/30/2019 Phys 1412 Manual_2011

2/36

ii

CONTENTS

WRITING A PHYSICS LABORATORY REPORT .......................................................................... iii

ASSESSING A PHYSICS LABORATORY REPORT ....................................................................... iv

INSTRUCTIONS TO STUDENTS CONCERNING THE PHYSICS LAB .............................................. v

ON THE ESTIMATION OF ACCURACY ..................................................................................... vi

PHYS1412 SYLLABUS ............................................................................................................. xi

LIST OF EXPERIMENTS

EXP 1 INTRODUCTORY EXPERIMENT INTERFERENCE AND DIFFRACTION USING A

HELIUM-NEON LASER ............................................................................................. 1

EXP 2 MECHANICAL RESONANCE ..................................................................................... 6

Exp 3 PROPERTIES OF SINE WAVES ................................................... ................................ 8

Exp. 4 PLANE TRANSMISSION DIFFRACTION GRATING .................................................... 13

EXP. 5 NEWTON'S RINGS ................................................................................................. 15

EXP. 6 INTERFERENCE FROM A THIN WEDGE ................................................................... 18

EXP. 7 CLEMENT AND DESORMES EXPERIMENT ............................................................... 21

EXP. 8 CONSTANT VOLUME GAS THERMOMETER ............................................................ 24

7/30/2019 Phys 1412 Manual_2011

3/36

iii

WRITING A PHYSICS LABORATORY REPORT

The format required in the report is fairly standard and is briefly discussed here.

1. EXPERIMENT NUMBER, TITLE, DATE AND PARTNER

These must be written at the beginning of the report.

2. PURPOSE

A brief statement of the purpose of the experiment is required even if this is already given on

the instruction sheet for the experiment.

3. THEORY

This is normally given on the instruction sheet and need not be reproduced.

4. METHOD

This is also is normally given and can be omitted. Diagrams given also need not be included in

the report.

5. RESULTS

Readings are to be tabulated where necessary. Graphs are to be drawn using a suitable scale and

must be properly labelled.

6. ESTIMATION OF ACCURACY

An estimation of the accuracy of numerical results must be done. Examples of how this is to be

done are given beginning on a page vi.

7. DISCUSSION

The discussion should include results and conclusions related to the purpose of the experiment.

It is a good idea to reread the aim before starting to write your discussion. In your discussion you

should include descriptions of the graph(s) obtained and say what conclusion(s) can be drawn

from them. Do they relate to the theory given? Similarly, you should analyse your overall results

and draw some conclusions. Discuss the magnitude of error and how it affects the results and

comment on whether or not the purpose of the exercise has been achieved. Important

precautions that are observed in performing the experiment should also be noted. Appraisal of

the experiment should be constructive. It is particularly useless to say that 'better' results would

have been obtained if 'better' equipment had been provided.

7/30/2019 Phys 1412 Manual_2011

4/36

iv

ASSESSING A PHYSICS LABORATORY REPORT

Reports are marked on a scale 0-10 marks. Below is a rough guide of how marks are

allocated. However since experiments differ in their requirements, instructors may alter

slightly how the marks are apportioned depending on the emphasis of the experiment.

Maximum Marks

a. For successfully setting up the apparatus so as to

run the experiment. 1

b. For obtaining data and presenting it in tabloid or

graphical form where necessary. 3

c. For all calculations and manipulation of data,

equations or graphs. This includes finding slopes

and error calculations, where relevant. 3

d. For discussion/conclusion. This includes:

A detailed discussion of errors in the

experimental results and what they show

quantitatively and/or qualitatively.

A detailed discussion of the results of the

experiment as they relate to the purpose of the

experiment and the physical laws concerned.

This includes a discussion of the graphs

obtained or equations used. 3

It should be noted that a student will obtain a maximum of 4 marks for simply gathering the

data and plotting graphs, where relevant.

Instructors will apportion marks in each category above according to the accuracy,

correctness and relevance of the work done. In other words, it will not be automatic to get

marks for any section just by presenting something.

7/30/2019 Phys 1412 Manual_2011

5/36

v

INSTRUCTIONS TO STUDENTS CONCERNING THE PHYSICS LAB

1. Students are required to sign the ATTENDANCE SHEET provided by the Lab Supervisor in

the space appropriate to the experiment to be performed.

2. In general, students are required to work in pairs. More than two persons will be

allocated to use one set of equipment at the same time only in the event of equipment

failure.

3. Students should attend only the Lab session to which they have been assigned. A

student may be allowed to attend another Lab to make up for an assigned Lab that

he/she cannot attend only if permission is granted before the assigned Lab.

4. Absence from a Lab session will be counted against the student unless permission is

given before the Lab or a medical certificate is presented afterwards.

5. Lab reports should be written in Lab books which are on sale in the bookshop.

6. The name of the student and the day on which Lab is attended should be carefully

printed on the bottom edge of the book.

7. Lab reports are to be completed and submitted by the end of the session in which the

experiments arc performed.

8. Under normal circumstances it should then be unnecessary for the students to remove

the books from the Lab.

7/30/2019 Phys 1412 Manual_2011

6/36

vi

ON THE ESTIMATION OF ACCURACY

Whenever a numerical result is calculated, it is essential that the reliability of the result be

established even if this is done in a simplified manner. This estimation of accuracy is often

referred to as the estimation of errors. It is important that one realizes that the word "ERROR"

used in this context DOES NOT REFER TO MISTAKES BUT TO THE DEGREE OF UNCERTAINTY

ABSOLUTE ERROR

The absolute error in a quantity is usually expressed in the same unit as the quantity itself.

Example: Length of table, L = 1.65 0.05 m. In this case the absolute error L = 0.05 m.

If the same reading is taken more than once, the average value is used in the calculation and the

mean deviation is used as the absolute error,

Example: Suppose the length of the table is measured three times to obtain values of:

1.65 0.05 m

1.60 0.05 m

1.85 0.05 m

The average value = 1 65+1.60+1.85 = 1.70 m

3

The deviations from the average are then: -0.05, - 0.10 and + 0.1 5

Now the mean deviation = Sum of deviations regardless of sign

Number of readings

Therefore the mean deviation = 0.05+0.10+0.15 = 0.10

3

So we now express the length of the table as L = 1.70 0.10 m

Note that the absolute error in the average value may at times be larger than that in a single

reading.

FRACTIONAL ERROR (AND PERCENTAGE ERROR)

FRACTIONAL ERROR = ABSOLUTE ERROR

QUANTITY MEASURED

PERCENTAGE ERROR = FRACTIONAL ERROR 100%

7/30/2019 Phys 1412 Manual_2011

7/36

vii

For the average value of the length of the table quoted above,

The fractional error = 0.10 = 0.06

1.70

The percentage error = 0.06 x 100 = 6 %

SIMPLE RULES FOR ESTIMATING ACCURACY IN A CALCULATED RESULT

(1) When quantities are ADDED or SUBTRACTED, their ABSOLUTE ERRORS ADD.

(2) When quantities are MULTIPLIED or DIVIDED, their FRACTIONAL (AND PERCENTAGE)

ERRORS ADD.

Application of these rules will now be demonstrated in a few examples:

Ex. 1. In calculating a quantity, y, using the formula y = a + b - c,

one measures a = 2.1 0.2 mm b = 1.6 0.1 mm c = 0.50 0.05 mm

Hence, y = 2.1 + 1.6-0.5 = 3.2 mm

Absolute errorin y, y = 0.2 + 0.1 + 0.05 = 0.35 mm

The result is then y = 3.20 0.35 mm.

Ex. 2 In calculating a quantity, z, using the formulas

pqz =

one measures p = 7.5 0.5 kg q = 4.0 0.2 m s = 7.0 0.3 m

Hence, kgz 3.47

45.7=

=

Fractional errorin z = fractional errorp + fractional error in q + fractional error in s

In symbols

++=

+

+

=

0.7

3.0

0.4

2.0

5.7

5.0

s

s

q

q

p

p

z

z

= (0.067 + 0.05 + 0.043) = 0.16

Absolute errorin z, z = 0.16 z

z = (0.16 4.3) = 0.7 kg

The result is then z = 4.3 0.7 kg

Ex.3 If is calculated using the formulac

dba )( +=

7/30/2019 Phys 1412 Manual_2011

8/36

viii

+

+

+

+=

c

c

d

d

ba

ba

)(

; therefore

+

+

+

+=

c

c

d

d

ba

ba

)(

Ex.4 Ifu and vare measured in order to calculatefusing the formula

vuf

111

+=

it is easier to simplify the formula before calculating the absolute error inf

Simplification gives)( vu

uvf

+= and therefore

+

++

+

=

)( vu

vu

v

v

u

u

f

f

Hencefmay be obtained.

Ex.5 Consider an experiment in which values ofyandxare measured and a graph ofyagainst

x is plotted. Suppose a relationship xl

zy

2= applies and z is to be calculated.

The slope of the graph isl

z2so l

slopez

2=

Since 2 is a known constant, there is negligible error in it.

Therefore

+

=

l

l

slope

slope

z

z

So in order to calculate z, it is necessary to calculate the error in the slope of the graph.

FINDING THE ERROR IN THE SLOPE AND INTERCEPT OF A GRAPH

Let us examine the typical graph illustrated below.

The best straight line is drawn so that

(i) the deviations of the points from the line are kept to a minimum, and

(ii) the points not on the line are approximately evenly distributed on either side of the line.

From this line one obtains the desired value of the slope.

7/30/2019 Phys 1412 Manual_2011

9/36

ix

The following steps are then taken to determine the error in the slope:

(1) A rectangle is drawn with its long sides parallel to and straddling the best straight line.The size of this rectangle is the smallestthat will enable it to enclose all (or nearly all) of

the points.

(2) The diagonals of the rectangle are now drawn and it will be noticed that one has a slope

greater than that of the best line while the other has a smaller slope. The slopes of the

diagonals are called MAX and MIN respectively.

(Note: The diagonals usually intersect on the best straight line at about the middle of the

range of the measured values).

(3) The best possible slope is the slope of the best straight line.

(4) The error in the slope is then calculated from the formula

nslope

2

slopeMINslopeMAX)(

= where n = number of points.

Similarly the best intercept is the intercept of the best straight line. To obtain the error in the

intercept, proceed as follows:

(1) Draw the best straight line and the lines of MAX and MIN slopes. Extend the lines of

MAX and MIN slopes to cut the axis on which the intercept is required (the following

figure shows this for an intercept on the y-axis), then measure the max and min

intercepts.

7/30/2019 Phys 1412 Manual_2011

10/36

x

(2) The error in the intercept is then calculated from the formula

n2

interceptmininterceptmax)intercept(

=

NOTE: If all points fall on the same straight line (e.g. as in figure below), then the error in the

slope can be obtained by estimating the errors in reading Y and X from the graph and

computing:

+

=

X

X

Y

Y

slope

slope

Y and X are usually taken as the smallest divisions on the yand xaxes respectively. In this

case also, the error in the intercept will be:

Y(for the intercept on the y-axis) OR X (for the intercept on the x-axis)

7/30/2019 Phys 1412 Manual_2011

11/36

xi

PHYS1412 SYLLABUS

Textbook: FUNDAMENTALS OF PHYSICS, 8th Edition

by Halliday, Resnick and Walker.

WAVES AND OPTICS (11 lectures)

Waves on a String

Sound waves

Optics

Coherence

The Phasor Method

HEAT AND THERMODYNAMICS (7 lectures)

Temperature

Kinetic Theory of Gases

Entropy and the Second Law

P14 students are strongly advised to read ahead. Lectures will usually follow (lie above

sequence and it is therefore quite easy to spend about 1 hours of private study for each

lecture and about the same for each tutorial.

An above average student should therefore expect to "beat books" for approximately six

hours per week for physics alone. This figure could be substantially increased - perhaps to

eight or ten hours - for a student with a weaker background in either physics or

mathematics.

Please arrange your work schedule accordingly.

7/30/2019 Phys 1412 Manual_2011

12/36

1

EXP 1 INTRODUCTORY EXPERIMENT INTERFERENCE AND

DIFFRACTION USING A HELIUM-NEON LASER

PURPOSE: To investigate the fringe patterns produced by single slit diffraction and double slitinterference.

PRECAUTION: Do not look into the laser bean or point it towards anyone.

The beam, or even its reflection off glass can damage the eye.

THEORY: Interference and Diffraction are discussed in Ch36 Halliday, Resnick & Walker

In this experiment we study the interference and/or diffraction patterns produced when

collimated, monochromatic light (i.e. laser light) passes through various arrangements of

apertures, and are observed on a viewing screen. When the apertures/slits are sufficiently

small, the light intensity on the viewing screen exhibits variations (successive maxima and

minima) which depend upon the wavelength of the light and the size and number of the

apertures. The existence of the patterns is confirmation of the wave nature of light.

(A) Single Slit Diffraction

A single slit diffraction pattern results when the light passes through one aperture in an

otherwise opaque surface. The light intensity on the viewing screen exhibits a bright central

peak surrounded by subsidiary peaks. The single slit diffraction pattern is shown in Figure1.

Fig. 1

7/30/2019 Phys 1412 Manual_2011

13/36

2

ym

When the path difference between light from one edge of the slit and light from the center of

the slit is a multiple of half of the wavelength, the waves destructively interfere and there is a

minimum in the pattern. Therefore for a point of minimum intensity we can write:

a sinm = m ----- (1)

where, a = the single slit width

m = order of the minima = 1, 2, etc.

m = the angular position of the mth

minima

= the wavelength

From the geometry of the experimental arrangement (Figure 2 below) we can also show

that: tanm = ym/L or m = tan-1

( ym/L) ----- (2)

Where, ym = the distance from the centre of the pattern to the mth

minima

L = the slit to screen distance

Fig. 2

(B) Double Slit Interference

A schematic of the double slit interference apparatus is shown in Figure 3. Waves from slits

S1 and S2 combine at P an arbitrary point on the screen, to produce the interference pattern.

7/30/2019 Phys 1412 Manual_2011

14/36

3

Fig. 3

The path difference between the waves (r1 and r2) is S1b. The condition for a maximum

intensity at P is: d Sin = m

The condition for a minimum intensity at p is:

d Sin = (m+ )

where d = the centre to centre distance between the slits.

It can also be shown (see text) thatx

Ld

= ----- (3)

wherex= the average separation between the fringes in the double slit interference

pattern.

METHOD:

Note: The Helium-Neon gas laser is a delicate and expensive piece of equipment. Please

handle it with care. Do not switch the laser on and off repeatedly during the experiment. It is

better for the laser if it is left on for the entire experiment.

The laser has a wavelength of 632.8 nm.

S1

S2

r1

r2

b

7/30/2019 Phys 1412 Manual_2011

15/36

4

(A) Single Slit Diffraction

1. The plate provided contains a number of single and double slits. For this section use only

the single slit labelled 5 on the plate (see also Figure 4). Switch on the laser and direct

the beam through the single slit. Observe the diffraction pattern on a sheet of paper

placed a distance, L , approximately 2 metres from the slit.

2. The diffraction pattern should have an intensity distribution as shown in Figure 1.

3. The values for ym for m = 1 to 6 are shown in Table 1. These readings were taken using a

ruler

Table 1 Results for Single Slit Diffraction

m ym /cm

1 1.6

2 2.7

3 3.7

4 4.9

5 5.9

6 6.9

(Note that in determining ym it is more accurate to measure the distance between the

corresponding fringes on the right and left of the central bright pattern and halving the

distance).

4. L is given as 2.0m.

5. From your results plot a graph ofsinmversus m.

6. Find the slope of the graph. Hence determine a value for the slit width a.

7. Calculate the error in the slope and the error in the slit width a.

(B) Double Slit Interference

1. For this section use the double slits labelled A on the plate. Direct the laser beam

through the double slits and observe the interference pattern on a sheet of paper placed

a distance, L , approximately 2 metres from the slits.

2. The values for the interference fringes are shown in Table 2.

m x/cm

1 0.9

2 1.0

3 1.1

4 0.9

5 1.0

6 1.1

7/30/2019 Phys 1412 Manual_2011

16/36

5

3. Calculate the average fringe separationx.

4. The distance L to the screen is given as 2.358m.

5. Use the relationship to calculate dfor the double slits.

6. Also sketch the intensity distribution for the interference pattern produced by slits.

7. Discuss your results.

Plate With Labels

2

4

3

1

A

D

C

B

5

Fig. 4

7/30/2019 Phys 1412 Manual_2011

17/36

6

EXP 2 MECHANICAL RESONANCE

PURPOSE: To observe the phenomenon of resonance by studying standing waves on a

string under tension.

THEORY: Mechanical Resonance is discussed in Ch17-12 Halliday, Resnick & Walker

Whenever a system is given a periodic series of impulses at a frequency equal to (or very

nearly equal to) one of its natural frequencies of oscillation, the amplitude of the oscillations

becomes fairly large. This is the phenomenon of resonance.

In this experiment a string under tension as in Figure 1 has one of its ends vibrated

periodically by a mechanical rotator. The rotator has a knurled-head screw which permits

the spindle speed to be varied continuously by moving the spindle friction ring toward the

edge or centre of the drive plate on which it rests. The friction ring may be locked in any

position on the drive plate by a set screw provided. A revolution counter is mounted on the

spindle and can be engaged by applying finger pressure to its starting lever.

Fig.1

CARE SHOULD BE TAKEN NOT TO APPLY MORE PRESSURE THAN IS NECESSARY TO ENGAGE

THE GEAR ON THE COUNTER AS IT MAY BE DAMAGED BY EXCESS PRESSURE.

At resonance the standing waves must be such that the ends of the string are nodes. This

condition is satisfied if the length of the string is given by where n =

1,2, 3, n therefore represents the number ofhalf-wave segments in

the envelope of the vibrations of the string.

l

pulley

rotator

Mg

2

nl =

7/30/2019 Phys 1412 Manual_2011

18/36

7

It can be shown that the natural frequencies of vibration of the system are given by

where = mass/unit length of the

string

and Mg = tension in the string.

If we expressfin Hz, lin metres, M in kg,g in m/s2, then will be in kg/m.

METHOD:

(a) Varying tension, constant frequency

1. Set up the apparatus as in Figure 1. Adjust the spindle frequency close to its maximum

and lock it in place.

2. Measure the number of revolutions that occur over a period of about a minute, and

hence calculate the frequency. This measurement should be repeated during the

experiment to ensure that the frequency remains fairly constant.

3. By adjusting the value of the hanging mass obtain standing waves for as many values of

n as possible. Record corresponding values ofM and n.

4. Plot a graph ofn2

againstM

1.

(b) Varying frequency, constant tension

1. Attach a mass of about 50g to the end of the string.

2. By varying the frequency, obtain standing waves for as many values ofn as possible.

Record corresponding values offand n.

3. Plot a graph offagainst n and determine its slope.

(c) Calculation of the mass/unit length

1. Measure land M and hence calculate the value of from the slope of the graph off

against n.

2. Obtain a value of by direct measurement using the sample string provided. Do not

detach the string from the rotator.

Discuss your results

Mg

l

nf

2=

7/30/2019 Phys 1412 Manual_2011

19/36

8

EXP. 3 PROPERTIES OF SINE WAVES

PURPOSE: To investigate the properties of sine waves.

THEORY:If there are two waves with the same amplitude, frequency and wavelength travelling in

the same direction within the same space, with a phase difference of between them we

may represent the two waves using the equations:

(1)

and (2)

where, ym is the amplitude, k= 2/, = 2f.

If we superimpose the two waves the resultant wave may be expressed as:

(3)

Where ( )2cos2 my is the amplitude of the resultant wave.

If there are two waves with the same frequency and wavelength but different

amplitudes travelling in the same direction within the same space, with a phase difference

of between them we may represent the two waves using the equations:

(4)

and (5)

Since we cannot factor out the amplitudes, the equation for the resultant wave is written as:

( )+= tkxyyRmR

sin (6)

The phasor method is then applied to find the components ofR and complete the wave

equation as shown in Figure 1.

21 yyyR +=

( ) += tkxym

sin

( ) ( )[ ] ++= tkxtkxym

sinsin

( ){ } ( )2sin2cos2 += tkxy m

+=

2cos

2sin2

tkxym

( ) + tkxym sin

( )tkxyym

= sin1

( ) += tkxyym

sin2

( )tkxyym

= sin11

( ) += tkxyy m sin22

7/30/2019 Phys 1412 Manual_2011

20/36

9

Figure 1 Phasor method for solving wave equations

Using the Cosine rule we get:

2

2my= Cosyyyy RmmRmm 1

22

1 2+ (7)

Using the Sine rule we get:

)=

sin(sin12 mm yy (8)

METHOD:

Switch on the oscilloscope. If the single horizontal green line trace appears on the screen

and is suitable proceed to part (a). If not, adjust the INTEN and FOCUS controls for clarity

and centre the trace on the screen using the X-POS and Y-POS controls. The TIMEBASE

control may have to be set to a value which produces a steady trace. See Figure 2.

7/30/2019 Phys 1412 Manual_2011

21/36

10

Figure 2 Diagram of Oscilloscope

(a) Frequency/Wavelength Analysis

1. Connect the the signal generator in parallel to the input terminal channel 1.

2. Set the generator frequency to 100Hz and the Y-AMPL variable control to the calibrate

position.

3. Adjust the size of the signal from the generator to give a convenient reading and

measure the corresponding peak-to-peak distance using the oscilloscope. This is

obtained by measuring the vertical distance between the top of the sinusoidal trace to

the bottom of the trace. This is the amplitude of the sine wave.

4. When a steady trace is observed the oscilloscope may be used to obtain the wavelength

of the trace.

5. Vary the frequency of the signal generator and measure the corresponding wavelength.

6.

Draw a graph of f vs. and find its gradient.7. What does this graph suggest about the relationship between f and ?

8. What does the gradient of the graph represent?

In ut

Y-POS X-POS

Timebase

VariableFocusIntensity

Voltage

Gain

Display

7/30/2019 Phys 1412 Manual_2011

22/36

11

(b) Superposition Analysis of waves with the same amplitude, frequency

and wavelength

1. Connect the signal generator in parallel to the input terminal channel 1.

2. Set the generator frequency to 50Hz and the Y-AMPL variable control to the calibrate

position.


measure the amplitude of the sine wave.


of the trace.

5. Using equation (1), write an expression for the equation of the wave.

6. Connect the signal generator in parallel to the input terminal channel 2 while still

connect to channel 1. This produces a second wave with a phase shift () of zero.

7. Using equation (2), write an expression for the equation of this second wave.

8. Switch the position knob to DUAL to observe both waves. Ensure that the voltage gain

on both channels is the same.9. Now switch the position knob to ADD to superimpose the two waves.

10.Sketch the input and output waves on the same graph sheet denoting the values for y

and .

11.Using equations (3) write an expression for the equation of the resultant wave.

(c) Superposition Analysis of waves with the same frequency and

wavelength

1. Connect the signal generator in parallel to the input terminal channel 1.

2. Set the generator frequency to 160Hz and the Y-AMPL variable control to the calibrateposition.


measure the amplitude of the sine wave.


of the trace.


6. Connect the signal generator in parallel to points A and C on the board provided as

shown in Figure 3.

Figure 3 Schematic for phase shift circuit.

1k1F

7/30/2019 Phys 1412 Manual_2011

23/36

12

7. Connect the input terminal channel 2 to points B and C. This produces a second wave

with a phase shift ().


9. Switch the position knob to DUAL to observe both waves. Ensure that the voltage gain

on both channels is the same.

10.Now switch the position knob to ADD to superimpose the two waves.11.Sketch the input and output waves on the same graph sheet denoting the values for y

and .

12.Using the phasor method and equation (7), calculate the value for and hence complete

the wave equation given in equation (6).

13.Calculate also the magnitude of the phase shift () using equation (8).

14.Given thatfRC

2

1=tan calculate the theoretical value of and compare with the

value obtained from the experiment.

15.Discuss your results.

7/30/2019 Phys 1412 Manual_2011

24/36

EXP. 4 PLANE

PURPOSE: To observe the m

to the observed li

THEORY: The Di fraction G

Light incident normally on a pl

given by

grating, and m is an in

METHOD:

1. Adjust the spectrometer fo

distant object outside the l

this point the slit image

telescope. The width of th

image. Now rotate the tele

ensure this and clamp the t

d

m=sin

TRANSMISSION DIFFRACTION GRA

ercury spectrum and to use the wavelengths c

nes to calculate the spacing of the grating.

ating is discussed in Ch 37-7 Halliday, Resnick

ane diffraction grating will be diffracted thro

here is the wavelength of the light, dis the s

teger denoting the order of the spectrum.

r parallel. This may be done by focussing the t

ab. Set the telescope exactly in line with the

hould lie exactly on the cross wires in the

slit may have to be adjusted to give a suitabl

cope through exactly 90 using the telescope

lescope in this position.

13

ING

orresponding

Walker

ugh angles

pacing of the

lescope on a

ollimator. At

field of the

y narrow line

ngle scale to

7/30/2019 Phys 1412 Manual_2011

25/36

14

2. Mount the grating on the prism table and adjust the table until light is reflectedinto the

telescope. Adjust the levelling screws on the table until the slit image is exactly in the

centre of the field of view. This adjustment sets the grating upright. Adjust the grating

until the reflected slit image is on the cross-wires. This sets the grating in a plane at 45

to both the telescope and collimator. Read the prism table scale and then rotate it

through exactly 45 so that the plane of the grating is perpendicular to the collimator.

3. Unclamp the telescope and locate a diffracted image of the slit at as large an angle of

deviation as possible. Adjust only the table levelling screw that is approximately in the

plane of the grating until the image is in the centre of the field of view. This adjustment

is to get the grating rulings vertical. If a large adjustment has to be made at this point, it

is advisable to repeat the adjustment procedure.

4.

Measure the angle of diffraction for as many lines of the mercury spectrum as you canidentify, for the first and second orders. For accuracy you should take readings of the

images on both sides of the direct beam and halve the angle between them. Note that

short wavelength light is diffracted less than the long wavelength and that the second

order spectrum is diffracted more than the first.

5. For each wavelength and order observed, calculate a value of the grating spacing d,

using the values of listed below.

6. Calculate the average value ofdand its mean deviation.

7. Discuss your results

MERCURY LINES

VIOLET (moderate) 405 nm

VIOLET (weak) 408 nm

VIOLET (strong) 436 nm

BLUE-GREEN (weak) 492 nm

GREEN (strong) 546 nm

YELLOW (strong) 577 nm

YELLOW (strong) 579 nm

7/30/2019 Phys 1412 Manual_2011

26/36

EXP. 5

PURPOSE: To investigate th

THEORY: Interference is dis

If monochromatic light is incide

R is resting on a plane glass su

observed. Interference takes pla

and those reflected at the plan

path difference of twice the thi

lens surface (see Figure l). On

change of 180 as the rays are r

of the medium in which the inci

Because the thickness of the ai

from the point of contact of the

are alternately satisfied. Since

nature, the interference pattern

The condition for MAXIMA is:2

= wavelength of light used a

The term is introduced beca

NEWTON'S RINGS

interference pattern known as Newton's Ring

cussed in Ch 36 Halliday, Resnick & Walker

t on the air film formed when a lens of radiu

face, the interference pattern known as New

ce between rays that are reflected at the lowe

e glass source. Rays reflected from the plane

kness of the air film more than those reflecte

reflection from the glass block the rays und

eflected from a medium of refractive index hig

ent rays are travelling.

r film changes as the point under observation

lens and glass block, the conditions for maxim

the contours of constant air film thickness a

is circular.

Fig.1

+=

2

1

m where m =0, l, 2 .

d d= thickness of film.

use of the phase change of 180 on reflection.

15

.

of curvature

ton's Rings is

r lens surface

glass travel a

at the lower

rgo a phase

her than that

moves away

and minima

re circular in

7/30/2019 Phys 1412 Manual_2011

27/36

16

The condition for MINIMA is: 2d = m where m = 0, 1, 2

It can however be shown that where x is the radius of the interference ring

observed and R is the radius of curvature of the lens.

Therefore the condition for MINIMA becomes Rmx 2

Procedure:

1. Set up the apparatus as shown in Figure 2.

Fig.2

2. Switch on the sodium lamp observing carefully the sequence listed on the rheostat.

Adjust the microscope slide in its holder until the light is reflected onto the lens. At this

stage it should be possible to see the rings when looking vertically downwards without

the aid of the travelling microscope. It may be necessary to clean the lens and glass

block surfaces to obtain an interference pattern.

R

xd

2

2

7/30/2019 Phys 1412 Manual_2011

28/36

17

3. Focus the travelling microscope on the pattern and record what is observed. Make sure

that the centre of the pattern lies directly below the microscope. In this arrangement

the microscope will move along a diameter when it is moved horizontally.

4. Record the vernier readings when the cross-hairs of the microscope are set on selected

rings to the left of the centre.

5. Repeat the process on the right of the centre.

6. Calculate the diameter and hence the radius of the ring, x, for each value of the number

of the ring, N, as numbered from the centre.

7. Plot a graph ofx2

against N and determine its slope.

8. Given that = 589 nm for sodium light, calculate the radius of curvature of the lens.

9. Discuss your results and observations.

7/30/2019 Phys 1412 Manual_2011

29/36

EXP. 6 IN

.

PURPOSE: To investigate th

water) between t

THEORY: Interferenceis di

Consider a uniform wedge of air

If the wedge is illuminated by m

pattern due to interference bet

slide and those reflected at the

like B travel a distance of2AB m

a phase shift of 180 (or /2).

A dark band (minimum) will b

integer.

SupposeA'B'is another minimu

observed in going from B to B'.

of the wedge

L

d

l

ABBA=

''

ERFERENCE FROM A THIN WEDGE

interference pattern produced by a thin we

o plane glass surfaces.

cussed in Ch 36 Halliday, Resnick & Walker

formed between two plane glass surfaces as in

Fig .1

nochromatic light as shown, one should obser

een rays reflected at the lower surface of the

pper surface of the glass block. The rays reflec

ore than those reflected atA. Reflection at B al

observed if 2AB = m. Hence AB = m/2 w

. ThenA'B' - AB = N/2 where N is the numbe

ith notation in the diagram, it can be seen tha

.

18

ge of air (or

Figure 1.

ve a regular

icroscope

ted at points

o introduces

here m is an

of minima

t , the slope

7/30/2019 Phys 1412 Manual_2011

30/36

So if one selects an arbitrary mi

horizontal distance lagainst the

and are known, the diameter

If a liquid of refractive index

changed to .

Procedure:

Part One

1. Set up the apparatus as in F

Switch on the sodium lamp

1. Observe the interference p

2. Repeat the observation wit

the slope of the wedge.

d

L

2

imum as the origin where N = 0 and l= 0, a gra

number of the minima N should have a slope o

f the wire dmay be calculated.

is introduced into the wedge, the slope of

igure 2 using one of the three wire samples pr

and adjust it to illuminate the field of view.

ttern produced.

the other wires in turn and describe the effec

Fig. 2

19

ph of the

f . IfL

the graph is

vided.

t of changing

d

L

2

7/30/2019 Phys 1412 Manual_2011

31/36

20

Part Two

1. Adjust the smallest wire near to one end of the microscope slide until the lines of the

interference pattern are perpendicular to the horizontal movement of the travelling

microscope.

2. Select a suitable minimum for which N is to be taken as zero and record the reading on

the horizontal vernier scale of the travelling microscope.

3. Move the microscope along a suitable number of minima and again record the vernier

reading.

4. Repeat this procedure for several other values ofN.

5. Plot a graph ofI against N and determine its slope.

6. Use the microscope to measure L, the distance from the point of contact of the

microscope slide and glass block to the wire.

7. Given that = 589 nm for sodium light, calculate d, the diameter of the wire.

Part Three

1. Introduce a drop of water between the slide and the glass block. Note what happens to

the interference pattern.

2. Measure lfor N = 50 and also measure L.

3. Calculate the refractive index of water using the values ofdand from Part Two.

7/30/2019 Phys 1412 Manual_2011

32/36

EXP. 7 CLE

PURPOSE: To determine the

THEORY: The Kinetic Theor

Air is pumped into a vessel of v

temperature. The air is allowe

ambient pressure of the room,

had a volume V1 before expansi

the diagram), i.e. if it had b

expansion, it would have ende

allowing the air contained in th

gain heat from the surroundin

pressure,

diagram).

For the adiabatic expansionAB

where is the ratio of the specif

For the isothermal change AC

Combining (1) and (2), we get

MENT AND DESORMES EXPERIMEN

ratio of the specific heats of air.

of Gases is discussed in Ch20 Halliday, Resnic

lume V0 and allowed to reach a steady pressu

to expand rapidly (i.e. adiabatically) until i

p0. The air which then fills the vessel, volume

n. If the air had expanded from V1 to V0 isoth

een allowed to maintain room temperatur

d at a higher pressure, p2. This state can b

vessel after the adiabatic expansion (AB in th

gs until it reaches room temperature and h

p

0101 VpVp = ----- (

ic heat capacities of air.

0211 VpVp = ----- (

=

2

1

0

1

p

p

p

p

21

& Walker

rep1 at room

reaches the

V0, will have

rmally (ACin

during the

attained by

e diagram) to

s the steady

(BC in the

1)

2)

7/30/2019 Phys 1412 Manual_2011

33/36

22

Taking logs,21

01

loglog

loglog

pp

pp

= ----- (3)

Now pressures in the vessel are read from a manometer.

Thus 101 ghpp += ----- (4)

where h1is the height difference between the arms of the manometer and is the density

of the liquid in it.

Similarly, p2 =po+gh2 ----- (5)

Substituting (4) and (5) in (3), we obtain

+

+

+

=

0

20

0

10

0

0

10

1log1log

log1log

p

ghp

p

ghp

pp

ghp

so that

+

+

+

=

0

2

0

1

0

1

1log1log

1log

p

gh

p

gh

p

gh

----- (6)

Expanding (6) by the log series and neglecting squared and higher terms (justified becausegh1 andgh2 are much smaller thatpo).

21

1

0

2

0

1

0

1

hh

h

p

gh

p

gh

p

gh

=

=

----- (7)

METHOD:

1. Make sure that the release valve is closed. Connect the pump to the vessel at the outleton top and pump air into the vessel until a value ofh of about 15-20 cm is indicated on

the manometer.

2. For some time after pumping has been discontinued the pressure indicated by the

manometer will fall slowly. This is due to the air, which was heated during the

compression, slowly attaining room temperature. When a stationary pressure is

indicated, read the height difference h1.

7/30/2019 Phys 1412 Manual_2011

34/36

23

3. Depress the release valve, thus opening the vessel, for about 1-3 seconds. Then allow

the valve to close again. This will allow the pressure to fall to that of the atmosphere

sufficiently rapidly for no passage of heat to occur during the expansion. The expansion

will therefore be adiabatic. The temperature of the air in the vessel will slowly increase

to that at the start of the experiment, during which time the pressure in the vessel will

rise top2.

4. After a steady state is reached, record the height difference h2.

The greatest source of error in this experiment will occur if insufficient time is allowed for

steady conditions to be obtained. Five (5) minutes generally suffices but it is an advantage

to take readings of pressure against time before and after releasing the air. This will enable

you to determine the value ofh at which steady state is reached.

5. Repeat the experiment four times recording h1and h2in each case.

6. Calculate a value of for each set of readings. Calculate also the mean value of and the

mean deviation. Find out the accepted value of for air and discuss your results in

relation to this value.

7/30/2019 Phys 1412 Manual_2011

35/36

24

EXP. 8 CONSTANT VOLUME GAS THERMOMETER

Aim: To plan and design a lab to calibrate and test a constant volume gas thermometer.

Theory

The relationship between the pressure, temperature, mass, and volume for gases at

relatively low pressures and high temperatures is referred to as the ideal gas equation of

state:

pV = nRT [1]

where, p = pressure

V = volumeT = temperature

n = number of moles

R = universal gas constant = 8.315J/(mol.K)

From this is equation we see that p T. Thus we may use this thermometric property of

gases to design a thermometer. Given that the volume of the system is constant equation

[1] becomes:

TV

nRp = = (constant)T

Procedure:

Part 1 Taking Temperature and Pressure Readings

1. Calibrate the sensor:

Connect the pressure sensor to one of the Analog Channels of the interface. Open DataStudio

and create a new experiment. Click on the Add Sensor or Instrument tab and add the pressure

sensor (absolute). Make sure the syringe is not attached and that the tube and sensor are

open to the atmosphere. Select a sample rate of 20Hz. Select the Calibrate Sensors tab and

select the option 1 Point (Adjust offset only) then click on the button Read from Sensor. This

should give the reading for atmospheric pressure.

7/30/2019 Phys 1412 Manual_2011

36/36

25

2. Connect the pressure sensor to the side arm of the round bottom flask via the rubber

tube.

3. Insert the rubber bung with the thermometer at the mouth of the flask to seal the flask.

Ensure that the thermometer is not touching the sides of the flask.

4. Pour the boiling water into calorimeter to about half full.

5. Place the flask into the water and cover the calorimeter. Ensure that the flask is

completely immersed.

6. Open the Data window by dragging the graph icon and dropping it in the window. This

shows a pressure vs. time graph.

7. Allow the air in the flask to heat up and record the maximum temperature reached.

8. Press the start collection button to begin taking readings from the pressure sensor.

9. Record the corresponding temperature reading by clicking on the note button (A) and

entering the temperature value for the relevant pressure on the graph.

10.Allow the water to cool and record the temperature every minute.

11.Once the cooling has slowed add a few chips of ice and record the temperature and

pressure after a minute.

12.Repeat for at least 8 additional temperature and pressure readings. Include in these

readings a reading as close to 0oC as possible.

Part 2 Calibrate and Test the Constant Volume Gas Thermometer

1. Use the readings from Part 1 to design an experiment to create a constant volume gas

thermometer. Include in your design:

a. Clear description of your experimental procedure including the steps taken to

calibrate the thermometer

b. The use of the theory above to justify your procedure

c. Potential sources of error

d. Appropriate precautions to minimize experimental error.

2. Test your thermometer by measuring the value for room temperature.

3. Compare this value with the value measured directly using the mercury thermometer.

4. Discuss your design and state how this design be improved?

phys 1412 manual_2011

Documents