Instruction Manual

B.Tech Physics Laboratory

Applied Physics Department

Sardar Vallabhbhai National Institute of Technology,
Surat395007. India

1
 Contents

S.N Practical Name Page

A Note to Students 3

Error Analysis 5

1 Radiation correction 11

2 Prism Angle 14

3 Magnetic Field of Circular Coil 16

4 Malus’ Law: Polarization of light 18

5 Stefan’s Law 21

6 Plank’s Constant using Photovoltaic Cell 24

7 Diffraction Grating 27

8 Newton’s Ring 29

2
 A Note to Students

Introduction:

The objective of Lab Experiments along with the theory classes is to understand the basic concepts
clearly. The experiments are designed to illustrate important phenomena indifferent areas of Physics and
to expose you to different measuring instruments and techniques. The importance of labs can hardly be
overemphasized as many eminent scientists have made important discoveries in homemade laboratories.
In view of this, you are advised to conduct the experiments with interest and an aptitude of learning.
This manual will provide the basic theoretical backgrounds and detail procedures of various
experiments that you will perform in the Physics laboratory. Before that, here are some specific
instructions for you to follow while carrying out the experiments. It also outlines the approach that will be
undertaken in conducting the lab. Please read carefully the followings.

Specific Instructions:

1. You are expected to complete one experiment in each class. Come to the laboratory with certain
initial preparation. The initial preparation will involve a prior study of the basic theory of the
experiment, the procedure to perform the experiment so as to have a rough idea of what to do. In
addition, it will also involve a partial preparation of the lab report (journal) in advance as
mentioned later in this section.
2. You must bring with you the following materials to the laboratory: This instruction manual,
journal (lab report)and graph sheets if necessary, pen, pencil, measuring scale, calculator and any
other stationary items required.
3. The format of a lab report (journal) shall be as follows:
(a) The first sheet (page) will contain your name, branch name and roll number, date and title of the
experiment.
(b) Each experiment should contain the following in order. Experiment Number, aim of experiment,
apparatus needed, a brief theory with working formulae, observation tables with units, figures or
diagrams whenever necessary. Write procedure in brief.
(c) Experimental observations: Data from experimental observations should be recorded in proper
tabular format with well be documented headings for the columns. The data tables should be

3
 preceded by the least counts of the instruments used to take the data and numerical value of any
constant, if any, used in the table.
(d) Graphs: (whenever applicable) Always label your graph properly. Be very clear to write the
proper units, scale, experiment number, etc.
(e) Relevant calculations: Calculations should be done neatly and carefully in proper unit. Error
analyses must to present your result.
(f) Final results along with error estimates.
(g) Remarks if any.

4. You must record your data directly in your lab record (Journal). Switch off any power supply etc.
used and put back the components of the apparatus in their proper places. Complete the rest of the
relevant calculations, error analysis, graphs (if necessary), results, and conclusion and obtain your
grade of the performed experiment before leaving the laboratory from concerned Faculty
(Instructor).
5. Last but not the least - please handle the instruments with care and maintain utmost discipline and
decorum of the laboratory.
6. Be honest in recording your data. Never cook up the readings to get desired/ expected results. You
never know that you might be heading towards an important discovery.

4
 Graphs
A graph is simply a diagram illustrating the relationship between two quantities, one of which varies as
the other is changed. The quantity that is changed is called “independent variable”, the other is called the
“dependent variable”. The following general points should be noted:
1. Scale must not be too small – loss of accuracy, scale should not be too large – exaggeration of
accidental errors. Scales on each axis are chosen usually the same unless one variable changes
much more rapidly than the other, in which case it is plotted on a smaller scale.
2. The independent variable is placed / plotted horizontally and dependent variable placed / plotted
vertically.
3. The origin need not represent the zero values of variables – unless definite reference to the origin
is required.
4. Graph should be titled. It should have captions containing - a – standard name of variable – b – its
symbol, if such a thing exists, and – c – standard abbreviation for the unit of measure.
5. Numerals representing scale values should be placed outside the axis. Values less than unity
should be written as 0.47, not .47 . Use of too many ciphers should be avoided. Thus if scale
numbers are 10,000; 20,000; 30,000 etc. They should be written as 1.0, 2.0, 3.0 with the caption –
say pressure in 104 N/m2. Similarly scale numbers 0.0001; 0.0002; 0.0003 etc. Should be written as
1.0, 2.0, 3.0 with the caption – say pressure in 10-4 N/m2
6. All letterings should be easily readable from the bottom of the graph.

Example:

200
180 Sample 1
Sample 2
160
Temperature (deg. C)

Sample 3
140
120
100
80
60
40
20
0 1 2 3 4 5
Distance (cm)

5
 AN INTRODUCTION TO ERROR ANALYSIS
Suppose the length of an object is measured with a meter scale and the result is given as 11.3 cm. Does it
mean that the length is exactly 11.3 cm? The chances are that the length is slightly more, or slightly less,
than the recorded value but as the least count of the scale is one mm (it cannot read fraction of a mm) the
observer rounds off the result to the nearer full mm. Thus, any length greater than 11.25 cm and less than
11.35 cm we can only conclude that the actual length is anywhere between 11.25 and 11.35 cm. The
maximum uncertainty (on either side) or the maximum possible error, δ1, is 0.05 cm which is half the less
count of the scale.
Let the object under consideration be a glass plate. To obtain the volume of the plate, suppose we measure
the width ‘b’ with slide calipers and the thickness ‘t’ with a screw gauge – whose least counts are
respectively 0.1 mm and 0.01 mm. Let the result obtained, after averaging over many measurements, be
b = 2.75 cm
t = 2.52 mm = 0.252 cm
and 1 = 11.3 cm
as measured by a meter scale with one end at zero exactly! We note that the coincidences noted in the
vernier scale on the head scale of the screw gauge might not have been exact and represent only the
nearest exact reading. Hence these measurements also include the corresponding uncertainties each equal
to half the least count. So we have
1 = 11.3 ± 0.05cm
B= 2.75 ± 0.005 cm
t = 0.252 ± 0.0005 cm
Note that ± 0.05 cm, ± 0.005 cm, ± 0.0005 cm are actually instrumental errors. Personal errors – like
reading 11.3 as 11.2 or 11.4 are not taken into account. To avoid personal errors average values of many
readings has to be used. The volume calculated from the recorded values of 1, b and t is
V = (11.3 × 2.75 × 0.252) = 7.8309 cm3
Take care to avoid writing cm as mm, mm as cm etc. This is also personal error but a careless one at that.
However, since each observation is subject to an uncertainty, there should be an uncertainty in the result V
too. How can the cumulative effect of the individual uncertainties on the final result be estimated?
Let the maximum error in V due to δ1, δb, and δt be δV. Then,
(V ± δV) = (1±δ1)(b ± δb)(t ± δt)
V + δV will corresponds to maximum positive values of δ1, δb, δt,
(V + δV) = (1+ δ1)(b +δb)(t + δt)
Or

6
V(1 + δV/V) =1bt (1+δ1/1)(1 +δb/b)(1 + δt/t)
Cancelling V = 1bt from both sides and using the approximation
(1 + x) (1 + y) (1 + z) = 1 + x + y + z as x<<1, y<<1, z<<1,
We obtain
δV/V = δ1/1 + δb/b + δt/t
The relative error in the product of a number of quantities is the sum of the relative errors of the individual
quantities.
δ 1 /1 = 0.05 / 11.3 =0.0044
δb / b = 0.005 / 2.75 = 0.0018
δt / t = 0.0005/ 0.252 = 0.002
δV / V = 0.0082
From the value V= 7.8309 , we have
δV = 7.8309 × 0.0082 = 0.064213 cm3
(rounded off to one significant digit).

The result of the measurements is therefore

V = 7.8309 ± 0.06 cm3
An important point to be noted is that writing the volume as 7.8309 cm3 would convey the idea that the
result is measured accurate to 0.0001 cm3. We know from the calculated error that this is not the case and
error is in the second decimal place itself. We are not certain that the second decimal is 3 but it may be 3 +
6. The volume may be anywhere in the range 7.77 to 7.89 cm3. As the second decimal place is subject to
such an uncertainty, it is meaningless to specify the subsequent digits. This result should therefore be
recorded only up to the second decimal place. [ The error could be much larger if the least counts
themselves are taken into account].
Thus V = (7.83 ± 0.06) cm3
It is the calculation of the maximum error in the result, based on the least counts of the different
instruments used that can indicate the number of significant digits to which the final result is accurate.
Suppose we now measure the mass of a plate correct to a milligram and the result is
m = (18.34 ± 0.005)gm
The density ‘d’ can be calculated from m and V.
d = m/ v = 18.34/ 7.83 = 2.3423 gm cm-3
To estimate the uncertainty in d , we write

7
 (d + δd) = m + δm/ 𝜈 - δν
As the maximum density will correspond to the greatest mass and least volume.
𝑚 (1+𝛿𝑚/𝑚)
d(1 + δd/d) = 𝛿𝜈
𝜈 1−
𝜈

𝛿𝑚 𝛿𝜈 -1
1 + δd/d = (1 + ) (1 − )
𝑚 𝜈

𝛿𝜈 𝛿𝑚
As and are very much less than 1,
𝜈 𝑚
𝛿𝑚 𝛿𝜈
δd/d = +
𝑚 𝜈

The relative error in the quotient of two quantities is (also equal to the sum of the individual relative
errors).
𝛿𝑚 0.005
= = 0.0003
𝑚 18.34
𝛿𝑑
= 0.0085
𝑑
𝛿𝑑 = 0.0085 × 2.3423 = 0.02 gm/ cm-3
Therefore d= (2.3423 ± 0.02) or (2. 34 ± 0.02) gm / cm-3
[The error in measurements may be many times the least count if the instrument is not properly designed.
Least count may often signify readability/ resolution and not the accuracy. Repeated measurements falling
outside the least counts are indicative of this]
Other situations:
1. Suppose x is the difference of two quantities a and b, whose measurements have maximum
possible errors as δa and δb. What is δx?
X =a – b
(x ± δx) = (a ± δa) – (b ± δb)
The maximum value of the difference x corresponds to maximum a and minimum b
(x + δx) = (a + δa) – (b - δb)
= (a - b) + (δa + δb)
Cancelling x = a – b,
δx =δa + δb
In a sum or difference of two quantities, the uncertainty in the result is the sum of the actual uncertainties
in the quantities – (Not the relative uncertainties).
𝑥𝑦 2 𝛿𝑝
2. If p = 𝑎𝑏 (1 + 𝑚), 𝑤ℎ𝑎𝑡 𝑖𝑠 ?
𝑝

8
 First δ(1 + m) = δ1 + δm

Y2 can be dealt with as a product of y and y.

𝛿𝑦 2 𝛿𝑦 𝛿𝑦 𝛿𝑦
= + = 2
𝑦2 𝑦 𝑦 𝑦

𝛿𝑝 𝛿𝑥 𝛿(𝑦)2 𝛿𝑎 𝛿𝑏 δ1 + δm
= + + + +
𝑝 𝑥 𝑦2 𝑎 𝑏 (1 + 𝑚)

𝛿𝑥 𝛿𝑦 𝛿𝑎 𝛿𝑏 δ1 + δm
= + 2 + + +
𝑥 𝑦 𝑎 𝑏 (1 + 𝑚)
Questions:
1. Suppose x = (a+b)/ (c-d). To minimize the uncertainty in x, which of the four quantities must be
measured to greatest accuracy, if all four quantities a, b, c, d are of the same order of magnitude?

2. The period of a simple pendulum is measured with a stop watch of accuracy 0.1 second. In one
trial 4 oscillations are found to take 6.4 secs, in another 50 oscillations take 81 secs. In this relative
uncertainty depends only on the least count of the instrument – in this case the stop watch? How
can the relative uncertainty in the period be minimized?

3. The refractive index of a glass slab may be determined using a vernier microscope as follows. The
microscope is focused on a marking on an object placed on a platform and the reading, a, on the
vertical scale is noted. The glass slab is placed over the object. The object appears raised. The
microscope is raised to get the image is focus and the position on the scale, b, is again noted. The
last reading, c, is found raising the microscope to focus on a tiny marking on the top surface of the
slab. The least count of the vernier scale is 0.01mm. The readings a, b, c are respectively 6.128 cm,
6.497 cm, and 6.128 cm. Calculate the refractive index and the percentage error in the result.
Express the result to the accuracy possible in the experiment, along with the range of error.

Note:
In the above case cited we have used our judgment i.e. the ability to estimate the reading to ONE HALF
the least count of the instrument. If we take that the actual error is ONE least count on either side of the
measured quantity all the errors calculated in the above cases would be doubled.
References
1. Practical physics – by G.L.Squires, Cambridge University Press,4th edition, 2001.
2. A text book of Practical Physics by M.N. Srinivasan, S. Balasubramanian and R. Ranganathan,
Sultan Chand and Sons, First edition, 1990.

9
10
 Experiment-1
The radiation correction

Aim: To find the radiation correction in the final temperature Joule's experiment.

Apparatus: Joule's calorimeter, thermometer, Rheostat, voltmeter, ammeter, stop-clock etc.

Theory: When the water in the calorimeter is heated by passing electric current, loss of heat takes place
due to radiation even the calorimeter is placed in the wooden insulating box. As a result the temperatures
of water recorded by the thermometer are not true, and hence are to be corrected using an appropriate
method. This correction is known as radiation correction. Correction in 'temperatures are done as per
illustration given as under.

Time Temp. Mean Temp dθ/dt Correction Corrected

(minute) ( θ ○C) ( θm ○C ) temp.
0 30 - - - 30
1 31 30.5 δ1 δ1 30+δ1
2 32 31.5 δ2 δ1+δ2 32+δ1+δ2
3 33 32.5 δ3 δ1 +δ2+δ3 33+δ1+δ2+δ3

Method: Connect the circuit as shown in the fig. Take adequate amount of water in the calorimeter.
Record the initial temperature of water and ensure that initial temperature of water and room temperature
are same. Pass 1·8 to 2·0 ampere current in the circuit. Record the temperature of water at the interval of
one minute, till the final temperature of water is minimum 5°C higher than the initial temperature. Switch
off the current and record the temperatures of the cooling water at the interval of two minutes till the fall
in temperature is minimum l○ C. Draw the cooling curve and find the average rate of cooling dS/dt at any
mean temperature (Sm.) Take dS/dt equal to zero at room temperature. Using above two values of dθ/dt
and corresponding temperatures. Prepare dθ/dt→ θm graph. Use this graph to find the rate of cooling at
different mean temperatures and apply corrections to the recorded temperatures and find the final
corrected temperature.

11
Observation Table:
[1] Heating part observation:

Ob. Time Observation Avg. Correction Total Correction Final

No. (minute) Temp. (θ) Temp.(θm) δθ ∑δθ θ
○ ○ ○ ○ ○
C C C C C

[2]Cooling part observation:

Ob. Time Temp.

No. (minute) θ ○C

Table No. :-[3]

Avg. Temp. (θ ○C)

○
dθ/dt C/

12
Result: The radiation correction in the temperatures of the system (calorimeter + water) is done by using an
appropriate method. The graph of corrected temperatures  lime is plotted. The correction in final temperature
(θf____ °C) comes out to be ∑δn =_____°C

13
 Experiment-2
Prism Angle

Aim: To measure the reflecting angle of prism using spectrometer by (i) keeping prism table fixed and
rotating the telescope. (ii) Keeping the telescope locked and rotating the prism table.
Apparatus: Spectrometer, prism, Hg-source, magnifying lens, reading lamp.
Method:
Measurement of prism angle A by rotating telescope and keep fixing the prism table.
Adjust the spectrometer for parallel rays.
Mount the prism as shown in the fig.1 such that the apex coincide with the center of the prism table.
View the reflection of the slit on the left side of prism and bring it on the cross wire and remove the
parallax. Note down the reading of both the windows as α and β.
Now rotate the telescope so that reflection of the slit from the right hand side face of the prism coincide
with the telescope cross wire. Again Note down the reading of both the windows as α and β. Take the
average and find A
Measurement of prism angle A by rotating prism table and fixing the telescope.
Mount the prism as before and take the reading on R.H.S reflection of any one windows say β.
Now fix the telescope and rotate the prism table in clock wise direction till the reflation of slit from the
other side of the prism coincides with the telescope cross-wire. Note down the reading as β’ (fig.2).
From the geometry of fig.2 it is apparent that
θ = |β – β’| and A = 180 – θ
Diagram:

Figure.1

14
 Figure.2
Observation Table. 1: Fixed the prism table
Reflecting Spectrometer Reading Angle between
Mean
Surface of reflected rays from left A°
Window 1 Window 2 2A°
Prism and right surface (2A°)
Left surface
α= β= α~α=
Right surface
α' = β' = β ~ β’ =

Observation Table. 2: Fixed the telescope

Spectrometer Reading
(note down any one
Reference: Turning Angle Prism Angle
windows reading)
Right θ°= β ~ β’ A° = 180°- θ
Before After
Reflecting
rotation, β rotation, β'
(Fig.2)

Calculations:

Result: The reflecting angle of prism, A=……°

Conclusion:

15
 Experiment-3
Magnetic Field of Circular coil
Aim: To study the variation of magnetic field along the axis of a circular coil carrying steady current.
Apparatus: Circular coil, Battery, Rheostat, one-way key, Reversing key, Ammeter, Magnetic compass,
Connection wires.
Formula: - 𝐵𝑥 = 𝐵𝐻 tan 𝜃
Where x = Distance between the center of the coil and the center of magnetic needle
BX = Magnetic field due to the current carrying Circular coil at X.
BH = Horizontal component of the earth’s magnetic field (0.3610-4 Weber/m2)
θ= Deflection of the magnetic needle of the compass in degrees.
Circuit Diagram: -

Reversing key

16
Observation Table:
1) Constant Current (I) passing through the coil = mA
X Deflection (in degrees) Mean BX
Obs. No. tan
m 1 2 3 4  (10–5 Wb/m2)
Centre 0
LHS 1
2
3
4
5
6
7
RHS 1
2
3
4
5
6
7

2). At centre of coil;

I Deflection (in degrees) Mean BX
Obs. No. tan
(mA) 1 2 3 4  (10–5 Wb/m2)
1
2
3
4
5
6
7

Graphs: BX
1. Plot graph between magnetic field vs position (Wb/mB2)m

2. Plot graph between magnetic field vs current

B=0.707
Bm
Result: Radius of circular coil, X
LH 0R RH
R =………………….cm (m)
S S
Conclusion:

17
 Experiment-4
Polarization of light: Malus’ Law
Aim: To study the polarization of light, to verify Malus law and to find the Brewster angle for glass.
Apparatus: Laser source, polarizer, analyzer, photodiode, battery, multimeter, glass slab, optical table
and stand.
Basic Theory: There are a number of ways an unpolarised light can be converted into a plane polarized
light. You are given two polarizing sheets (polaroids). The light passing out of a polarizer is linearly
polarized with the electric field E fixed in one direction in space as determined by the orientation of the
polarizing sheet. If this light passes through a second polarizer (analyzer), then the light output depends on
the relative orientation of the two polarizers. If the pass plane of the second polarizer is making an angle 𝜃
with respect to the electric field E, then the magnitude of the field in the output wave is cos𝜃 and the
output intensity is proportional to cos2 𝜃 thus the output intensity I of the light transmitted by the analyzer
is given by
𝐼 = 𝐼0 𝑐𝑜𝑠 2 𝜃 … … … … … (1)
Where I0 is the intensity of the polarized light on analyzer. This is known as Malus law.
Alternatively one can obtain polarized light by using a beam that is reflected at an interface at a particular
angle called Brewster angle. Consider a polarized beam falling on an interface YZ (fig. 1). The beam is in
XY plane and the polarization of the light is in the plane of incidence (electric field EI is in XY plane).

Fig. 1 Fig. 2
The magnitude of the reflected electric field is given by
𝛼−𝛽
𝐸𝑅 = ( ) 𝐸 … … … … … … … … … … . . (2)
𝛼+𝛽 𝑡
cos 𝜃𝑇 𝜇 𝑛
Where 𝛼 = cos 𝜃𝐼
and 𝛽 = 𝜇1 𝑛1. 𝜇 is the magnetic permeability of the material and n is the refractive
2 2
index of the material.

18
Thus the reflectivity (ER /EI) depends on angle of incidence for the inplane polarisiation and goes to zero
𝑛1
B given by tan 𝜃𝐵 = . This fact can be used to
𝑛 2
get a polarised beam from an unpolarised beam. An unpolarised beam is made to incident at an interface
at Brewster angle. The reflected beam will contain the perpendicular component only.
Experimental Setup
The set-up consists of a laser light source (partially polarised), polariser, analyser, and a photodiode (Fig.
2). The analyser unit is fitted with a circular scale to record the angular readings. Photodiode is used to
measure the intensity of light. All the components can be mounted on an optical bench for proper
alignment

Fig. 3: Experimental set-up: Malus’ law.

Procedure
Set-up and procedure:
1. The experiment is set up according to Fig. 1. It must be made sure that the photocell is totally
illuminated when the polarization filter is set up.

2. If the experiment is carried out in a non-darkened room, the disturbing background current
i0 must be determined with the laser switched off and this must be taken into account during evaluation.

3. The laser should be allowed to warm up for about 30 minutes to prevent disturbing intensity
fluctuations.
19
4. The polarization filter is then rotated in steps of 5° between the filter positions +/- 90° and the
corresponding photo cell current (most sensitive direct current range of the digital multimeter) is
determined.

Observation:

1. The experiment is set up according to Fig. 1. It must be made sure that the photocell is totally
illuminated.

2. Using a digital multimeter the disturbing background current i0 must be determined with the laser
switched off. This must be taken into account during evaluation.

3. Switch ON the laser. It should be allowed to warm up for about 30 minutes to prevent disturbing
intensity fluctuations.

4. The polarization filter is then rotated in steps of 5° between the filter positions +/- 90° and the
corresponding photo cell current (most sensitive direct current range of the digital
multimeter) is determined.

5. Make the table required for angle and the corrected photo current. Identify the intensity peak and show
that the polarization plane of the emitted laser beam has already been rotated by this angle against the
vertical. It may look like Fig. 3 below.

6. Show that the corrected and normalized photo cell current as a function of the angular position of the
analyser. It may look like Fig. 4 below. Malus's law is verified from the slope of the line.

Observation Table:
No Angle (Degree) Current (IT) µA
1
2
3
4
5
…
…

Results and Discussion:

1. Estimate the experimental errors.
2. Explain different light phenomenon happening duri

20
 Experiment-5
Stefan's Law
Aim: To verify Stefan's fourth power law of cavity radiation.
Apparatus: Battery eliminator, 6 watt bulb, mill-ammeter, voltmeter, etc.
Theory : The radiation of the cavity radiator is directly proportional to the fourth power of absolute
temperature of the black body i. e.

𝑅 = 𝜎𝑇 4
Where, R = Cavity radiancy
𝜎= Stefan’s constant
T= Temperature of the radiator

The radiancy is directly proportional to the power radiated by the bulb.

𝑅 ∝ 𝑇4
Using (1) and (2) we can have
𝑊𝑅 ∝ 𝑇 4

𝑙𝑛𝑊𝑅 = 4𝑙𝑛𝑇 + 𝑐𝑜𝑛𝑠𝑡.

The graph 𝑙𝑛𝑊𝑅 → 𝑙𝑛𝑇 is a straight line whose slope is four (4) which proves the Stefan's Fourth Power
Law of cavity radiator.

Method:
1. Connect the circuit as shown in the fig.
2. Pass the current through the filament (If) of the bulb and measure corresponding P. D. across
filament. Start with some low value of current. (It is not necessary that in beginning bulb should
glow)
3. Take eight different values of the filament current (If) in equal steps and record corresponding
filament voltage (Vf).
4. Find the resistance of the filament of the bulb for all values of currents using Ohm's Law.
5. Calculate the Power consumed by the filament of the bulb using W = VfIf
6. Determine temperature of the filament by Rt = R0(1+αt)
Where. Rt = Resistance as per step (4) and α = T.C.R of the filament
7. Plot 𝑊 → 𝑅𝑡 graph and determine (WR) power lost by radiation by eliminating (Wc) Power lost by
conduction for known values of Rt.
8. Plot 𝑊𝑅 → 𝑙𝑛𝑇 graph.
9. Find the value of the slope of the graph.

21
Circuit:

22
Graphs:

Result: The graph 𝑊𝑅 → 𝑙𝑛𝑇 is straight line. The slope of the line comes out to be 4 which is the power
of the law 𝑅 = 𝜎𝑇 4 and hence the law is verified.

23
 Experiment-6
Plank’s Constant
Aim: To determine Planck's constant "h" using Photovoltaic cell.

Apparatus: Battery Eliminator, 6 Watts Lamp, Photovoltaic Cell, Rheostate, meter. Voltmeter.
Microammeter.

Theory: The Planck's Law of black body (cavity radiator) radiation is given by;

𝐶1 1
𝑅𝜆 =
𝜆5 𝐶
( 2)
[𝑒 𝜆𝑇 − 1]

Where, 𝐶1 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡,

ℎ𝑐
𝐶2 = 𝑘 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝐵

ℎ = 𝑃𝑙𝑎𝑛𝑘 ′ 𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

𝑐 = 𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡

𝜆 = 𝑊𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑅𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛

For short wavelength and/or Low temperature equation (1) can

be expressed as

𝐶1 1
𝑅𝜆 =
𝜆5 𝑒 ℎ𝑐/𝜆𝑘𝑡

In the actual experiment the intensity of the bulb is recorded

in terms of photocurent (Ip).

It is clear that.

1
𝐼𝑝 ∝
𝑒 ℎ𝑐/𝜆𝑘𝑡

ℎ𝑐 1
𝑙𝑛𝐼𝑝 = 𝐶𝑜𝑛𝑠𝑡. −
𝜆𝑘 𝑇

The graph 𝑙𝑛𝐼𝑝 → 1/𝑇 is a straight line. (According to equation (4)).

24
Method:

1. Connect the circuit as shown in the figure.

2. Pass the current through the filament of the bulb so that bulb glow become white. (In this situation
filament of the bulb can be treated as black body radiator.)
3. Allow to fall the black body radiation on photovoltaic cell after proper filtering as shown in the
figure.
4. Record filament current (If) filament voltage (Vf) and photo current (Ip) (Filament current (If)
should be approximately more than 300 rnA.)
5. Repeat the experiment for different value of filament current (If) and measure corresponding value
of filament voltage (Vf) and photocurrent (Ip)
6. Determine Rt (resistance of the filament of the bulb) using Ohm's law.
7. Determine the temperature of the filament using Rt = R0(1+αt) relation.
Where. Rt = Resistance of the filament at to C
Ro = Resistance of the filament at 0° C
α = Temperature Coefficient of the resistance of the material of the filament
8. Plot the graph 𝑙𝑛𝐼𝑝 → 1/𝑇 and obtain slope of the line anc;l find h using equation (5).

25
26
 Experiment-7
Diffraction Grating

Aim: To determine the wavelength of the given sodium light source using plane transmission grating.
Apparatus: Sodium light source, Spectrometer, Plane Transmission Grating, Spirit-level, Magnifying
glass, etc.
Formula : ( e  d ) sin   n 
Where (e + d) = grating element = 2.54 cm/N
N= No. of lines per inch in the grating
 = angle of diffraction
n = order of the spectrum
 = wavelength of given light source

Diagram :

Simplified view of grating Grating element (e + d)

27
Observation Table:

Least Count of Spectrometer:

Order of Spectrometer Readings

Position of
spectrum 21 = A ~ B 22 = C~D
Telescope Window 1 Window 2
n
1st A: LHS
B: RHS
2nd C: LHS
D:RHS
Mean:21 = 22 =
1 = 2 =

Note: To eliminate Backlash error, take your observations in the following

order: CABD or DBAC

Calculation: (1) For the first order of spectrum (n = 1):

( e  d ) sin  1
1  Å
1

(2) For the second order of spectrum (n = 2):

( e  d ) sin  2
2  Å
2

(3) Mean wavelength of the given sodium light source

 =(1 + 2)/2 Å

Result: The wavelength of the given sodium light source  = Å

28
 Experiment-8
Newton’s Ring
Aim: To determine the radius of curvature of a given plano-convex lens using a source of known
wavelength and the phenomenon of interference of light viz. Newton’s rings.
Apparatus: Traveling microscope, Plano-convex lens, glass plates, sodium light source, etc.

𝐷 2 −𝐷 2
𝑚 𝑛
Formula: 𝑅 = 4𝜆(𝑚−𝑛)

Where, R  Radius of curvature of given plano-convex lens.

Dm  Diameter of the mth ring
Dn  Diameter of nth ring
m, n,  number of the ring as measured from center of the ring
 Wavelength of the light source
Diagram:

29
PROCEDURE:
• Please ensure that all the glass plates and lenses are clean.
• Familiarize yourself with the Traveling Microscope (TM); in particular, with the fine and coarse
motion of the TM.
• Recall how to read the scales on the TM: identify the Main Scale and the Vernier Scale. Find the
Least Count of the TM and make sure that you know how to read the scale (see below).
• Align the source of light of the given wavelength such that the light is incident at the center of the
inclined glass plate as shown in the diagram. (Note: The success of optic experiments depends
largely on good alignment.).
• Focusing of the TM: First of all, move the eyepiece back and forth until the cross-wires are
distinctly observed. Now take a small piece of paper and mark on it a ‘cross’ and put it on the top
of the horizontal glass plate. Focus the TM on the marked ‘cross’. Do not disturb this focusing
arrangement throughout the experiment. Do not forget to remove the paper after focusing is done.
• Identify the flat and the curved surfaces of the plano-convex lens. Take the plano-convex lens and
place it on the horizontal glass plate as shown in the diagram.
• If your adjustments are OK then you should be able to see the Newton’s Rings. If not, then go
back and repeat the previous steps carefully.
• Once the rings are obtained ensure that the center of the pattern of the rings and the intersection of
the cross-wires coincide. The horizontal cross-wire should be along the diameter of the rings.
• Count the rings from the center, which is taken as the zeroth ring, and go to the left-hand side until
you reach the 18th ring. Arrange the transverse cross-wire along the tangent line to the bright/dark
18th ring. Note the readings on the horizontal scale of the TM. Take the readings for the other
numbered rings as mentioned in the observation table below. In particular, move the TM in one
direction only (say, left to right) while taking the readings. This will prevent errors due to what is
known as the “back-lash” error. Using the value of the wavelength, find the radius of curvature of
the given plano-convex lens.
• Now without disturbing the TM (in particular, do NOT change the lens) replace the source with
the source of unknown wavelength. Repeat the procedure as in the last step. Enter your
observations in a new observation table.
• Find the wavelength of the second source and hence find the energy band gap for the LED source.

30
Observations:

Smallest division on the main scale (SDMS)= …….;

Total Number of Divisions on the Vernier Scale (TNDVS) = _______ ;

Least count= SDMS/TNDVS= ……

Observation Table:
1) Least count of the traveling microscope = -------------- cm
2) Wavelength of the light source λ = -------------- nm

Obs. Number Microscope Readings Diameter of D2

No. of Ring [cm2]
LHS RHS Ring D
[cm] [cm]
(LHS~RHS)
1 18
2 16 [cm]
3 14
4 12
5 10
6 8
7 6
8 4

Note: You need to make another table for another source.

Graph 1 (No. of rings vs diameter square) for the known wavelength source

Slope = AB/BC
R = slope/ 4λ

31