BS 8161 - PHYSICS LABORATORY

DETERMINATION OF RIGIDITY MODULUS –TORSIONAL PENDULUM

AIM:

To determine the moment of inertia of a given disc by Torsional oscillations and the rigidity
modulus of the material of the suspension wire.
APPARATUS:
Torsional pendulum, Stop clock, Meter scale, two symmetrical mass, Screw gauge.

FORMULA
Moment of inertia of the circular disc,

Rigidity modulus of the wire,

m mass of one cylinder placed on the disc(100 gm) kg

d1 Closest distance ( minimum) between suspension wire and the centre of mass of the cylinder m
d2 Farthest distance ( maximum) between suspension wire and the centre of mass of the cylinder m
T0 Period of oscillation without any mass on the disc s
T1 Period of oscillation when equal masses are placed on the disc at a distance d1 s
T2 Period of oscillation when equal masses are placed on the disc at a distance d2 s
l length of the suspension wire m
r Radius of the wire m

1
Time period of oscillations
Length of suspension wire l = cm

Time for 10 oscillations

Time period
Position of equal masses Trial 1 Trail 2 Mean (Second)
(Second) (Second) (Second)

Without masses To =

Masses at closest distance.

T1 =
d1 = ……… x 10-2 m

Masses at maximum
distance. T2 =
d2 =……….x 10-2 m

Radius of the Wire (r):

LC = 0.01 mm Z.E = …..div
Z.C =……mm
HSR= HSC x LC Observed Reading Correct Reading
S. No. PSR HSC = PSR+ HSR = OR ± ZC
Unit mm div mm mm mm

Mean (d) =-------------------------- x 10-3 m

Radius of the specimen wire (r) = d/2 = ……. x 10-3 m
CALCULATION:

RESULT:

The moment of inertia of a given disc (I) = kgm2

The rigidity modulus of the given wire (n) = Nm-2

2
 YOUNG’S MODULUS – NON-UNIFORM BENDING
AIM
To determine the young’s modulus of the material of a beam by non-uniform bending.
APPARATUS REQUIRED:
A uniform rectangular beam, Two knife edges, A weight hanger with slotted weight,
Travelling microscope, pin, screw gauge and vernier caliper.

FORMULA: Fig.
2.
Young’s modulus of the material of the beam
𝑴𝒈𝒍𝟑
Y = 𝟒𝒃𝒅𝟑 𝒚 Nm-2

y Mean depression for a load meter

g Acceleration due to gravity m/s2
l Distance between the two knife edges meter
b Breadth of the beam (meter scale) meter
d Thickness of the beam (meter scale) meter
M Load applied kg
Depression (y)
LC = 0.001 cm TR = MSR + (VSC x LC)
Microscope Reading Depression
Load Mean
S.N Loading Unloading y for M kg
M
o. MSR VSC TR MSR VSC TR
x 10-3kg cm
Cm Div cm cm div cm Cm

Mean

3
Breadth of the beam using vernier caliper:
LC = 0.01cm Z.E = Nil
Z.C = Nil

Observed Reading = Corrected Reading =

MSR VSC
S.No. MSR + (VSC X LC) (OR ± ZC)
cm div
cm cm

Mean

Thickness of the beam using screw gauge :

LC = 0.01mm Z.E =
Z.C =

Observed Reading = Corrected Reading

PSR HSC
S.No. PSR + (HSC X LC) (OR ± ZC)
mm div
mm mm

Mean

CALCULATION:

Load applied at mid-point M= x10-3 kg.

Acceleration due to gravity g= ms-2.

Breadth of the beam b= x10-2 m

Thickness of the beam d= x10-3 m

Length of the beam between the knife edge 𝒍= x 10 -2 m

𝑴𝒈𝒍𝟑
Y = 𝟒𝒃𝒅𝟑 𝒚 Nm-2

4
RESULT:
The young’s Modulus of the material of the given beam = Nm-2

Grating

Laser x1
x
source Laser
x2

Dl

OBSERVATION:
Distance between grating and screen (D) = ___________________ x 10-2m
Number of lines in grating per meter (N) = ___________________ lines/meter

Order of Diffraction image 𝑥 𝑠𝑖𝑛𝜃

S.No. θ = tan-1( 𝐷𝑛) λ=
diffraction meter 𝑁𝑛

5
(n) Left Right Mean degree meter
xn xn xn

6
 WAVELENGTH OF LASER LIGHT SOURCE
EXPT NO: DATE:
AIM:
To determine the wavelength of the laser of light using grating.
APPARATUS REQUIRED:
Laser source, Laser Grating with stand, Screen, Scale
FORMULA:
Wavelength of the given laser source of light
𝑠𝑖𝑛𝜃
λ= metre
𝑁𝑛

N Number of rulings in the grating lines/meter

n Order of spectrum No unit
θ Angle of diffraction Degree
PROCEDURE:
To find the number of lines per meter in the grating
The initial adjustments of the spectrometer are made. The direct ray is coincided with the
vertical crosswire and the telescope is fixed. Now the vernier table is released and both the verniers
are made to coincide with 0º and 180º and the vernier table is fixed. The telescope is released and
moved towards the right side through 90º and fixed. The grating is mounted on the grating table and
rotated to the reflected image and coincided with vertical crosswire. Now the vernier table is rotated
45º towards collimator and grating will become perpendicular to the light rays. Telescope is moved to
left and right and the perpendicular order ray is coincided and the readings are noted in both the scales.
𝑠𝑖𝑛𝜃
The number of lines per unit length of the grating can be calculated as follows N= 𝜆𝑛

The laser source is focused on the screen. The grating is made exactly perpendicular to the
light rays. If we use a 1, 00, 00 lines per meter on the grating, nearly 15 orders of diffracted images are
formed. The diffracted images can be viewed on the screen. The image has central maxima and several
orders in the right and left of the central maxima. The distance(x1) of the left side first order dot is
measured from the central maxima and is noted down. Similarly the distance (x2) of the first order dot
on the right from the central maxima is also measured. All the distances of the dots are measured and
noted down in the tabular column.

CALCULATION:
7
8
RESULT:
Wavelength of the laser light source = meter.

9
 Screen
Glass Plate with
fine particles

LASER

OBSERVATION:
Distance between glass plate and the screen (D) = _______________ x 10-2m
Wavelength of the laser source (λ) = _____________ x 10-10m

Distance
between the
Distance
central Particle size
between screen Order of
bright point 𝑛𝜆𝐷
S.No and glass plate Diffraction d=
th 𝑥𝑛
and n
(D) (n) cm
fringe
cm
(xn)
cm

Mean =

10
 PARTICLE SIZE DETERMINATION BY USING LASER
AIM:
To determine the size of the micro particle using laser.
APPARATUS REQUIRED:
Laser source, Fine micro particles of nearly uniform size (Lycopodium powder), Glass
plate, White screen, Stands, Meter Scale.
FORMULA:
Particle size (diameter) d is given by
𝒏𝝀𝑫
d= metre
𝒙𝒏

n Order of diffraction
λ Wavelength of the laser source meter
Xn Distance between glass plate and the screen meter

D Distance between the glass plate and the screen meter

PROCEDURE:
Sprinkle a thin uniform layer of lycopodium powder on a glass plate. Mount the screen
and glass plate upright. The light from laser source transmitted through the layer of lycopodium in
the glass plate is adjusted to form a diffracted image in the centre of the screen. Diffracted circular
fringes of laser color will be visible on the screen.
After adjusting the distance of the glass plate from the screen so that the first ring radius
(x1) and second ring radius (x2) are measured from the central spot. Note the distance (l)
between screen and plate. Repeat the experiment radius of the first and second rings after
adjusting the distance between screen and plate. Calculate the value of the diameter of the particle.

RESULT:
Average size of the particle = meter.

11
 Laser source

Optical fiber cable

jig

Numerical aperture

Laser
Fiber

OBSERVATION:
Distance from the
Radius of the
fibre end to Acceptance angle
circular image r
S.No. circular image θ=d NA = sinθ
(r)
(d) degree
meter
meter

mean
CALCULATION:

12
 NUMERICAL APERTURE AND ACCEPTANCE ANGLE IN OPTICAL FIBER
AIM:
To determine the numerical aperture and acceptance angle of the given optical fibre.
APPARATUS REQUIRED:
Optical fiber cable, Laser source, Numerical aperture, White screen, with concentric circles,
scale.
FORMULA:
𝒓
Acceptance angle (θ) = 𝒅 radians

Numerical aperture (NA) = sin θ

r Radius of the circular image meter

d Distance from the fibre end to circular image meter
PROCEDURE:
The numerical aperture jig consists of an iron or plastic stand with a moving screen. In
this screen, a number of concentric rings of varying diameter are present. In front of it, a stand
with a circular slit in the centre is provided which is connected to the laser light source through the
optical fiber cable. By moving the screen back and forth the laser light from the circular slit is made
to fall exactly on the circles with different diameters. The distance „l‟ between the circular slit in
the jig and screen for various circular diameters are noted on a moving scale situated at the
bottom of the jig. Thus by knowing the values of l and w, the value of the numerical aperture is
calculated. The maximum divergent angle (the acceptance angle) is also determined.

RESULT:
Acceptance angel of the optical fibre = radian.
Numerical aperture of the optical fibre =

13
14
 THERMAL CONDUCTIVITY OF A BAD CONDUCTOR – LEE’S DISC
EXPT NO: DATE:
AIM:
To determine the coefficient of thermal conductivity of a bad conductor using Lee’s disc
apparatus.
APPARATUS REQUIRED
Lee‟s disc apparatus, bad conductors, stop-clock, thermometers, screw gauge, vernier
calipers, steam boiler
FORMULA
Thermal conductivity of a bad conductor
𝑑𝜃
𝑀𝑆( ) 𝑑 (𝑟+2ℎ)
𝑑𝑡 𝜃2
K = 𝜋𝑟 2 (𝜃 Wm-1K-1
1 − 𝜃2 )(2𝑟+2ℎ)

M Mass of the metallic disc kg

S Specific heat capacity of the material of the disc J kg-1 K-1
𝑑𝜃 Rate of cooling at θ2 o
C/s
( )
𝑑𝑡 𝜃2
r Radius of metallic disc meter
h Thickness of metallic disc meter
d Thickness of bad conductor meter
θ1 Steady temperature of a steam chamber o
C
θ2 Steady temperature of the metallic disc o
C

PROCEDURE:
The thickness of the bad conductor say card board and thickness of the metallic disc are
determined using a screw gauge. The radius of the metallic disc is found using a vernier caliper. The
mass of a metallic disc is also found using a common balance. The readings are tabulated.

15
To find the radius of the metallic disc using vernier caliper(r):
LC = 0.01cm Z.E = Nil
Z.C = Nil

MSR VSC Observed Reading = Corrected Reading =

S.No.
x 10-2m div MSR + (VSC X LC) (OR ± ZC)
x 10-2 m x 10-2 m
1.

2.

3.

4.

5.

Mean

To find the thickness of the bad conductor using screw gauge (d) :
LC = 0.01cm Z.E =
Z.C =

PSR HSC Observed Reading = Corrected Reading

S.No.
x 10-3m div PSR + (HSC X LC) (OR ± ZC)
x 10-3 m x 10-3m
1.

2.

3.

4.

5.

Mean

16
 The whole Lees disc apparatus in suspended from a stand. The given bad conductor is placed
in between the metallic disc and the steam chamber. Two thermometers T1 and T2 are inserted into
respective holes. Steam from the steam boiler is passed into the steam chamber until the temperature
of the steam chamber and the metallic disc are stead. The steady temperature (θ1) and the steam
chamber (θ2) of the metallic disc recorded by the thermometers are noted.
Now the bad conductor is removed and the steam chamber is placed in direct contact with the
metallic disc. The temperature of the disc rapidly rises when the temperature of the disc rises about
10oC above θ2, the steam chamber is carefully removed after cutting of the steam supply.
When the temperature of the disc reached 10oC above the steady temperature of the disc, stop
clock is started. Time for every one degree Celsius fall of temperature is noted until the metallic disc
attains a temperature (θs-10)oC
A graph is drawn taking time along the x-axis and temperature along the y-axis. The cooling
𝑑𝜃
curve is obtained. To obtain the rate of the cooling( 𝑑𝑡 ) . From this graph, a triangle is drawn by
𝜃2

taking 1oC above and 1oC below the steady temperature θ2. Then the slope AB/BC gives the rate of
𝑑𝜃
cooling at( 𝑑𝑡 ) . From these readings and using formula thermal conductivity of the given bad
𝜃2

conductor is calculated.

17
To find the thickness of the metallic disc using screw gauge (h) :
LC = 0.01mm Z.E =
Z.C =

PSR HSC Observed Reading = Corrected Reading

S.No.
x 10-3m div PSR + (HSC X LC) (OR ± ZC)
x 10-3 m x 10-3m
1.

2.

3.

4.

5.

Mean

Temperature Time
o
C (t) second

18
CALCULATION:
Mass of the metallic disc M= kg
Specific heat capacity of the metallic disc S = 370 Jkg-1K-1
Radius of the metallic disc r= x 10-2 m
Thickness of the metallic disc h= x 10-3 m
Thickness of the bad conductor d= x 10-3 m
Steady state temperature of steam chamber θ1 = o
C
θ1 = K
Steady state temperature of the disc θ2 = o
C
θ2 = K
𝑑𝜃
Rate of cooling ( 𝑑𝑡 ) at steady state temperature =
𝜃2
𝑑𝜃
𝑀𝑆( ) 𝑑 (𝑟+2ℎ)
𝑑𝑡 𝜃2
K = 𝜋𝑟 2 (𝜃 Wm-1K-1
1 − 𝜃2 )(2𝑟+2ℎ)

19
RESULT:
Thermal conductivity of the given bad conductor = Wm-1K-1

20
OBSERVATION:
Type of liquid: Frequency of generator = Hz
No. of Micrometer Reading 2d Velocity
d = R1 – R2 λ= n
S.No. oscillations PSR HSC TR υλ
meter meter
(n) mm div mm ms-1

Mean:

21
 ULTRASONIC INTERFEROMETER
EXPT: DATE:
AIM:
To determine the velocity of sound waves in the medium of the liquids using ultrasonic
intrefrometer.
APPARATUS REQUIRED:
Ultrasonic interferometer (High frequency generator, measuring cell) experimental liquid etc.
FORMULA:
𝟐𝒅
Wavelength of the ultrasonic waves (λ) = m
𝒏

Velocity of ultrasonic waves in a liquid (V) = υλ ms-1

𝟏
Compressibility of the liquid (K) = 𝑽𝟐 𝝆 m2N-1

d distance moved by the micrometer meter

υ Frequency of the ultrasonic wave Hertz
n Number of maxima readings of anode current ---
ρ density of the given liquid Kg/m3
V Velocity of the given liquid ms-1
PROCEDURE:
The measuring cell which is an especially double walled cell for maintaining the temperature
of the liquid constant during the experiment is filled up with given liquid. The measuring cell is
connected to the output terminal of the high frequency generator through a coaxial cable
provided with the instrument. The micrometer screw is initially set as 25 mm. The generator is
switched on to excite the quartz crystal at its frequency to generate ultrasonic waves in the liquid.
This has to be done only after filling the liquid in the measuring cell and not earlier. The generator
consists of two knobs namely gain and adj knobs, which for sensitivity regulation for greater
deflection and for initial adjustment of micrometer at zero initially. The adj knob is adjusted slightly
to adjust the position of the needle on the ammeter which is used to notice the number of
maximum deflections. The gain knob is rotated and set it to show maximum reading in the
ammeter. The micrometer screw is adjusted which is on the top of the measuring cell which can
lower or raise the reflector in the liquid in the measuring cell through a known distance, to
move downwards.

22
CALCULATION:

23
 The ammeter readings vary from maximum to minimum and from minimum to maximum
value and in between these maxima to minima there occur extra peaks due to a number of reasons,
but they do not affect the value of λ/2. The rotation of the micrometer screw is continued in the
same direction as before. The micrometer reading for the first maximum is noted down and then
for successive maxima shown by the interferometer and 20 such readings are recorded. The
distance moved by the micrometer screw for x maxima is found and its mean value is found. The
velocity of the ultrasonic waves in the liquid medium. The density of the liquid if given is noted, if
not given it standard value from the table has to be noted down. Then by substituting all the values
in the formula the compressibility of the given liquid can also be found.

Result:
The velocity of ultrasonic waves in the given liquid = ms-1
Compressibility of the given liquid = m2N-1

24
25
 SPECTROMETER - GRATING
EXPT NO: DATE:
AIM:
To determine the wavelengths of the prominent lines of the mercury spectrum using grating.
APPARATUS:
Spectrometer, grating, sodium and Mercury vapour lamps etc.
FORMULA:
Wavelength of the prominent lines of the mercury spectrum
𝑠𝑖𝑛𝜃
λ= m
𝑁𝑛

θ Angle of diffraction degree

N Number of lines per metre in the grating lines/meter
n Order of the diffraction
PROCEDURE
To standardize the grating using sodium light:
The preliminary adjustments of the spectrometer are made. The slit is illuminated with
sodium light. The telescope is brought in a line with the collimator and the direct reading is
taken on both the verniers. The prism table is firmly clamped and the telescope is turned through

900 and fixed in this position. The grating is mounted on the table so that the rulings on it are
parallel to the slit. The grating platform is rotated till the image of the slit reflected from the surface
of the grating is seen in the telescope.
The platform is fixed in the position at which the vertical crosswire coincides with the

fixed edge of the image of the slit. The vernier table is rotated through exactly 45 0 in the proper
direction, so that the surface of the grating becomes normal to the collimator. The prism table is a
fixed in this position, now the grating is adjusted for normal incidence. The telescope is now
released and brought to the position of the direct image. On either side of it are seen the diffracted
images of the first order. The telescope is turned to the left to view the first order diffracted
image. The vertical crosswire is made to coincide with the fixed edge of the image of the slit.
𝑠𝑖𝑛𝜃
Readings of lines per metre N of the grating is calculated using the relation N = λ𝑛

26
Determination of wavelength of
spectral line
Order of
Number of lines (N) = spectrum (n)
lines/meter =
Difference
Reading of the differaction image between the
readings

Left Side Right Side

Sepectral Mean
Line θ λ = sinθ/Nn
2θ
Vernier A Vernier B Vernier A Vernier B 2θ 2θ
(A1) (B1) (A2) (B2) A1- B1-
A2 B2

MS VS MS VS MS VS MS VS
TR TR TR TR
R C C C C C C C

27
(B) Determination of Wavelength of the prominent line of the Mercury spectrum:

Without disturbing the spectrometer replace the sodium vapour lamp by Mercury
vapour lamp whose wavelengths are to be determined. Rotate the telescope and observe the
dispersed diffracted spectral lines of Mercury light of first order and second order on either side of
central undispersed direct image. Take reading on both side for the first order diffraction pattern.
The angle of diffraction θ for the different lines of the first order is measured. The wavelength λ of
𝑠𝑖𝑛𝜃
each line is calculated using the relation λ = 𝑁𝑛

28
CALCULATION:

29
RESULT:
The wavelength of the prominent spectral lines in the mercury source are calculated and
tabulated.

30
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32
 DETERMINATION OF THICKNESS OF A THIN WIRE

EXPT.NO. DATE:

AIM:

To determine the thickness of the given wire using air wedge method

APPARATUS REQUIRED:
Vernier microscope, two optical plane rectangular glass plates, sodium vapour lamp, thin wire,
glass plate and condensing lens
FORMULA:
𝜆𝑙
Thickness of the wire, t = 2𝛽 m

where,
λ - Wavelength of the sodium light (5893 Å)
l - Distance of the wire from the edge of the contact (m)
β − Mean fringe width (m)
PROCEDURE:
Two optical plane glass plates are placed one over another. One of their edges is tied with rubber
band. The given wire is placed in between the two plates at the other end. This forms an air wedge
arrangement.
This arrangement is placed on the horizontal bed of the vernier microscope. Light from the
sodium vapour lamp is rendered parallel with the help of a condensing lens. The parallel beam of the
light is allowed to fall on a glass plate inclined at 45o. The refracted light from the plate is made to fall
vertically on the air wedge. The interference pattern is seen through the eye-piece of the microscope
held just above the air wedge.
Large number of equi-spaced alternative bright and dark fringes can be seen. The vertical cross
wire is made to coincide with any one of the dark fringes (n) at one end. The microscope reading given
by the vertical scale is noted. Then the cross wire is made to coincide with n + 5, n + 10, n + 15 etc., up
to n+50 and the corresponding reading are noted. The readings noted are tabulated and from the reading,
bandwidth is β calculated. The distance between the wire and the edge of contact is measured with the
microscope. Assuming the wavelength of sodium light, the thickness of the wire is determined

33
Determination of the Band Width (β):

Travelling Microscope Readings: L.C =0.001cm

Mean Width
of one band
(β)
Microscope Reading Width of 10 bands x 10-2m
Order of
MSR VSC TR=MSR+(VSCxLC)
-2
Sl.No. the band x 10 m div x 10-2m

1 n

2 n+5

3 n+10

4 n+15

5 n+20

6 n+25

7 n+30

8 n+35

9 n+40

10 n+45

Mean (β) = __________ x10-2 m

34
35
Determination of distance between Edge of contact
and wire (l):
L.C =0.001cm

MSR VSC TR
Position Cross Wire Distance
x 10-2m div x 10-2 m

Rubber Band

Edge of contact

Calculation:

36
Result:
The thickness of the thin wire (t) = m

37