1. NEWTON’S RINGS
AIM:
To determine the radius of curvature of a plano convex lens by forming Newton’s Rings.
APPARATUS:
Plano convex lens of long focal length, travelling microscope, thick glass plates,
magnifier torch, sodium vapour lamp.
FORMULA:
The radius of curvature of plano convex lens is
𝑅=
2
2
𝐷𝑚
− 𝐷𝑛
4𝜆(𝑚−𝑛)
cm
Where
λ = Wavelength , A0
D = Diameter of the dark ring, cm
R = Radius of curvature of the lens, cm
m, n are order of the dark rings.
DIAGRAM:
PROCEDURE:
1
1. Clean the lens, L and the glass plates smoothly with a cotton dipped in carbon
tetrachloride. See that they are from dust particles and scratches.
2. The cross wire to the 10th ring. Note the main scale reading and the vernier coincidence.
Keep the lens on top of the glass plate, G. Arrange this combination on the bench of the
travelling microscope.
3. Arrange the microscope M, vertically above the centre of the lens and focus it on to the
glass plate, G.
4. Fix the glass plate, between the lens and the microscope.
5. Adjust the glass plate, P such that it is at an angle of 450 to the incident light from the
source, for normal incidence. It is achieved by adjusting the glass plate for a bright field
of view in the microscope.
6. Slightly adjust the focus of the microscope to get alternate bright and dark rings in the
field of view.
7. Move the microscope horizontally until the centre of the ring system coincides with the
cross wires of the microscope.
8. Move the microscope either to left or right, by counting the number of dark rings. When
the microscope is past the 10th ring. Lock the position of the microscope.
9. By turning the fine adjustment knob, coincidence.
10. Similarly, note down the microscope reading for the 9th, 8th, 7th ……….. 1st ring. In each
case note the M.S.R and V.C.
11. Move the microscope in the same direction with the help of the fine adjustment knob.
Note down the microscope reading for 1st, 2nd, 3rd, 4th, ……… 10th dark rings on the
other side of the centre.
12. The difference of the two readings of a given ring, taken on either side of the centre
gives its diameter.
13. Note down the readings in the following tabular form.
OBSERVATIONS:
1. Value one main scale division
=
2. Number of divisions on the vernier
=
3. Least count of the microscope, L.C
=
cm
4. Wavvelength of sodium light
=
cm
2
cm
Travelling Micro Scope Readings
Left
Sl.No
No.
M. S. R
of
Dark Cm
Rings
V.C
Right
Dl =
M. S. R
M.S.R + Cm
VC x LC
cm
V.C
Dr =
M.S.R +
VC x LC
cm
D = Dl
difference
Dr cm
GRAPH:
Plot a graph between the order of the ring, n and the square of the diameter. Draw a
straight line passing through most of the points and the origin.
cm
3
D2
cm
PRECAUTIONS:
1. To move the microscope across ring by ring, lock it and make use of fine adjustment knob.
2 .Move the microscope in one direction only , to avoid backlash error.
3. While taking readings, see that the cross wire exactly coincides with the ring.
RESULT:
Radius curvature of plano-convex lens is
= ………… cm.
Questions:
1. How are the alternate bright and dark rings formed?
2. What is the reason for the formation of circular and concentric fringes?
3. The light coming for the source is made to fall on a glass plate held at 450 to the vertical –
why?
4. What is the reason for selecting a lens of large radius of curvature?
5. What is the reason for the formation of a central dark spot?
6. Does sodium lamp give one or two wavelengths?
7. Why is the fringes are broad at the centre and as we move outwards they get narrower ?
4
2. SONOMETER - VERIFICATION OF LAWS OF STRECHED STRINGS
AIM :
To verify the laws of transverse vibrations of stretched strings using sonometer.
APPARATUS :
Sonometer, slotted weights (500 gms each) , three tuning forks of known
frequency, rubber hammer, screw gauge, steel , brass and copper wires.
DESCRIPTION :
A sonometer consists of a hallow rectangular box about 125 cm long 15 cm
broad, made of seasoned teak wood and covered with a thin plank of soft wood as shown in fig.
The box is provided with two long fixed knife edges parallel to its breadth, about 6 cm, from
each side. At one end two or three pegs are provided to which strings of various materials and
radii can be firmly attached. These strings may be passed over the fixed knife – edges, carried
over tiny smooth pulleys at the other end of the box and attached o their ends. The vibrating
segments of the string can be adjusted by the movable knife edges.
Pulley
Paper rider
Knife edges
Resonance takes place when the frequency of the external body(tuning fork) is equal to
the natural frequency of the segment of the wire. At resonance energy transfer from the external
body(tuning fork) takes place and the segment of the wire between ‘B’ and ‘C’ vibrates with
maximum amplitudes.
THEORY:
A stretched string when pluck at its middle and released, it vibrates in a single
loop, which is the fundamental mode of transverse vibrations and a note of frequency n
depending on the tension (T) , the length of the vibrating loop ‘l’ and the mass per unit length
‘m’ of the wire. The relation connecting the above quantities is given by then the frequency of
fundamental mode of vibration of stretched string is given by
𝑛=
1
2𝑙
√
𝑇
𝑚
Hz
5
…………………(1)
From the above relation, the laws of transverse vibration of stretched strings may be stated as:
(i)
The frequency frequency of fundamental mode of vibration (n) of a stretched string is
inversely proportional to its length l, and m being constant. That is
nl = constant
(ii)
…………….(2)
The frequency frequency of fundamental mode of vibration (n) of a stretched string is
inversely proportional to the square of its linear density m, T and l being constant.
That is
n2m = constant ………(3)
(iii)
The frequency frequency of fundamental mode of vibration (n) of a stretched string is
proportional to the root of its tension T, m and l being constant. That is ,
[n2/T] = constant
………………..(4)
It is very difficult to verify the third law directly. Hence they are verified indirectly as follows :
We have from equation (1)
1
𝑇
𝑛 = 2𝑙 √𝑚 Hz
Or
n2
=1/4l2 (T/m) ……………….(5)
From equation (5) it follows that if (T/l2) is shown to be constant. It can be assumed that
n2 m = constant, and the second law is verified.
Similarly, from equation (5) if (m l2) is shown to be constant, it can be assumed that (n2/T) is
constant and the third law is verified.
Therefore to verify the laws of stretched strings, the following relations are to be verified.
1.
2.
3.
The product (nl) is constant , when T and m are constant.
The ratio (T/l2) is constant, when n and m are constant.
The product (ml2) is constant, when n and T are constant.
6
PROCEDURE:
1. Verification of first law:
Suitable number of weights are placed on the weight hanger which is attached to one end
of the sonometer wire to create sufficient tension in the wire. One of the tuning forks is
excited by stricking the prongs of the tuning fork with the rubber headed hammer. The stem
of the tuning fork is set vertically on the top of the sounding box. In doing so , the prongs of
the tuning fork should not be touched or should not touch the sonometer wire. The length of
the wire between the knife edges adjusted by slowly moving the knife edges ‘B’ and ‘C’
nearer to one another or apart, until the natural frequency of the segment ‘BC’ is equal to that
of the tuning fork. To know whether the wire between B and C is under resonance or not, a
small V shaped paper rider is placed at the middle point of the segment BC of the wire. The
tuning fork is struck and the stem of the fork is placed on the sounding box.The length of the
wire between Band C is slowly varied by moving ‘B’ in small steps, each time placing the
paper rider about the mid point of BC. At some positions of B , the paper rider flutter
violently and may even be thrown of due to symmetric vibrations in the segment BC. The
position of the B, for which the paper is thrown of gives the length for resonance. This length
is BC = l. The procedure is repeated with 2 or 3 forks of different frequencies and the results
are tabulated in table 1.
2. Verification of second law
[T/l2 is constant, when n and m are constant]
To verify the law, the same tuning fork and wire are used throughout the experiment,
and the tension applied to the wire is varied. For different tensions, the resonating lengths
are noted and results are tabulated.
3. Verification of third law
[ml2] is constant when n and T are constant ]
To verify the third law, three wires of different linear densities (m) are taken and a
tension T is applied. A tuning fork of known frequency is excited and the stem of it is
placed by the side of the wire and the resonating length “l” of the wire is noted. Similarly,
the resonating length of the other two wires for the same tuning fork are determined. The
results are tabulated in table 3.
7
MODEL GRAPH :
l
1/n
TABLE 1
Linear density of the wire m=
Tension applied to the wire T=
S.NO
Frequency of
the tuning
fork n (Hz)
Length “l” of the vibrating segment in (cm)
Trail 1
Trial 2
8
Mean l
n×l=constant
Model Graph:
l
√𝑻
TABLE 2
Frequency of the tuning fork used n =
Linear density of the wire m =
S.NO
Tension
applied in
gm. (T)
Length “l” of the vibrating segment in (cm)
Trail 1
Trail 2
9
Mean length
l
T/l2=
constant
TABLE 3
Frequency of the fork n=
Hz
Tension applied
dynes
S.NO
Type of
wire.
T=
Linear
density of
the wire in
gm/cm.
Resonating length of the wire “l” in
cm.
Trail 1
Trail 2
Mean
length “l”.
Model Graph:
l
√𝒎
Result:
10
ml2 =
constant
Questions:
1. What is the difference between a stationary and a progressive wave?
2. Upon what factors does the frequency of vibration of the sonometer wire depend?
3. How do we verify the law of tension?
4. How do we verify the law of length for the transversely vibrating stretched string?
5. What is the purpose of the holes in the sonometer board?
11
3. STUDY OF NORLMALMODES IN A STRING USING FORCED
VIBRATIONS IN RODS
(Melde’s experiment)
AIM:
To determine the frequency of a vibrating bar or tuning fork using Meldy’s
arrangement.
APPARATUS:
Storage cells, rheostats, plug keys, connecting wires, meter scale. Thread, card board pan,
weight box, smooth pulley fixed to a stand, electrically maintained vibrator or tunning fork.
DESCRIPTION :
An electrically maintained tuning fork consists of an electro magnet between the two
prongs of a tuning fork without touching either of the prongs, as shown in fig. To one of the
prongs a thin brass plate with an adjustable screw is riverted on it. By adjusting the screw,
contact is established with the thin brass plate.
Electrical connections are made as shown in fig. When plug is inserted in the key, the
circuit is completed and the electrical current is flows through the circuit energizing the electro
magnet there by pulling both the prongs inwards. The circuit is broken immediately at the point
S, the electro magnet loses its magnetism and the prongs fly back to its original position.
Consequently contact is once again established at S, the circuit is closed and the process repeats
automatically as before. This causes the prongs of the fork to vibrate.
One end of a thin thread is connected to a small screw provided on one of the tuning
fork. The other end of the thread is connected to alight card board pan and the thread is passed
over a small friction pulley fixed on to a stand kept at a distance of 3 to 4 meters from the fork.
Small weights are placed in the cardboard pan so that sufficient tension is created to the string.
The tension in the string can be altered by changing the weights in the cardboard pan.
The tuning fork is arranged as shown in fig (a). For a longitudinal vibrations, i.e, the
vibrations of the prong are parallel to the length of the string. After noting the observations in
this position, the tuning fork is arranged as shown in fig (b). for transverse vibrations, i.e. the
vibrations of the prong are perpendicular to the length of the string.
It is to be noted that in both the cases, the stretched string should vibrates at right
angles to us length(and both the cases are transverse vibrations of the stretched strings). In case
the stretched string after forming loops rotates, then small weights are either to be added into the
pan or removed from the pan to create sufficient tension in the string and the loops formation
vertical.
12
THEORY:
(a) Transverse arrangement:
The fork is placed in the transverse position and by adjusting the length of the string
and weights in the pan, the string starts vibrates and form many well defined loops. This is
due to the stationary vibrations set up as a result of the superposition of the progressive wave
from the prong reflected wave from the pulley. Well defined loops when the frequency of
each segment coincides with the frequency of the fork. The frequency η of the transverse
vibrations of the stretched string by a tension of T dynes is given by
𝑛=
1
2𝑙
√
𝑇
𝑚
Hz
Where
m = Mass per unit length of the string
l = length of the single loop.
B
E
A
N
S
R
(b) Longitudinal Arrangement:
When the fork is placed in the longitudinal position and the string makes
longitudinal vibration, the frequency of the stretched string will be half of the frequency of the
fork. That is , when well defined loops are formed on the string, the frequency of each segment
of the string is exactly half the frequency of the fork.
13
A
A
A
E
N
N
B
S
R
During longitudinal vibrations , when the prong is in right extreme position, the
strings corresponding to a loop gets slackened and comes down and when the fork is in its left
extreme position, the slackened string moves up to its initial position and becomes light. But
when the prong is again in its right extreme position, thereby completing one vibration, the string
goes up, its inertia carrying it onwards and thereby completes only a half vibration.
Hence the frequency of each loop is
1
𝑛=
2𝑙
√
𝑇
𝑚
Hence the frequency of the vibrator is
= 2η1 =
1
=
𝑙
√
1
𝑇
𝑚
√𝑚
√
𝑇
𝑙
………………(2)
PROCEDURE:
The apparatus is first arranged for transverse vibrations, with the length
of the 3 or 4 meters and passing over pulley. The electric circuit is closed and the rheostat is
adjusted till the fork vibrates of loops(say between 4 and 10) with well defined nodes and
maximum amplitude at the antinodes are formed, the vibrations of the string being in the vertical
plane.
14
The number of loops(x) formed in the string between the pulley and the fork are noted. The
length of the string between the pulley and the fork (d) is noted. The (l) of single loop is
calculated by
L = {d/x} cm
Let p = mass of the cardboard pan
M= Load added to the cardboard pan
Tension (T) = (M + P) g dynes
Where g =
Acceleration due to gravity at the place.
The experiment is repeated by increasing or decreasing the load (M), So that the
number of loops increase or decrease by one. The experiment is repeated till the whole string
vibrates in one or two loops and the observations are recorded in table 1.
Next, the fork or vibrator is arranged for the longitudinal vibrations. The
experiment is repeated as was done for the longitudinal vibrations are recorded in table 2.
Observations:
1. Linear density of the thread (m) = 0.0021 grams/cm
2. Mass of the cardboard pan
(p) = …………. grams
15
TRANSVERSE ARRANGEMENT
S.No
Load applied
into the
pan(M)grams
Tension
T =(M+ρ)g
Dynes
No. of
loops
Average of √T/l =
16
Length of
‘x’
loops=d
cm
Length of
each loop
l=d/x cm
√T
√T/ l
LONGITUDINAL ARRANGEMENT
S.No
Load applied
into the pan
(M) grams
Tension
T =(M+ρ)g
Dynes
Average of √T/l
No. of
loops
=
17
Length of
‘x’
loops=d
Cm
Length
of each
loop
l=d/x cm
√T
√T/ l
RESULT:
Questions:
1. What type of waves are produced in a fork or a bar when excited?
2. What is a transverse wave and a longitudinal wave?
3. What is stationary wave?
4. What is the difference between a note and a tone?
5. What are beats?
6. What are nodes and antinodes?
18
4. INTERFERENCE FRINGES – WEDGE FILM
AIM:
To determine the thickness of a thin foil and hence to determine the angle made by it
in a wedge film using interference fringes.
APPARATUS:
A pair of glass plates with a thin foil in between them, traveling microscope,
thick glass plates, magnifier torch, sodium vapour lamp.
FORMULA:
If α is the angle of a wedge film, then from interference we have
N (λ/2 )
tan α
t
= d tan α
= N λ / (2d)
= L tan α
Where
t : thickness of the film (cm)
N
: No . of fringes measured
d
: width of N fringes, cm
α : angle of the wedge ,rad .
L :
Length of the wedge
19
DIAGRAM :
Microscope
Glass plate
Source
Wedge film
PROCEDURE:
1. Clean the glass plates smoothly with in carbon tetra chloride. See that they are free from
dust particles and scratches.
2. Keep the two glass plates(slides) together. Place a thin foil, T under one of their ends so
as to form a wedge.
3. Arrange the microscope, M vertically above the centre of the wedge and focus it
on to the glass plates.
4. Fix another thin glass plate, P between the slides and the microscope.
5. Adjust the glass plate, P such that it is at an angle of 450 to the incident light from the
source, for normal incidence. It is achieved by adjusting the glass plate for a bright field
of view in the microscope.
6. Slightly adjust the focus of the microscope to get alternate bright and dark fringes in the
field of view.
7. Move the microscope horizontally to one of the fringe system. Lock the microscope.
8. With the help of the fine adjustment screw, see that the cross wires of the microscope
coincides exactly with a fringe. Note down the microscope reading.
9. Move the microscope slowly in the same direction simultaneously count the number of
fringes that cross the field of view. When the cross wires coincide the 10th fringe, stop the
microscope and note down its reading.
10. Repeat step (8), for every 10 fringes i.e. note down the microscope readings of 20 th, 30th
,40th , …………… fringes.
20
11. Find out the difference between the successive readings to get the fringe width, d of 10
fringes.
12. At the end of the experiment, using microscope measure the length, L of the wedge
distance between the closed end to the position of the foil.
OBSERVATIONS:
1. Value of one main scale division
:
cm
2. Number of divisions on the vernier
:
3. Least count of the microscope
:
4. Wave length of sodium light
:
cm
5. Length of the wedge, L
:
cm
6. Number of fringes in group, N
cm
:
Microscope Readings (cm)
S.No
No. of fringes
(n)
MSR (a)
cm
VC (n)
VC x LC (b)
cm
21
TR (a+b)
cm
Width of 10 fringes d (cm)
PRECAUTIONS:
1. To move the microscope across fringe by fringe, lock it and make use of fine adjustment
knob.
2. Move the microscope in one direction only, to avoid backlash error.
3. While taking the readings, see that the cross wire exactly coincides with the fringe.
4. Move the microscope slowly to avoid missing of fringes while counting.
RESULT:
(a) The angle of the wedge is
=
rad
(b) The thickness of the foil is
=
cm.
Questions:
1. What is the principle involved in the formation of fringes in the experiment?
2. Why are the fringes formed in the experiment are straight and parallel, while in Newton’s
rings experiment the fringes are circular?
3. What is meant by Interference of light?
4. How can coherent sources be obtained?
5. What is meant by optical path difference?
22
5. VOLUME RESONATOR
AIM:
To verify the relation between the resonating volume of an air cavity and the
frequency of the note producing resonance in it.
APPARATUS:
Aspirator bottle, tuning fork of different known frequencies and a measuring jar.
DISCRIPTION:
The volume resonator consists of an aspirator bottle of 1 to 2 liter capacity,
having opening in its side near the bottom. It is fitted with a one holed rubber –stopper into
which a short glass tube is inserted. A rubber tube is connected with the glass tube and a pinch
cock is attached to it. When the aspirator is fitted with water, a required amount of water may be
drawn out by opening the pinch cock.
T
PROCEDURE:
The natural frequency of the air in the resonator is given by,
= V
2л
√(A/ ν L)
Where V is the velocity of sound in air , ν is the volume of the vibrating air up to the neck of
the bottle and L is the length of the neck. A is the cross sectional area of the neck, since V, A
and L are constants.
N ∞1/ (√ν)
or
23
n2ν = constant
If ‘e’ is the end correction at the mouth of the bottle, n2 (ν + e ) = constant. This relation is
verified experimentally.
The pinch cock is closed and the aspirator bottle is filled with water up
to its neck. One of the tuning fork is taken and it is excited by the hammer. The tuning fork is
held above the neck of the aspirator bottle with out the prongs of the fork touching the neck and
water in the aspirator bottle is slowly let out and collected in a jar, by opening the pinch cock.
When the volume of air inside reaches a particular value a sharp loud note or resonance is
produced. Then the pinch cock is closed and the volume of air in the aspirator is found by
measuring the water that flowed out with a measuring jar. The experiment is repeated twice with
the same fork and the mean volume (v) of the air in the bottle resonating with a tuning fork of
known frequency is found. The experiment is repeated with four or five tuning fork of different
frequencies. The results are tabulated as shown in below.
S. No
Frequency of
tuning fork
(n) Hz
Air resonating volume (v) ml
n2
Trail 1
Trail 2
24
Mean
1 / n2
n2 (ν +e )
=
Constant
Model Graph:
A graph is plotted by taking ν on y axis and 1/n2 on x axis. The negative
intercept on y axis gives the end correction e. From the graph the unknown frequency of a
tuning fork can be determined by using the resonating volume with the fork.
ν
1/n2
e
PRECAUTIONS:
1. The tuning fork should be held with its prongs horizontal.
2. The position of the maximum sound should be noted carefully.
RESULT:
The relation between natural frequency and its volume is verified.
The unknown frequency of tuning fork is
Questions
1. Define longitudinal and transverse waves.
2. What is node and anti node?
3. What is resonance?
25
………
6. REFRACTIVE INDEX OF LIGHT
AIM:
To determine the refractive index of the light source by given prism.
APPARATUS:
Spectrometer, mercury lamp, flint glass prism.
PRELIMINARY ADJUSTMENTS:
The following adjustments are to be made before the commencement of an experiment
with a spectrometer.
i)
EYE PIECE ADJUSTMENT:
The telescope is turned towards a bright object say a white wall about 2 to 3 meters way
and the eye piece is adjusted so that the cross wires are very clearly seen. This ensures that
whenever an image is clearly seen on the cross wires, the eyepiece is an unstrained condition.
ii)
TELESCOPE ADJUSTMENT:
The telescope is now turned towards a distant and its length is until the distant object is
clearly seen in the plane of the cross-wires; that is the image suffers no lateral displacement with
the cross-wires of the eye shifted slightly to and fro. In this position the telescope is capable of
receiving parallel rays. This means that whenever any image is seen clearly on the cross-wires, it
may be taken that the rays entering the telescope constitute a parallel bundle.
iii)
COLLIMATOR ADJUSTMENT:
The slit of the collimator is illuminated with light. The telescope is turned to view the
image of the slit and the collimator screw is adjusted such that a clear image of the slit is
obtained with out parallax cross-wires. The slit of the collimator is also adjusted to be vertical
and narrow.
THEORY:
The refractive index of the material of the prism.
µ =
Sin (A+Dm )/2
Sin (A/2)
where A = angle of the prism=600
Dm = angle of minimum deviation.
26
When the angle of the incidence is small, the angle of deviation is large. As the angle
also increased, the angle of deviation begins to diminish progressively, till for one of the
incidence is particular value. This angle is known as the angle of minimum deviation Dm.
TABLE:
Spectroscope Readings
Minimum deviation
position
Sl.No
Color
M. S. R
of
the Cms
line
V.C
Direct readings
D1 =
M. S. R
M.S.R + Cms
VC x LC
cms
27
V.C
D2 =
M.S.R +
VC x LC
cms
D = Dl ~D2
cms
OBSERVATIONS&CALCULATIONS:
Least count of the vernier of the spectrometer =
Angle of the prism (A) = 600
Direct reading :
Vernier 1 =
Vernier 2 =
The refractive index of the given material of the prism is
Refractive index of the blue ray µB =
Refractive index of the red ray
Sin (A+DB )/2
µR =
Sin (A/2)
Sin (A+DR )/2
Sin (A/2)
The refractive index of the given material of the prism is = (µB+µR)/2 =……….
Where µB = refractive index of the blue ray.
µR = refractive index of the red ray.
µ = (µB+µR)/2 the mean of µB and µR
PROCEDURE:
The prism is placed on the prism table with the ground surface of the prism on to the left
or right side of the collimator care is to be taken to seen the ground surface of the prism do not
face either collimator or the telescope. The vernier table is then fixed with the help of the vernier
screw.
The rays of light passing through the collimator strikes the polished surface of the prism
and undergo deviation and emerges out of the prism from the another face. The deviated ray is
seen through the telescope. Looking at the spectrum the prism table is now slowly moved on to
28
one side, so that the spectrum moves towards undeviated path of the beam. The deviated ray also
moves on the same side for some time and then the ray start turning back even through the prism
table is moved in the same direction. The point at which the rays start turning back is called the
minimum deviation position. In the spectrum is sufficient if one colour is adjusted for the
minimum deviation position. In this limiting position of the spectrum, deviation of the beam is
minimum. The telescope is now fixed on the violet colour and tangent screw is slowly operated
until the point of intersection of the cross-wires is exactly on the image. The reading for violet
colour is noted. In vernier 1 and vernier 2 and tabulated in the table. This reading is called the
minimum deviation reading for the violet colour. The telescope is now moved on to the red
colour, without disturbing the prism table, and again the readings on vernier1 and vernier2 are
noted and tabulated in the table.
Next the telescope is released and the prism is removed from the prism table. The
telescope is now focused on to the direct ray and reading in vernier1 and vernier2 are noted in
the table.
The difference of readings between the deviated reading for violet and direct reading
gives the angle of minimum deviation reading for violet colour and the deviated reading for red
and direct reading gives the angle of minimum deviation for red colour DR. the refractive indexes
for violet and red colors are calculated using the above equation.( assuming the angle of the
equilateral prism, A=600) , the value of µ can be calculated.
RESULT:
The refractive index of the material of the given prism µ =
Questions
1. What is dispersive power?
2. Distinguish between prism spectrum and grating spectrum.
3. If you replace mercury vapor lamp with sodium vapor lamp in the present
experiment, what colors do you observe in the spectrum?
4. Which color in the spectrum is having more refractive index?
5. Why we should keep the prism in the minimum deviation position?
29
7. DIFFRACTION GRATING
AIM:
To determine the wavelengths of different colors of the spectrum of mercury
source, using diffraction grating by normal incident method.
APPARATUS:
Spectrometer, diffraction grating, mercury vapor lamp and Magnifier Torch.
FORMULA:
𝜆=
𝑆𝑖𝑛 𝜃
𝑁𝑛
A0
Where
N = No of lines per cm on the grating=15,000/2.54
n = order of the spectrum.
Θ =angle of diffraction.(degrees)
DIAGRAM:
ө
C
C
450
450
GGG
G
T
T
T
Left side
Right side
T
Direct
1. Grating set for normal to the
incident light
2. Diffracted images
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PROCEDURE:
1. Focus the telescope to a distant object for receiving parallel light.
2. Keep the collimator aperture to the source of light. Adjust the width of the
aperture to get a narrow beam of light.
3. Turn the telescope towards the collimator. Observe the vertical image of the
collimator in the telescope. Adjust the focus of the collimator to get a sharp image.
4. Adjust the eye-piece of the telescope to coincide the cross-wires to the image of
the collimator.
5. Lock the collimator and the telescope. Note down the telescope reading.
6. Release the telescope and turn it so that the reading on the scale is altered exactly
by 900 lock the telescope again.
7. Place the grating, G on its holder so that the normal to its plane is approximately
half-way between the telescope and the collimator.
8. Seeing through the telescope, adjust the grating holder slowly until the reflected
light from the grating is coinciding with the cross wires.
9. Keeping the telescope locked, release the circular scale. Turn the circular scale
exactly by 45o such that the grating is normal to the incident light from the
collimator. Lock the circular scale again.
10.Release the telescope, and turn it to see the direct image once again.
11.Turn the telescope slowly to L.H.S. to observe the first ordered spectrum.
12.Adjust the telescope and coincide the cross wire with a particular colour of the
spectrum. Use fine adjustment screw, if required. note down the telescope
reading.
13.Repeat step (12) for each of the color in the spectrum.
14.After recording the spectrum on L.H.S, turn the telescope to the spectrum on
R.H.S.
15.Repeat steps (12) & (13) for corresponding colors on the R.H.S
16.The difference between the readings of the telescope for corresponding color on
L.H.S &R.H.S gives the twice the angle of diffraction (2θ).
17. Enter the readings in a tabular form.
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OBSERVATIONS& TABULAR FORM:
1. Value of M.S.D
=
2. No. of divisions on the vernier scale
=
3. Least count
=
4.
Number of lines per cm,
N
=
5.
Order of the spectrum,
n
=
minutes
minutes
Telescope reading in deg. & min.
Color of
L.H.S (1)
R.H.S (2)
the
θ2 =
Spectral
θ1 =
S.No
M.S.R V.C
M.S.R V.C (M.S.R+V.C
line
(M.S.R+V.C×L.C)
×L.C)
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θ =(θ1- θ2)
⋋=
sin θ /
(N n)
Θ
Color
λ(A)
D
Wavelength
standard λ
(Ao)
Difference in
λ (Ao)
CONCLUSION:
1. The wavelength of the spectral lines of the mercury lamp is calculated using diffraction
grating.
2. The dispersive power of the grating for the corresponding colours is calculated.
PRECAUTIONS:
1. The image of the collimator must be narrow and set vertical.
2. Note down the vernier coincidence accurately.
3. When coinciding the cross-wire to the spectral line, lock the telescope and use fineadjustment screw.
4. Hold the grating at its edges only. Avoid finger prints to form on the surface of the
grating.
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RESULT:
Questions
1. What is meant by diffraction of light?
2. How does the grating form diffraction images when monochromatic light falls
on it?
3. What is the grating element and how its value is calculated?
4. Differentiate between a plane grating and a concave grating?
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8. RIGIDITY MODULUS
(Torsional pendulum)
AIM:
To determine the modulus of rigidity (η) of the material of the given wire using a torsional
pendulum.
APPARATUS:
A circular brass disc provided with a chuck and nut at its centre, steel wire,
another chuck nut fixed to a wall bracket or a rigid clamp, stop watch, meter scale, screw gauge,
vernier calipers.
DESCRIPTION:
The torsional pendulum consists of a uniform circular metal disc of about 8 to
10 cm diameter with 1 or 2 cm thickness, suspended by a wire at the centre of the disc as shown
in figure. The lower end of the wire is gripped into the chuck at the center of the disc and the
upper end is gripped in to another chuck, which is fixed to a stand.
THEORY:
At the equilibrium position of the disc a radial line is drawn from the centre to “p”
as shown in figure. When the disc is rotated in a horizontal plane to the radial position “Q”, the
wire gets twisted. the twisted wire will exert a torque on the disc tending to return it to the
position “p”. this is the restoring torque. For small twists, the restoring torque is proportional to
the amount of twist, or the angular displacement (Hooks law.) so that
T= (-) Cθ …………………………..(1)
Where “C” is called the tortional constant.
The negative sign shows that torque is directed opposite to the angular displacement θ.
Eqn(1) is the condition for angular simple harmonic motion. The equation of motion for such a
system is
T=Iα =I (d2 θ /dt2)…………………..(2)
From(1) &(2), we get
-Cθ = I (d2 θ /dt2)
(d2 θ /dt2)= -Cθ /I ………….(3)
The solution of the eqn (3) is, a simple harmonic oscillation,
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θ = θm Cos(ωt+δ )……………………(4)
where θm is the maximum angular displacement.
The period “T” of the oscillation is given by
𝐼
𝑇 = 2𝜋√ …………..(5)
𝐶
Where, I=moment of inertia of the disc about the axis of the rotation and
C-couple per unit twist of the wire.
If “a” is the radius of the wire, “l” is the length of the wire between the chucks and “η” is the
rigidity modulus of the material of the wire, then the couple “C” per unit twist of the wire is
given by;
C= (a4 η π /2l)……………………………(6)
Squaring eq.(5), we get
T2 = 4 π2I /C
C = 4 π2I / T2 …………………….. (7)
From equations (6) & (7), we have
η = 8 π I / a4 ( l / T2 )………………..(8)
the moment of inertia, I of a circular disc whose geometric axis coincides wiyh the axis of
rotation is given by;
I =MR2/2………………………… (9)
Where M = mass of the disc, R = radius of the disc. Substituting the value of 1 from (9) in (8)
we get,
η = 4 π MR2 / a4 ( l / T2 ) …………… (10)
PROCEDURE:
The circular metal disc is suspended as shown in figure. The length of the wire
between the chucks is adjusted to 90 cm. when the disc is in equilibrium position, a small mark is
made on the curved edge of the disc. This marking will help to note the number of oscillations
36
made by the disc, when the disc is oscillates. The disc is set to oscillate by slowly turning the
disc through a small angle. care is to be taken to see that there is no lateral movement of the disc.
When the disc is oscillating, the time taken for 20 oscillations is noted with the help of a
stop watch and recorded in the observations table in trail 1; the procedure is repeated for the
same length of the wire and again the time taken for 20 oscillations is noted and recorded in the
table in trail 2. From trail 1 & trail 2, the mean time for 20 oscillations is obtained. The time
period (T), i.e the time taken for 1 oscillation is calculated.
The experiment is repeated, by decreasing the length of the wire in steps of 10 cm and results
are tabulated in table.
The radius of the wire “a”, is to be found accurately with the help of a screw gauge. The
radius of the disc “ R” is measured with a vernier calipers and the mass of the disc “M” is noted.
The mean value of (l/T2) is substituted in equation (10) and η is calculated.
37
GRAPH:
A graph is plotted with l on x-axis and T2 on the y-axis. It will be as shown in graph. From
the graph, the value of T2 for as large as a value of “l” is noted and this value of (l/T2) is
substituted in equation (10) and the rigidity modulus of the material of the wire is calculated.
T2
l
OBSERVATIONS:
(1). Mass of the disc M
=…………….gm
(2).Radius of the disc R
=……………..cm
(3).Average radius of the wire = ……………cm
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S.No
Length of
wire ‘l’
b/w
chucks
(cm)
Time taken for 20 oscillations (sec)
Trail 1
Trail 2
Average
Time
period
T
(sec)
T2
l/T2
cm/sec
RESULT:
Questions
1. Upon what factor does the periodic time depends?
2. What is periodic time?
3. Rigidity is determined for a thick wire and thin wire, both of the same
material, which wire (thick or thin) has a greater rigidity?
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