B. Sc.

Physics Lab Manual

Department of Physics

Ramakrishna Mission Vivekananda Centenary College

Rahara, Kolkata – 700118

Title of the Experiment

To determine the dispersive power, Cauchy constants and (at

a given )of the material of a prism using known source
 To determine the dispersive power, Cauchy constants and (at a given ) of the
material of a prism using known source

Prepared by

Palash Nath
palashnath20@gmail.com
Department of Physics, Kaliyaganj College
Kaliyaganj, Uttar Dinajpur, W. B.

(November, 2020)

Theory :
Refractive index (μ) of the material of a prism is not constant; it depends on the wavelength (λ)
of the light passing through it. The phenomena of dependence of refractive index of a medium with
wavelength is known as dispersion and the medium is called dispersive medium. If μ(λ) is the
wavelength dependent refractive index of the material of a prism, then, in the visible range it follows
Cauchy’s relation;
( )= + (1)
where, and are two constants (depends on the medium) are called Cauchy’s constants. The plot of
( ) vs 1/ will give a straight line; in which can be obtained by taking the intercept at axis and
can be obtained as the slope of the straight line.
Dispersive power of prism between two specified colours having refractive indices and
respectively is defined as;
~
= = (2)
−1 −1
where, = ( + )/2
If, prism angle is and minimum deviation angle is δ then, refractive index can be measured from the
relation,
+
= 2 (3)
2

Helium spectra

Apparatus :
i) Spectrometer
ii) Prism
iii) Spirit level
iv) Sodium light source
v) Source with known wavelengths (Mercury / Helium etc.)

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Procedure :
1. Adjustment of the spectrometer (as discussed in a separate note entitled ‘Spectrometer.pdf’)
using sodium yellow light.
a) Levelling of telescope
b) Levelling of collimator
c) Mechanical levelling of prism table
d) Crosswire focusing
e) Optical levelling of prism
f) Focussing for parallel ray by Schuster’s method
2. Determine the vernier constant of the circular scale of the spectrometer.
3. Part – 1 : Finding the prism angle:
a) Place the prism on prism table as depicted in following figure.
b) See the images of the slit formed due to reflection from both refracting surfaces of the prism.
Record the scale reading for both two images at two different position of the telescope
(Position-1 and Position-2).

4. Part-2 : Finding the minimum deviation angles for known source of light:
a) Replace the sodium light by the known source. Move the source to get sharp and intense
spectral lines. Do not disturb the focusing and alignment of the telescope.
b) Adjust for minimum deviation angle for red spectral line and record both vernier reading.
c) Repeat (b) for other observed spectral lines and record the vernier readings.
d) Remove the prism without disturbing the prism table. Move telescope to get direct light from
the collimator. Record both vernier reading as direct reading.

Experimental results :
· Determination of vernier constant :
1 smallest division in main scale = 20
60 vernier divisions = 59 main scale divisions = 59 × 20
×
1 vernier divisions =
Therefore,

(
Vernier constant = 1 main scale division – 1 vernier division = 20 −
×
)= 20"

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· Table – 1 : To determine the prism angle
Vernier Obs. Telescope position – 1 Telescope position – 2 Difference Mean Prism
Nos. No. Main Vernier Total Mean Main Vernier Total Mean ∼ difference angle
scale scale ( )
2
0 0 0 0
# 56 10 56 176 40 176
1
1st 0’ 03’ 40’ 53’
20” 560 20” 1760 1200
2 560
20 560 15’ 1760
40 1760 53’ 38’
20’ 26’ 00” 40’ 53’ 20” 20” 1200 600
40” 20” 31’ 15’
1 2360 40 2360 3560 20 3560 30” 45”
2nd 0’ 13’ 40’ 46’
20” 2360 40” 3560 1200
2 2360 40 2360 23’ 3560 28 3560 48’ 24’
20’ 33’ 20” 40’ 49’ 00” 40”
20” 20”
Obtained value of angle of the prism = 600 15’ 45”
# Sample calculation :

Total = Main scale + ( vernier scale reading X vernier constant )

= 560 0’ + 10 X 20”
= 560 0’ + 200”
= 560 0’ + 3’20” ( since, 60” = 1’ So, 200” = 3’20” )
= 560 03’20”

· Table – 2 : Telescope reading at the minimum deviation position

Colour with
wavelength Vernier No. Obs. No. Main scale Vernier Total Mean
(in nm)
1st 1 67° 40’ 42 67° 54’ 00” 67° 53’ 30”
Red 2 67° 40 39 67° 53’ 00”
667.8 2nd 1 247° 40’ 46 247° 55’ 20” 247° 54’ 40”
2 247° 40 42 247° 54’ 00”
1st 1 67° 00’ 35 67° 11’ 40” 67° 10’ 50”
Yellow 2 67° 00’ 30 67° 10’ 00”
587.6 2nd 1 247° 00’ 44 247° 14’ 40” 247° 15’ 00”
2 247° 00’ 46 247° 15’ 20”
1st 1 65° 40’ 45 65° 55’ 00” 65° 55’ 50”
Green 2 65° 40’ 50 65° 56’ 40”
501.6 2nd 1 245° 40’ 41 245° 53’ 40” 245° 53’ 00”
2 245° 40’ 37 245° 52’ 20”
1st 1 65° 40’ 18 65° 46’ 00” 65° 45’ 30”
Blue - I 2 65° 40’ 15 65° 45’ 00”
492.2 2nd 1 245° 40’ 26 245° 48’ 40” 245° 48’ 20”
2 245° 40’ 24 245° 48’ 00”
1st 1 64° 40’ 13 64° 44’ 20” 64° 44’ 40”
Blue - II 2 64° 40’ 15 64° 45’ 00”
447.1 2nd 1 244° 40’ 25 244° 48’ 20” 244° 48’ 40”
2 244° 40’ 27 244° 49’ 00”

Page : 3
· Table – 3 : Direct reading of the telescope :

Vernier No. Obs. No. Main scale Vernier Total Mean

1st 1 1180 40’ 15 1180 45’ 00” 1180 45’ 20”

2 1180 40’ 17 1180 45’ 40”
2nd 1 2980 40’ 27 2980 49’ 00” 2980 48’ 30”
2 2980 40’ 24 2980 48’ 00”

· Table – 4 : Determination of the angle of minimum deviation and refractive index :

Prism angle found out : = 600 15’ 45”

Colour with Direct ray Telescope Minimum Mean
wavelength Vernier reading reading at deviation minimum +
(in nm) No. (a) minimum angle deviation = 2
deviation (a ~ b) angle 2
(b) ( )
Red 1st 1180 45’ 20” 67° 53’ 30” 500 51’ 50” 500 52’ 50” 1.64315
667.8 2nd 2980 48’ 30” 247° 54’ 40” 500 53’ 50”
Yellow 1st 1180 45’ 20” 67° 10’ 50” 510 34’ 30” 510 34’ 00” 1.64987
587.6 2nd 2980 48’ 30” 247° 15’ 00” 510 33’ 30”
Green 1st 1180 45’ 20” 65° 55’ 50” 520 49’ 30” 520 52’ 30” 1.66251
501.6 2nd 2980 48’ 30” 245° 53’ 00” 520 55’ 30”
Blue - I 1st 1180 45’ 20” 65° 45’ 30” 520 59’ 50” 530 00’ 00” 1.66370
492.2 2nd 2980 48’ 30” 245° 48’ 20” 530 00’ 10”
Blue - II 1st 1180 45’ 20” 64° 44’ 40” 540 00’ 40” 540 00’ 15” 1.67324
447.1 2nd 2980 48’ 30” 244° 48’ 40” 530 59’ 50”

· Table – 5 : To plot − and − curve :

in nm in nm-2

667.8 (Red) 2.24237 X 10-6 1.64315

587.6 (Yellow) 2.89625 X 10-6 1.64987
501.6 (Green) 3.97452 X 10-6 1.66251
492.2 (Blue - I) 4.12778 X 10-6 1.66370
447.1 (Blue - II) 5.00254 X 10-6 1.67324

Page : 4
Page : 5
Calculations :

· Dispersive power calculation (using table - 5) :

Colour and wavelength =( + )/2 ~
=
in nm −1
667.8 (Red) = 1.64315 1.6582 0.0457
447.1 (Blue - II) = 1.67324

· from − plot :
0.0275
= = = 1.424 × 10
193.75

· Cauchy constants from − plot :

= intercept at Y-axis = 1.618
.
= slope of − curve (straight line) = = = 10666
. ×

Page : 6
 B. Sc. Physics Lab Manual

Department of Physics

Ramakrishna Mission Vivekananda Centenary College

Rahara, Kolkata – 700118

Title of the Experiment

To determine wavelength of sodium light using Newton’s rings

Page :1
Brief theory :
Newton’s rings are basically circular interference pattern produced due to interference by
division of amplitude. The ray diagram for the formation of Newton’s ring is shown in the Fig. 1a
and corresponding interference pattern (alternate dark and bright concentric rings) is shown in
Fig. 1b.

Monochromatic light of wavelength λ from sodium source is falling on half-reflecting glass

plate (G). A part of which is reflected towards the system of plano-convex lens mounted on a
plane glass plate. The incident ray on the system of lens and plate gets reflected from two
different surfaces:
i) From the convex (lower portion) surface of the lens
ii) From the top surface of the glass plate
These two reflected light waves are monochromatic and coherent. However they posses a path
difference produced due to small special gap between glass plate and the convex surface of the
lense. Due to thid path difference, theses reflected light beams produce a stable interference
pattern which is localized at the lower convex surface of the plano-convex lens.
Here, in the experiment, by measuring the diameter of Newtons ring i.e. the circular
interference pattern (Fig. 1b) we can measure the wavelength of the source if the radius of the
plano-convex lens is provided. Let us get the formula for this purpose.

Consider Fig. 2, in which we have depicted the magnified part of the lens-glass plate system.
Let n-th circular ring is produced at B point of radius rn.
The air film thickness at this point =d

Page :2
Then path difference at this point = 2d
From the geometry of Fig. 2 we can write down,
+ =
Or,
+( − ) =
In the limit ≪ , we get,

2 = (1)

One of the interfering rays is reflected from rarer medium (convex surface to air film interface)
and another one from denser medium (air film to glass plate interface). Therefore, two
interfering waves already have a phase shift by amount of π; that means equivalent path
difference of λ/2.

Hence, the condition to get n-th bright ring,

λ
Path difference = 2 = (2 + 1) (2)
2
and the condition to get n-th dark ring,
λ
Path difference = 2 = 2
2
Now if we consider the bright rings, then, from equation (1) and (2) we get,
λ
Path difference = 2 = = (2 + 1)
2
Or,
λ
= (2 + 1) (3)
2

If be the diameter of the n-th bright ring, then, from equation (3),

=( + ) ( )

This relation (4) is used to measure the wavelength of the source.

Page :3
Theory and working formula (for experiment) :

If a monochromatic beam of light of wavelength λ produces Newton’s ring pattern within

the air film of plane glass plate and plano-convex lens of radius then diameter of the n-th
bright ring is given by,
λ
= (2 + 1)
4 2
The same for (n+m)-th bright ring will be,
λ
= (2 + 2 + 1)
4 2
From these two relations we obtain,
−
= ( )

This is the working formula to determine wavelength of monochromatic light using Newton’s
rings.

Apparatus :
Newton’s ring apparatus have two parts; in one of these parts, interference pattern is
formed and another part is used to observe and measure the ring diameter. A typical Newton’s
ring apparatus is depicted in Fig. 3.

Page :4
Procedure (in brief) :
1. The followings are adjusted with attached screws attached with the parts respectively
to get sharp concentric Newton’s rings with dark spot at the centre.
a) System of plano-convex lens and glass plate are adjusted by pressure screws
attached with this part.
b) Half reflecting glass plate is rotated about horizontal axis by a 450 with the
attached screw with it.
c) Screw S1 is rotated for sharp focusing on the rings while viewed through the
eyepiece.
2. Rotation of screw S2 gives rise to horizontal movement of microscope over a linear
scale graduated in millimetre. S2 is attached with a circular scale (in some case there
exist vernier scale instead of circular scale). Typically, 100 uniform circular divisions
present on the circular scale. A complete rotation of circular scale produces 1 mm
translation of linear scale. S2 is rotated to focus crosswire on the central dark spot of
the rings.
3. After focusing on the central dark spot, rotate S2 such that the crosswire moves along
the direction from left to right ( → ). Count the bright rings and focus crosswire on
25-th bright ring.
4. Now, rotate S2 in opposite direction so that the cross wire moves along → . Focus
crosswire on right edge of 20-th bright ring. Take main scale and circular scale
reading in Tab. 1. This is the reading at right edge of 20-th bright ring for crosswire
motion → (see Fig. 4).
5. Rotate S2 in the same direction of procedure-4 and focus crosswire on right edges of
19-th, 18-th, 17-th …….... up to (say) 5-th bright rings successively. Note down both
linear and circular scale reading for these. These are the readings at right edges of
bright ring for crosswire motion → .
6. Rotate S2 in the same direction but do not take readings for initial 4 rings from centre.
Focus crosswire on the left edge of 5-th ring. Take reading as left edge for crosswire
motion → .
7. Follow step-6 for 6-th, 7-th, ……… up to 20-th bright ring. Take linear and circular
scale reading for left edges with crosswire motion → .
8. Focus, on 25-th ring but do not record data for 21st to 25th rings.
9. Start rotating S2 such that crosswire moves along → .
10. Focus crosswire on left edge of 20-th bright ring. Take main scale and circular scale
reading. This is the reading at left edge of 20-th bright ring for crosswire motion
→ .
11. Focus crosswire on left edges of 19th, 18th, 17th, ………. up to 5th bright rings
successively. Take main scale and circular scale reading. This are the readings at left
edges for crosswire motion → .
12. Avoid data collection for 4 rings in the central region either sides.
13. Focus crosswire on right edges of 5th, 6th, 7th, ………. up to 20th bright rings
successively. Take main scale and circular scale reading. This are the readings at right
edges for crosswire motion → .
14. Now, determine the diameter of any n-th ring by taking difference between left edge
and right edge reading of that particular ring.

Page :5
 15. Fig. 4 pictorially shows how the field of view appears through eyepiece. The crosswire
is indicated by red cross (it appears black in the experiment).

16. Plot ring number ( )vs square of the corresponding ring diameter( ). It will give a
straight line. From this graph take any p-th and (p+m)-th ring and determine and
then, use equation (5) to determine wavelength.

Data recording :
 Given that radius of the plano-convex lens =90 cm
 Determination of least count of circular scale:
100 circular scale divisions equivalent to one main scale division = 1 mm
Therefore, Least count = = 0.01
 Table for recording of microscope reading to determine ring diameter
(Here we give few data to understand the graph and further calculations)
Ring Crosswire Right edge reading Left edge reading Mean
No. movement Main Circular Total Main Circular Total (mm) (mm) (mm2)
( ) scale scale (mm) scale scale (mm)
(mm)
(mm)
20 → 45 61 45.61 52 34 52.34 6.73 6.60 43.56
→ 45 33 45.33 51 80 51.80 6.47
19 → -- -- -- -- -- -- --- -- --
→ -- -- -- -- -- -- --
18 → -- -- -- -- -- -- --- -- --
→ -- -- -- -- -- -- ---
17 → -- -- -- -- -- -- --- -- --
→ -- -- -- -- -- -- ---
16 → -- -- -- -- -- -- --- -- --
→ -- -- -- -- -- -- ---
15 → 46 03 46.03 51 75 51.75 5.72 5.66 32.03
→ 45 70 45.70 51 30 51.30 5.60
14 → -- -- -- -- -- -- --- -- --

Page :6
 → -- -- -- -- -- -- ---
13 → 46 22 46.22 51 56 51.56 5.34 5.30 28.09
→ 45 89 45.89 51 15 51.15 5.26
12 → -- -- -- -- -- -- --- -- --
→ -- -- -- -- -- -- ---
11 → -- -- -- -- -- -- --- -- --
→ -- -- -- -- -- -- ---
10 → 46 49 46.49 51 17 51.17 4.68 4.655 21.67
→ 46 20 46.20 50 83 50.83 4.63
9 → -- -- -- -- -- -- --- -- --
→ -- -- -- -- -- -- ---
8 → -- -- -- -- -- -- --- -- --
→ -- -- -- -- -- -- ---
7 → 46 86 46.86 50 83 50.83 3.97 3.965 15.72
→ 46 54 46.54 50 50 50.50 3.96
6 → -- -- -- -- -- -- --- -- --
→ -- -- -- -- -- -- ---
5 → 47 10 47.10 50 59 50.59 3.49 3.47 12.04
→ 46 78 46.78 50 23 50.23 3.45

Calculations and results :

The above figure shows variation of with ring number ; which is a straight line.

Page :7
  Table for calculation of from graph :

p m p+m −
λ=
(mm2) (mm2) (mm) 4

39 − 18
8 18.0 10 18 39.0 900 4 × 10 × 900

= 583 × 10
= 583 nm

Therefore, wavelength of the light coming from the source =

Discussions :
1. First few rings in the central region are deformed, so, data should not be taken for
these rings
2. During the experiment the system of glass plate and plano-convex lens must not be
disturbed.

Page :8
 Appendix: Support manual for prism spectrometer
In some of the optics experiments, we will use a spectrometer. The spectrometer is an instrument
for studying the optical spectra. Light coming from a source is usually dispersed into its various
constituent wavelengths by a dispersive element (prism or grating) and then the resulting
spectrum is studied. A schematic diagram of a prism spectrometer is shown in Fig. 1. It consists
of a collimator, a telescope, a circular prism table and a graduated circular scale along with two
verniers. The collimator holds an aperture at one end that limits the light coming from the source
to a narrow rectangular slit. A lens at the other end focuses the image of the slit onto the face of
the prism. The telescope magnifies the light dispersed by the prism (the dispersive element for
your experiments) and focuses it onto the eyepiece. The angle between the collimator and
telescope are read off by the circular scale. The detail description of each part of the
spectrometer is given below.

Telescope Collimator
Eye piece

Prism Leveling
Focus
Table screws
Knob Adjustable slit

Leveling Leveling Focus

screw screw Knob
Height adjustment
Verniers
screw for prism table
Telescope rotation:
Fine adjustment screw
Clamp screw

Circular
scale
Magnifying glass Base leveling screws
to read vernier

Prism table rotation:

Clamp screw
Fine adjustment screw

Fig. 1: Different parts of spectrometer

1
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 (i) Collimator (C): It consists of a horizontal tube with a converging achromatic lens at one end
of the tube and a vertical slit of adjustable width at the other end. The slit can be moved in or out
of the tube by a rack and pinion arrangement using the focus knob and its width can be adjusted
by turning the screw attached to it. The collimator is rigidly fixed to the main part of the
instrument and can be made exactly horizontal by adjusting the leveling screw provided below it.
When properly focused, the slit lies in the focal plane of the lens. Thus the collimator provides a
parallel beam of light.
(ii) Prism table (P): It is a small circular table and capable of rotation about a vertical axis. It is
provided with three leveling screws. On the surface of the prism table, a set of parallel,
equidistant lines parallel to the line joining two of the leveling screws, is ruled. Also, a series of
concentric circles with the centre of the table as their common centre is ruled on the surface. A
screw attached to the axis of the prism table fixes it with the two verniers and also keep it at a
desired height. These two verniers rotate with the table over a circular scale graduated in fraction
of a degree. The angle of rotation of the prism table can be recorded by these two verniers. A
clamp and a fine adjustment screw are provided for the rotation of the prism table. It should be
noted that a fine adjustment screw functions only after the corresponding fixing screw is
tightened.

(iii) Telescope (T): It is a small astronomical telescope with an achromatic doublet as the
objective and the Ramsden type eye-piece. The eye-piece is fitted with cross-wires and slides in
a tube which carries the cross-wires. The tube carrying the cross wires in turn, slides in another
tube which carries the objective. The distance between the objective and the cross-wires can be
adjusted by a rack and pinion arrangement using the focus knob. The Telescope can be made
exactly horizontal by the leveling screws. It can be rotated about the vertical axis of the
instrument and may be fixed at a given position by means of the clamp screw and slow motion
can be imparted to the telescope by the fine adjustment screw.

(iv) Circular Scale (C.S.): It is graduated in degrees and coaxial with the axis of rotation of the
prism table and the telescope. The circular scale is rigidly attached to the telescope and turned
with it. A separated circular plate mounted coaxially with the circular scale carries two verniers,
V1 and V2, 180° apart. When the prism table is clamped to the spindle of this circular plate, the
prism table and the verniers turn together. The whole instrument is supported on a base provided
with three leveling screws. One of these is situated below the collimator.

Adjustment of Spectrometer: The following essential adjustments are to be made step by step
in a spectrometer experiment: Leveling the apparatus means making (a) the axis of rotation of
the telescope vertical, (b) the axis of the telescope and that of the collimator horizontal, and (c)
the top of the prism table horizontal. The following operations are performed for the purpose.

(i) Leveling of telescope: Place a spirit level on the telescope tube making its axis parallel to that
of the telescope. Bring the air bubble of the spirit level halfway towards the centre by first
turning the two base leveling screws (i.e. leaving the base leveling screw below collimator) and
then turning the telescope leveling screw. Now rotate the telescope through 180° and adjust the
base and telescope leveling screws. Repeat the operations several times so that the bubble
remains at the centre for both positions of the telescope. Next place the telescope in the line with
the collimator and bring the air bubble of the spirit level at the centre by turning the base leveling

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 screw below the collimator. Again check the first adjustment for the previous orientations of
telescope. The axis of the rotation of the telescope has thus become vertical and the axis of the
telescope has become horizontal.

(ii) Leveling of collimator: Remove the spirit level from the telescope. Place it on the collimator
along its length. Bring the air bubble of the spirit level at the centre by adjusting the collimator
leveling screw provided below the collimator. This makes the axis of the collimator horizontal.

(iii) Leveling of the prism table: Place a spirit level at the centre of the prism table and parallel
to the line joining two of the leveling screws of the prism table. Bring the air bubble of the spirit
level at the centre by turning these two screws in the opposite directions. Now place the spirit
level perpendicular to the line joining the two screws and bring the bubble at the centre by
adjusting the third screw. This makes the top of the prism table horizontal.

(iv) Adjusting cross wires and focusing image

Rotate the telescope towards any illuminated background. On looking through the eye-piece, you
will probably find the cross-wires appear blurred. Move the eye-piece inwards or outwards until
the cross-wire appears distinct.
Place the telescope in line with the collimator. Look into the eye-piece without any
accommodation in the eyes. The image of the slit may appear blurred. Make the image very
sharp by turning the focusing knob of the telescope and of the collimator, if necessary. If the
image does not appear vertical, make it vertical by turning the slit in its own plane. Adjust the
width of the slit to get an image of desired intensity.

(v) Optical leveling of a prism: The leveling of a prism makes the refracting faces of the prism
vertical only when the bottom face of the prism, which is placed on the prism table, is
perpendicular to its three edges. But if the bottom face is not exactly perpendicular to the edges,
which is actually the case, the prism should be leveled by the optical method, as described
below:
(a) Illuminate the slit by sodium light and place the telescope with its axis making an angle of
about 90° with that of the collimator.
(b) Place the prism on the prism table with its vertex coinciding with that of the table and with
one of its faces (faces AB in Fig. 2) perpendicular to the line joining two of the leveling
screws of the prism table.
(c) Rotate the prism table till the light reflected from this face AB of the prism enters the
telescope. Look through the telescope and bring the image at the centre of the field of the
telescope by turning the two screws equally in the opposite directions.
(d) Next rotate the prism table till the light reflected from the other face AC of the prism enters
the telescope, and bring the image at the centre of the field by turning the third screw of the
prism table.
(vi) Focusing for Parallel rays by Schuster’s method: This is the best method of focusing the
telescope and the collimator for parallel rays within the space available in the dark room. In
order to focus the telescope parallel light rays are required and this in turn requires a properly
adjusted collimator. For this reason the adjustment of the telescope and the collimator are usually
done together.

3
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 Schuster's method is based on the fact that the
effect of the prism on the divergence of the beam
is different on opposite sides of this minimum
deviation position (see Fig. 2). The emergent
beam will be less divergent (or more divergent)
than the incident beam as the angle of incidence
is increased (or decreased) from the minimum
deviation value (i.e. as the apex A in Fig.2 is
rotated towards, or away from, the telescope).
This property of the prism can be used to obtain
an accurately collimated beam. The method is Fig. 2: Minimum deviation of light ray
explained below:
(a) Place the prism on the spectrometer table as shown in Fig.2.
(b) For your prism the angle of minimum deviation is around 50° so set the telescope at an angle
a few degrees greater than this (~55°).
(c) Illuminate the slit of the spectrometer with light from a sodium lamp. Rotate the prism table
and observe the images of the slit through the telescope as it passes through the minimum
deviation position.
(d) Lock the telescope at an angle a few degrees greater than this position.
(e) Turn the prism table away from its minimum deviation position so that apex A moves
towards the telescope and a spectral line is brought into the centre of the field of view of the
telescope. Adjust the focus of the telescope until this line image is as sharp as possible.
(f) Turn the prism table to the other side of the minimum deviation position until the same
spectral line is again at the centre of the telescopes field of view. Now adjust the focus of the
collimator until a sharp image is once more obtained.
(g) Repeat this process until no further adjustment is required. If the same line image is sharply
focused when viewed on either side of the minimum deviation position then the light beam
through the prism is properly collimated.

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 B. Sc. Physics Lab Manual

Department of Physics

Ramakrishna Mission Vivekananda Centenary College

Rahara, Kolkata – 700118

Title of the Experiment

Measurement of spring constant ( ) and

acceleration due to gravity (g)
Theory:
Time period of oscillation of a spring-mass system is given by,
+
=2 (1)

where,
= Mass of the pan attached to the end of vertically suspended spring
= Mass of the loads placed on the pan
= Spring constant
According to (1), gives a straight line and slope of this straight line is equal to 4 / .
Therefore, measuring this slope from experimental data we can get the value of .

Within elastic limit, elongation of a spring due to load is given by,

= (2)
Hence, gives an origin passing straight line. Slope of this line is equal to / .
Therefore, measuring this slope from experimental data we can get the value of with the help of
previously calculated value of .

Data recording:

1) Data for spring constant:

Sl. Nos. of Time taken Time period Average
Nos. (in gm) oscillations (sec) (T in sec) (in sec) (in sec2)

2) Data for :
Sl. Average
Nos. (in gm) (in cm) (in cm)
 B. Sc. Physics Lab Manual

Department of Physics

Ramakrishna Mission Vivekananda Centenary College

Rahara, Kolkata – 700118

Title of the Experiment

Measurement of acceleration due to gravity (g) by a bar pendulum

Theory:
Time period of oscillation of a bar pendulum is given by,

=2 (1)

where,
= Moment of inertia of the bar pendulum about the axis of rotation.
= Distance of the axis of rotation from the center of mass of the bar
= Mass of the bar pendulum
= Acceleration due to gravity
Let, is the moment of inertia of the bar pendulum about an axis passing through the center of
mass, then, according to parallel axis theorem,
= + (2)
Therefore, combining (1) and (2), we get,
+
=2 (3)

It gives a quadratic equation of ,

− + =0 (4)
4
Let, and be two roots associated with the above quadratic equation, then,

+ = (5)
4
From experiment, − curve is obtained and from this curve we can identify and + . Then
from (5), the value of can be estimated.
Data recording:
Sl. Nos. of Time taken Time period Average
Nos. (in cm) oscillations (sec) (T in sec) (in sec)

Calculation of from − curve:

(in cm) (in cm) (in sec) (in cm/s2)

 B. Sc. Physics Lab Manual

Department of Physics

Ramakrishna Mission Vivekananda Centenary College

Rahara, Kolkata – 700118

Title of the Experiment

To determine wavelength of sodium light using Fresnel’s Biprism

Page :1
Theory :
Formation of interference pattern by Fresnel’s biprism is depicted in Fig. 1.
Monochromatic light of wavelength emanating from slit S splits into two parts and forms two
virtual sources S1 and S2 separated by distance d. These two virtual sources (slits) form the
alternate dark and bright parallel band of interference fringes at the eyepiece field of view
located D distance apart from the slitS.

Fig. 1 : Interference pattern formation by Fresnel’s biprism

Fringe width is given by,

= (1)
If D1 and D2 are two different positions of eyepiece and let and are corresponding fringe
width, then, from equation (1) it can be shown,
−
= × (2)
−
This is the working formula to determine unknown wavelength of a monochromatic source by
using Fresnel’s biprism.
The separation between virtual sources (i.e; d) can be obtained by measuring the
separation of the image of these virtual slits formed by convex lens at two different positions
between biprism and eyepiece. If d1 and d2 are the separation of slit images then,
= (3)

Apparatus :
1. Fresnel’s biprism
2. Optical bench
3. Convex lens
4. Sodium light source
5. Micro-meter eyepiece

Page :2
Procedure :

Part – A: Adjustments
1. Mount the slit stand near zero of the optical bench. Make the slit vertical and very
narrow. Bring the slit at the middle of the optical bench using adjustment screw.
2. Mount the biprism on its stand facing its plane face towards the slit (see Fig. 1). Bring
its central line parallel to slit and at the same height of the slit. Move its stand to touch
the slit stand.
3. Place the sodium source at its position behind the slit. Look through the biprism
towards the slit and adjust the transverse screw of the biprism to show that the
common base of the biprism moves across the slit.Place biprism common base in the
same line of the slit as well as middle of the optical bench.
4. Place the eyepiece to see the fringe pattern. If there is no pattern at all, adjust
transverse screw of the biprism to move it lateral direction of optical bench. After
getting fringe pattern, adjust tangent screw of the biprism slowly (rotates the biprism)
to attain sharp fringe pattern.
5. Move the eyepiece away from the slit more than five times a distance of focal length of
the given convex lens. During this process move the eyepiece away from the prism
steadily and see through it, if fringe pattern goes out side the field of view, then, move
biprism perpendicular to optical bench by adjusting transverse screw.
6. Place an intense white source behind the slit without moving the sodium source (just
shut down the light exit window of the sodium source). Adjust transverse screw of the
eyepiece to bring the crosswire at the white central bright fringe of the coloured
fringe pattern due to white source. Move the eyepiece very close to the biprism and
obtain the central white fringe on the cross wire of the eyepiece by adjusting eyepiece
screws. Move eyepiece steadily away from the slit and adjust biprism transverse
screw to get central white fringe on the crosswire. Repeat this operation several times
to ensure that cross wire always remain on the white central fringe for all position of
the eyepiece.
7. After doing this remove the white light source and open sodium source window.

Part – B :Measurements
8. Illuminate the slit by sodium light. Fix the eyepiece more than five times of the focal
length of the given convex lens.
9. Take micrometre readings by succession of three fringe width. Repeat this process at
least twice while cross wire moves from → and → .
10. Perform step 9 for two another positions of eyepiece.
11. Mount the convex lens in between biprism and eyepiece and adjust its height
accordingly. Move the lens over the optical bench. For two different position of the
lens sharp image of the virtual slits will be observed through the eye piece. Measure
image slit width by micrometer screw attached with the eyepiece.

Page :3
Experimental results :
 Vernier constant of the optical bench
1 main scale division = 1 mm
10 vernier division = 9 main scale division = 9 mm
Vernier constant = 1 main scale division - 1 vernier scale division
= 0.1 mm
= 0.01 cm

 Least count of the micrometer screw of the eyepiece

50 circular divisions = 0.5 mm
Least count = 0.5/50 = 0.01 mm= 0.001 cm

 Table – 1 : Fringe width measurement

Slit to Fringe Eyepiece direction : → Eyepiece direction : → Mean gap Fringe
eyepiece Nos. Main Circular Total Gap Main Circular Total Gap between width
distance scale scale (mm) between scale scale (mm) between three
(cm) (mm) three (mm) three fringes (mm)
fringes fringes 3
(mm) (mm) (mm)
1 1.5 3 1.53 1.11 1.5 7 1.57 1.13
4 2.5 14 2.64 1.00 2.5 20 2.70 0.98
120 7 3.5 14 3.64 1.12 3.5 18 3.68 1.13 1.068 0.356
10 4.5 26 4.76 1.05 4.5 31 4.81 1.03
13 5.5 31 5.81 1.07 5.5 34 5.84 1.06
16 6.5 38 6.88 --- 6.5 40 6.90 ---
1 1.5 21 1.71 0.96 1.5 25 1.75 0.95
4 2.5 17 2.67 0.87 2.5 20 2.70 0.88
100 7 3.5 4 3.54 0.93 3.5 8 3.58 0.95 0.914 0.305
10 4.0 47 4.47 0.90 4.0 53 4.53 0.88
13 5.0 37 5.37 0.91 5.0 41 5.41 0.91
16 6.0 28 6.28 --- 6.0 32 6.32 ---
1 1.0 5 1.05 0.75 1.0 10 1.10 0.74
4 1.8 0 1.80 0.70 1.8 4 1.84 0.72
80 7 2.5 0 2.50 0.68 2.5 6 2.56 0.67 0.715 0.238
10 3.0 18 3.18 0.74 3.0 23 3.23 0.74
13 3.9 2 3.92 0.71 3.9 7 3.97 0.70
16 4.5 13 4.63 --- 4.5 17 4.67 ---

Page :4
  Table – 2 : Slit width measurement
Slit to eyepiece distance = 100 cm
Lens Eyepiece Left image reading Right image reading Distance Mean Slit
position direction between distance separation
slitimage (mm) =
Main Circular Total Main Circular Total ∼ (mm)
scale scale (mm) scale scale (mm) (mm)
(mm) (mm)
→ 1.0 31 1.31 6.5 6 6.56 5.25
1st → 1.0 39 1.39 6.5 10 6.60 5.21 5.227
→ 1.0 35 1.35 6.5 8 6.58 5.23 ( )
→ 1.0 41 1.41 6.5 13 6.63 5.22 1.984
→ 1.0 2 1.02 1.5 27 1.77 0.75 0.753
2nd → 1.0 4 1.04 1.5 32 1.82 0.78 ( )
→ 0.5 48 0.98 1.5 23 1.73 0.75
→ 1.0 3 1.03 1.5 26 1.76 0.73

Calculation :

d D1 D2 − Mean
= ×
(mm) (mm) (mm) (mm) (mm) − (nm)
(mm)
1200 0.356 1000 0.305 5.059 X10-4
1.984 1000 0.305 800 0.238 6.646 X10-4 585.3
1200 0.356 800 0.238 5.853 X10-4

Calculated value of the wavelength of sodium light = 585.3 nm

Page :5
 B. Sc. Physics Lab Manual

Department of Physics

Ramakrishna Mission Vivekananda Centenary College

Rahara, Kolkata – 700118

Title of the Experiment

To determine grating constant from known source and then

spectral lines of unknown source using plane diffraction grating

Page : 1
Theory and working formula :
Plane transmission grating is an optical instrument which is capable of forming
diffraction spectrum of visible light (depicted in Fig. 1). It is a system of uniform parallel lines of
openings and opaques arranged alternatively. If the width of opening is a and opaque is b, then,
the grating constant is defined as (a+b). Number of rulings per unit length of a transmission
grating is,
1
= (1)
+

Fig. 1 : Pictorial representation of plane transmission grating diffraction spectrum and associated
intensitydistribution.

Parallel beam of light passing through plane transmission grating forms diffraction pattern on
the other side. If be the angular position (with respect to incident beam direction) of m-th
bright diffraction band then,
( + ) = (2)
, = (3)
Using a known source one can determine grating constant( + ) and using this value unknown
wavelengths can be determined.

Apparatus :
1. Spectrometer
2. Prism
3. Transmission grating
4. Spirit level
5. Sodium light source
6. Unknown source

Page : 2
Procedure (in brief) :
1. Adjustment of the spectrometer (as discussed in a separate note entitled
‘Spectrometer.pdf’) using sodium yellow light.
a) Levelling of telescope
b) Levelling of collimator
c) Mechanical levelling of prism table
d) Crosswire focusing
e) Optical levelling of prism
f) Focussing for parallel ray by Schuster’s method
2. Determine the vernier constant of the circular scale of the spectrometer.
3. Adjustment of grating :
i) Keep sodium light at its position.
ii) First bring the telescope to receive the direct ray from collimator and then rotate the
telescope by 900.
iii) Mount the grating on the prism table along its diameter and such that the grating
plane is approximately normal to incident light from collimator. The grating lines is to
be parallel to the slit.
iv) Rotate the prism table to see the slit as reflected image from grating surface through
the telescope. Reflection from unruled surface is brighter than reflection from ruled
surface. Rotate prism table to receive reflected light from unruled surface of grating.
Coincide cross wire with reflected slit image. This sets the grating to receive light at
450 incident angle.
v) Rotate the prism table by 450 such that grating unruled surface faces the collimator.
vi) Adjust the appropriate prism table screw such that grating rotate on its own plane to
make the diffraction lines aligned properly, not up and down.

Experimental results :
 Determination of vernier constant :
1 smallest division in main scale = 20′
60 vernier divisions = 59 main scale divisions = 59 × 20′
× ′
1 vernier divisions =
Therefore,
59×20′
(
Vernier constant = 1 main scale division – 1 vernier division = 20′ − 60
)= 20"

Page : 3
 Table – 1 : To determine diffraction angle of known wavelength ( = . )

Dif
Or Ve fra
der rni cti
Left side reading Right side reading Mean
No er on
~ difference
No an
(2 )
gle
Main Ver. Total Mean Main Ver. Total Mean ( )
scale scale ( ) scale scale ( )
2060 8 2060 1990 2 1990
00’ 02’ 2060 20’ 20’ 1990 60
I 40” 02’ 40” 20’ 41’
1 2060 5 2060 10” 1990 0 1990 20” 50”
00’ 01’ 20’ 20’
40” 00” 60 42’ 50” 30
260 11 260 190 0 190 20’ 60 21’
II 00’ 03’ 260 20’ 00” 190 43’ 55”
40” 04’ 20’ 50”
260 13 260 00” 190 1 190 20’ 10”
00’ 04’ 20’ 20”
20”
2090 18 2090 1950 25 1950 1950 130
I 20’ 26’ 2090 40’ 48’ 20” 48’ 37’
00” 25’ 30” 10” 130 37’ 60
2 2090 16 2090 40” 1950 26 1950 00” 48’
20’ 25’ 40’ 48’ 40” 30”
20”
290 19 290 290 150 28 150 49’ 150 130
II 20’ 26’ 26’ 40’ 20” 50’ 36’
20" 50" 00” 50”
290 22 290 150 32 150 50’
20’ 27’ 40’ 40”
20”
2120 31 2120 2120 1920 18 1920 1920 200
I 40’ 50’ 49’ 20’ 26’ 00” 26’ 23’
20” 50” 10” 40” 200 22’ 100
3 2120 28 2120 1920 19 1920 30” 11’
40’ 49’ 20’ 26’ 20” 15”
20”
320 24 320 320 120 22 120 27’ 120 200
II 40’ 48’ 48’ 20’ 40” 27’ 21’
00” 20” 00” 20”
320 26 320 120 19 120 26’
40’ 48’ 20’ 20”
40”

Page : 4
 Table – 2 : To determine diffraction angle for unknown wavelength

Di
Or Ve ffr
der rni act
Left side reading Right side reading Mean
No er ion
~ difference
No an
(2 )
gle
Main Ver. Total Mean Main Ver. Total Mean ( )
scale scale ( ) scale scale ( )
2020 10 2020 2020 1960 18 1960 1960 60
20’ 23’20” 23’ 00’ 06’ 00” 06’ 16’
I 2020 7 2020 00” 1960 20 1960 20” 40”
1 20’ 22’ 40” 00’ 06’ 40” 60 17’ 00” 30 08’
220 14 220 24’ 220 160 20 160 06’ 160 60 30”
II 20’ 40” 24’ 00’ 40” 06’ 17’
220 11 220 23’ 10” 160 21 160 07’ 50” 20”
20’ 40” 00’ 00”
205° 18 205° 205° 1930 3 1930 1930 120
I 20’ 26’ 00” 25’40 00’ 01’ 00” 00’ 25’
205° 16 205° ” 1930 1 1930 40” 00”
2 20’ 25’ 20” 00’ 00’ 20” 120 25’ 60 12’
25° 19 25° 26’ 25° 130 0 130 00’ 130 120 50” 55”
II 20’ 20” 26’50 00’ 00” 00’ 26’
25° 22 25° 27’ ” 130 2 130 00’ 10” 40”
20’ 20” 00’ 40”
2080 5 2080 2080 1890 25 1890 1890 180
I 40’ 41’ 40” 41’ 40’ 48’ 20” 47’ 53’
2080 5 2080 40” 1890 22 1890 50” 50”
3 40’ 41’ 40” 40’ 47’ 20” 180 54’ 90 27’
280 10 280 43’ 280 90 27 9049’ 90 180 10” 05”
II 40’ 20” 43’ 40’ 00” 48’ 54’
280 9 280 43’ 10” 90 25 9048’ 40” 30”
40’ 00” 40’ 20”

Page : 5
Calculations and results :
 Table – 3 : To determine number of grating rulings using known source (Table –
1)

Known wavelength Order No. Diffraction angle Nos. of rulings per Mean N
m unit length ( cm-1 )
(cm)
=
( cm-1 )
1 30 21’ 55” 996
589.3 × 10 2 60 48’ 30” 1006 1000
3 100 11’ 15” 1000

 Table – 4 : To determine unknown wavelength (Table – 2, 3 )

Nos. of rulings per Order No. Diffraction angle Wavelength Mean

unit length m ( nm)
=
N
( cm-1 ) ( cm )

1 30 08’ 30” 548.05 × 10

1000 2 60 12’ 55” 541.32 × 10 545.6
3 90 27’ 05” 547.37 × 10

Obtained value of the wavelength of the unknown source = 545.6 nm

Page : 6